Answer:
Step-by-step explanation:
A gate-array logic circuit for the equation x² + 3xy - 14 = output could be designed as follows:
First, we need to calculate x² and 3xy. This can be done using AND, OR, XOR, and NOT gates.
Next, we need to add the two values obtained in step 1 using a full-adder circuit.
Finally, we need to subtract 14 from the sum obtained in step 2. This can be done using a subtractor circuit, which is essentially a full-adder circuit with an additional input for the subtrahend (in this case, 14).
Here is a schematic of the gate-array logic circuit:
_______________
| |
X--| AND/OR/XOR/NOT |---x²
Y--| AND/OR/XOR/NOT |---3xy
|_______________|
|
______
| |
x²--| Full |---(x² + 3xy)
3xy--| Adder|
|______|
|
______
| |
(x² + 3xy)--| Sub |---output
14--| tract|
|______|
Note that this is just one possible way to design the circuit, and there may be other ways to achieve the same result.
the directions on a sewing pattern; which equation can be used to find the length of the hypotenuse; elsa took out a 2-year loan
On solving the provided question, we got to know that -Pythagoras' Theorem - [tex]a^2 + b^2 = c^2 =[/tex][tex]5^2 + 8^2 = c^2[/tex]
What is the Pythagoras Theorem?The square of the hypotenuse of a right triangle (90 degrees) is equal to the sum of the squares of the other two sides, according to the Pythagorean theorem. Keep in mind that BC2 = AB2 + AC2 in the triangle ABC below. where BC is the hypotenuse, AB is the base, and AC is the height (height). Keep in mind that the hypotenuse of a right triangle is its longest side.
Pythagoras' Theorem -
[tex]a^2 + b^2 = c^2[/tex]
where the other two sides' lengths are a and b, and c is the length of the hypotenuse.
so
[tex]5^2 + 8^2 = c^2\\c^2 = 25 + 64\\c^2 = 89\\c = \sqrt{89}[/tex]
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hw to solve 6x-12/3+4=18/x
The two solutions of the equation:
(6x - 12)/3 + 4 = 18/x
Are x = 3 and x = -3
How to solve the equation?Here we have the following equation:
(6x - 12)/3 + 4 = 18/x
Notice that in the right side we have x on a denominator, then x can not be zero, so x ≠ 0.
Now, let's start by simplifying the left side:
(6x - 12)/3+ 4 = 18/x
2x - 4 + 4 = 18/x
2x = 18/x
Now we can multiply both sides by x so we get:
2x^2 = 18
Now divide both sides by 2:
x^2 = 18/2
x^2 = 9
Finally, apply the square root in both sides:
√x^2 = ±√9
x = ±3
The two solutions are x = 3 and x = -3
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Evaluate the surface integral. S (x + y + z) dS, S is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 + 2u + v, 0 ≤ u ≤ 8, 0 ≤ v ≤ 6.
After solving, the surface integral S is [tex]\int\int_{S}(x + y + z) dS[/tex] = 960√14.
In the given question, we have to evaluate the surface integral.
(x + y + z) dS, S is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 + 2u + v, 0 ≤ u ≤ 8, 0 ≤ v ≤ 6.
Now the surface integral is:
[tex]\int\int_{S}(x + y + z) dS[/tex]
x = u+v, y = u−v, z = 1+2u+v, 0 ≤ u ≤ 8, 0 ≤ v ≤ 6
The parametric curve is
r(u,v) = <u+v, u−v, 1+2u+v>
Then surface integral is calculated as
[tex]\int\int_{S}(x + y + z) dS=\int\int_{A}f(x(u,v), y(u,v), z(u,v))|r_{u}\times r_{v}| dudv[/tex]
Now find partial derivatives of parametric curve with respect to u and v
[tex]r_{u}[/tex](u,v) = <1, 1, 2>
[tex]r_{v}[/tex](u,v) = <1, -1, 1>
Now find cross product
[tex]r_{u}\times r_{u}[/tex] = <1, 1, 2> × <1, -1, 1>
[tex]r_{u}\times r_{u}[/tex] = <1+2, 2-1, -1-1>
[tex]r_{u}\times r_{u}[/tex] = <3, 1, -2>
Now parametric function is
x+y+z = u+v+u-v+1+2u+v
x+y+z = 4u+v+1
Then the surface integral is:
[tex]\int\int_{S}(x + y + z) dS=\int^{6}_{0}\int^{8}_{0}(4u+v+1)\sqrt{14}dudv[/tex]
[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}\int^{6}_{0}(4\frac{u^2}{2}+uv+u)^{8}_{0}dv[/tex]
[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}\int^{6}_{0}[(4\frac{(8)^2}{2}+8v+8)-(4\frac{(0)^2}{2}+0\cdotv+0)]dv[/tex]
[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}\int^{6}_{0}(128+8v+8)dv[/tex]
[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}\int^{6}_{0}(136+8v)dv[/tex]
[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}(136v+8\frac{v^2}{2})^{6}_{0}[/tex]
[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}[(136\times6+8\frac{6^2}{2})-(136\times0+8\frac{0^2}{2})][/tex]
[tex]\int\int_{S}(x + y + z) dS[/tex] = √14×(816+144)
[tex]\int\int_{S}(x + y + z) dS[/tex] = 960√14
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which of the following is equivalent to
235,000,000,000?
A2.35 x 10-⁹
B 2.35 x 10-10
C 2.35 x 1011
D 2.35 x 1012
Answer:
C 2.35 x 10¹¹
Step-by-step explanation:
You want the number 235,000,000,000 written in scientific notation.
Place valueThe exponent of 10 when a number is written in scientific notation is the same as the exponent of 10 for the most significant digit when the number is written in expanded form using exponents.
235,000,000,000 = 2×10¹¹ +3×10¹⁰ +5×10⁹ +0×10⁸ +... +0
The place value multiplier for the most-significant digit is 10¹¹, so this is the multiplier when the number is written in scientific notation.
2.35×10¹¹
The price of a gift plus 14% delivery charge comes to a total cost of $19.38. What was the price of the gift?
Step 1 of 2 : Describe the above situation as a linear equation, using "x" or "y" as variable names to describe the unknown quantity.
Answer:
1.14x = 19.38
$17
Step-by-step explanation:
Let the price before delivery charge = x.
The charge is 14%, so it is 14% of x, or 0.14x.
The original price plus charge is x + 0.14x, or 1.14x.
1.14x = 19.38
x = 19.38/1.14
x = 17
The price is $17
which of the following statement(s) is(are) a characteristic(s) of the normal distribution? it is symmetric. it has a bell shape. the values of the mean, median, and mode are equal.
Answer:
All of the three are correct characteristics.
Step-by-step explanation:
In a normal distribution, the following attributes are observed:
From the image, you can see symmetry and a bell-shaped distribution.
As you can see from the center-most point in the image, the mean, median, and mode are equal.
Therefore, all three characteristics are correct in a normal distribution.
SY 22-23_EGB_Math Grade 5_Mid-year Final answer key
Answer:
The answer is 2.9
Step-by-step explanations are not quite accurate
Determine the period.
Enter
The period is the time interval after curves repeat their behavior thus time period of the given curve will be 4.
What is a graph?The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.
For example plot of y = x³ ,y = sinx.
As per the given graph of a function,
The time period is the time interval after curves repeat their behavior.
The given graph repeats after 1 + 1 + 1 + 1 = 4 thus period will be 4.
Hence "The period is the time interval after curves repeat their behavior thus time period of the given curve will be 4".
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If you choose a group of four tiles, what is the probability you get four tiles that are each worth one point? Write your answer as a decimal with three decimal places (0.XXX), not as a percent.
The probability to choose a group of four tiles with each tile worth one point is 0.200.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Let there are total 25 tiles.
From this 20 tiles having one point each and 5 tiles having more than one point.
We have to choose a group of four tiles with each tile worth one point.
So,
probability = 4/20 = 0.200
Hence, the probability to choose a group of four tiles with each tile worth one point is 0.200.
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Can anyone help me graph this out. its the last question for my homework and im stuck on it
The required graph of the given function has been shown.
Given that,
To draw the graph of the composite function,
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
Illustrating the function on the graph for the respective domain
f(x) = 0 for x ≤ -1
f(x) = -x -1 for -1 < x ≤ 2
f(x) = -1 for x > 2
Thus, the required graph of the given function has been shown.
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S is the midpoint of RT. T has coordinates (-14,-15) and S has coordinates (11,-1) Find the coordinates of R
Answer:
(36, 13)
Step-by-step explanation:
to find the midpoint you have the add the x and the y and then divide by two
to find one of the endpoints you just do the opposite
you multiply the midpoint by 2
and then subtract the remaining endpoint from it
(11, -1) --> (22, -2)
now subtract T from it
(36, 13)
that is your answer
(a) Find the eigenvalues of Matrix A. (5 marks) (b) Find a corresponding eigenvector for each of the eigenvalues found in (a). (10 marks) (c) Use the above (a) and (b) results to solve the vector-matrix differential equation * = AX X(0) = 11 with the initial conditions
For the given matrix A ,(a) the eigen values are 0 and -3 . and the eigen vectors corresponding to the given eigen vectors are [tex]\left[\begin{array}{ccc}1 \\1 \\\end{array}\right][/tex] and [tex]\left[\begin{array}{ccc}2 \\1 \\\end{array}\right][/tex] .
In the question ,
it is given that ,
the matrix A is = [tex]\left[\begin{array}{ccc}-6&6\\-3&3\\\end{array}\right][/tex]
Part(a)
the eigen values of the matrix A can be found by the characteristic equation ,
|A - λI | = [tex]\left|\begin{array}{ccc}-6-\lambda &6\\-3&3-\lambda\\\end{array}\right|[/tex] = 0 ;
= -(6 + λ)(3 - λ) + 18
= λ² - 3λ + 6λ = 0
= λ² + 3λ = 0
So , λ = 0 and λ = -3 .
the eigen values are 0 and -3 .
Part(b)
for finding the eigen vectors ,
For eigen value λ = 0 , [A - λI]*X = 0
on solving [tex]\left[\begin{array}{ccc}-6&6\\-3&3\\\end{array}\right][/tex]*[tex]\left[\begin{array}{ccc}x_{1} \\x_{2} \\\end{array}\right][/tex] = 0 ,
we get x₁ = 1 and x₂ = 1 ,
the eigen vector corresponding to eigen value 0 is [tex]\left[\begin{array}{ccc}1 \\1 \\\end{array}\right][/tex] .
Similarly solving for eigen value λ = -3 ,
[tex]\left[\begin{array}{ccc}-3&6\\-3&6\\\end{array}\right][/tex]*[tex]\left[\begin{array}{ccc}x_{1} \\x_{2} \\\end{array}\right][/tex] = 0 ,
Solving further ,
we get , x₁ = 2 and x₂ = 1 ,
the eigen vector corresponding to eigen value -3 is [tex]\left[\begin{array}{ccc}2 \\1 \\\end{array}\right][/tex] .
Therefore , (a) the eigen values are 0 and -3 .
(b) the eigen vectors are [tex]\left[\begin{array}{ccc}1 \\1 \\\end{array}\right][/tex] and [tex]\left[\begin{array}{ccc}2 \\1 \\\end{array}\right][/tex] .
The given question is incomplete , the complete question is
The matrix is A = [tex]\left[\begin{array}{ccc}-6&6\\-3&3\\\end{array}\right][/tex] ,
(a) Find the eigenvalues of Matrix A .
(b) Find corresponding eigenvector for each of eigenvalues found in (a).
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On Abby Ellen’s graduation from law school, Abby’s uncle, Bull Brady, promised her a gift of $24,000 or $2,400 every quarter for the next 4 years after graduating from law school. If the money could be invested at 6% compounded quarterly, which offer should Abby choose? How much money will Abby have if she invests at 6% compounded quarterly? (Round your answer to the nearest cent.)
Abby choose:
Abby will have:
Abby will choose $2,400 every quarter for 4 years.
Abby will have $30455.65 if she invests at 6% compounded quarterly
What is interest rates?
The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal, or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR (APR).
The formula of compounded quarterly is
A = P ( 1 + r/n)^(4t)
P = Principal = $24,000
n = 4
r = rate of interest = 6% = 0.06
t = time = 4 years
Putting the value of P, r, t in the formula of compounded quarterly:
A = 24000 ( 1 + 0.06/4)^(4×4)
A = 30455.65.
Future Value of an Ordinary Annuity
[tex]S = R[\frac{(1+i)^n-1}{i} ][/tex]
Where
S is the future value;
R is the periodic payment;
i is the interest rate per period;
n is the number of periods.
The value of R is $2,400, i = 0.06/4 = 0.015
n = (4 × 4) = 16
[tex]S = 2400[\frac{(1+0.015)^{16}-1}{0.015} ][/tex]
S = 43037.69
Abby choose: $2,400 every quarter for 4 years.
Abby will have $30455.65 if she invests at 6% compounded quarterly.
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____________ is a test of a single population and is to determine if there is an association between two characteristics of that population. A) The chi-square test for independence B) Pearson product moment test C) The chi-square test for homogeneity D) Goodness-of-fit test E) Welch’s t test
The option a "The chi-square test for independence" is correct.
In the given question we have to find, a test of a single population and is to determine if there is an association between two characteristics of that population.
The given options are
A) The chi-square test for independence
B) Pearson product moment test
C) The chi-square test for homogeneity
D) Goodness-of-fit test
E) Welch’s t test
As we know that;
When a categorical variable has more than two levels, a chi-square test can be performed. A one proportion z test may be performed if there are precisely two categories. There must be no overlap between those category variable's levels. To put it another way, every situation must fall into exactly one group.
So, the chi-square test for independence is correct answer.
Option (B) and (E) are two-sample tests.
(C) involves two attributes.
(D) Doesn't check association.
Hence all these are incorrect.
So the option a "The chi-square test for independence" is correct.
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In one lottery, a player wins the jackpot by matching all five distinct numbers drawn in any order from the white balls (1 through 43 ) and matching the number on the gold ball (1 through 33). If one ticket is purchased, what is the probability of winning the jackpot?
Answer:
44
Step-by-step explanation:
Equations are given whose graphs enclose a region. Find the area of the region. (Give an exact answer. Do not round.) f(x) = x2; g(x) = â 1 5 (5 + x); x = 0; x = 3
The equations are given whose graphs enclose a region. when the area of the region is 301.5
The given function is f(x) and g(x), we need to calculate the area.
A = ₐ∫ᵇ (f(x) + g(x)) dx
A = ₀∫³ (x² + 15(x + 5)) dx
A = ₀∫³ (x²dx + ₀∫³15(x + 5)) dx
A = (x³/3) + 15x²/2 + 75x
A = ₀[x³/3]³ + ₀[15x²/2 + 75x]³
A = [(3 - 0)³/3] + [15(3 - 0)²/2 + 75(3 - 0)]
A = 27/3 + 15(9/2) + 75(3)
A = 9 + 15(4.5) + 7
A = 76.5 + 225
A = 301.5
Therefore, the equations are given whose graphs enclose a region. when the area of the region is 301.5
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Se tiene que f varía directamente con j
Si f=27 cuando j=9
Calcule el valor de j cuando f=9
Using direct variation, the value of j when f equals 9 is 3
VariationsA variation is a relation between a set of values of one variable and a set of values of other variables. Direct variation. In the equation y = mx + b, if m is a nonzero constant and b = 0, then you have the function y = mx (often written y = kx), which is called a direct variation.
In the question given, we have f varying directly with j
f ∝ j
f = k j
k = f / j
f₁ / j₁ = f₂ / j₂
Substituting the values into the equation;
27 / 9 = 9 / j₂
j₂ = 9 * 9 / 27
j₂ = 81 / 27
j₂ = 3
The value of j₂ = 3
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Translation: We have that f varies directly with j, if f = 27 when j = 9. Calculate the value of j when f = 9
Write the following expression using the fewest possible terms.
(−3x − 12) + (16 + 8x)
5x + 4
5x + (−4)
11x + 28
11x + (−4)
Therefore option a) 5x+4 is the simplified form of the equation.
What is equation?Equations in mathematics are logical statements with two algebraic expressions on either side of the equals (=) symbol. The equality of the expressions on the left and right in relation to one another is shown. LHS = RHS (left hand side = right hand side) is the first step in any mathematical equation. You can solve equations to determine a variable's or quantity's value. It is not an equation if the statement lacks the "equal to" sign. It will be thought of as a phrase. Later on in this essay, there will be an explanation of the distinctions between an expression and an equation.
Here,
Given:
=>(−3x − 12) + (16 + 8x)
=> -3x-12+16+8x
=> 5x+4
So 5x+4 is the simplified form of the equation
Therefore option a) 5x+4 is the simplified form of the equation
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simplify (1+i) ^18 using the demoivres theorem
Using De Moivre’s theorem, the complex number (1+i)¹⁸ simplifies to 512√2
How to simplify (1+i)¹⁸ using the demoivres theorem?For a complex number of the form z = a + ib, its polar form is written as:
z = r(cosθ + isinθ)
Where, r = √(a²+b²) and θ = tan⁻¹(b/a)
De Moivre’s theorem => (cos x + i sinx)ⁿ = rⁿ cos(nx) + i sin(nx)
Given: (1+i)¹⁸
To simplify (1+i)¹⁸, first needs to convert it into its polar form
z = 1 + i
r = √(1²+1²) = √2 and θ = tan⁻¹(1/1) = π/4
polar form:
z = √2 (cos(π/4) + isin(π/4))
Thus, (1+i)¹⁸ = [√2 (cos(π/4) + isin(π/4))]¹⁸
Using DeMoivre’s theorem, (cos x + i sinx)ⁿ = rⁿ cos(nx) + i sin(nx):
[√2 (cos(π/4) + isin(π/4))]¹⁸ = (√2)¹⁸ (cos(π/4) + isin(π/4))
= 512 (cos(π/4) + isin(π/4))
= 512 ((√2)/2 + (√2)/2)
= 512(√2)
Therefore, (1+i)¹⁸ = 512√2
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Tamika must plant 432 trees. In the past 6 days Tamika planted 288 trees. If she continues at this rate, how many more days will it take her to plant all the trees?
2
3
4
5
There are 3 more days will it take her to plant all the trees.
What is rate?
The numerator of a ratio in mathematics represents the rate of change in the other (dependent) variable if the denominator of the ratio is expressed as a single unit of one of the related quantities and it is assumed that this quantity can be changed systematically (i.e., is an independent variable).
Given:
Tamika must plant 432 trees.
In the past 6 days Tamika planted 288 trees.
She continues the planting tree at the same rate.
As she planted 288 trees in 6 days.
That means she plant 288 / 6 = 48 trees in a day.
The remaining trees are 432 - 288 = 144.
So, 144 trees will be planted in 144 / 48 = 3 days.
Hence, there are 3 more days will it take her to plant all the trees.
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Which of the following is not a polynomial a 3x 5 B 3y³ 4y² 2y?
Of the following, the option which is not a polynomial is 1/x+2. (Option D)
In mathematics, a polynomial refers to an expression consisting of indeterminates and coefficients, that only includes basic arithmetic operations of addition, subtraction, multiplication, and positive-integer powers of variables. In other words, it is a mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power. The general form of a polynomial is a + bx + cx^2. Hence, it is identified by noting which expressions contain only the operations of addition, subtraction, multiplication, and non-negative integer exponents. The non-polynomial expressions will be the expressions which contain other operations such as 1/x+2.
Note: The question is incomplete. The complete question probably is: Which of the following is not a polynomial (a) 3x+5 (b) 3y³-4y² +2y (c)x³-3 d) 1/x+2
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What type of triangle is congruent?
Congruent triangles are triangles having corresponding sides and angles to be equal.
Congruent triangles are triangles that have both the same size and the same shape and they have the same perimeter and the same area. Congruence is denoted by “≅”. For example, we can write ABC ≅ DEF. They have the same area and the same perimeter.
Congruent triangles have the same angle measures and the same side lengths.
On the other hand, the similar triangle is the term used for triangles that have the same shape, but not necessarily the same size.
Two triangles are considered to be congruent if they meet one of the following criteria.
All three pairs of corresponding sides should be equal.Two pairs of corresponding sides and the corresponding angles between them should be equal.Two pairs of corresponding angles and the corresponding sides between them should be equal.Two pairs of corresponding angles and one pair of corresponding sides (not between the angles) should be equal.The pair of hypotenuses and another pair of corresponding sides should be in two right triangles.To learn more about congruent; click here:
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consider the graph of function g
if f(x)=x^2 which equation represents function g?
Answer:
Step-by-step explanation:
The ratio of dye to pounds of clothing is constant. A worker develops the chart below to show the amount of dye needed for different amounts of clothing.
Clothes Dyeing
Weight of clothing (pounds)
Cups of dye
21 3
42 9
84 12
105 15
For which weight of clothing is the ratio of weight to dye different from the other ratios?
21 pounds
42 pounds
84 pounds
105 pounds
42 pounds has a weight of clothing to weight to dye different from the other ratios
How to determine for which weight of clothing is the ratio of weight to dye different from the other ratios?Ratio is used to compare two or more quantities. It is used to indicate how big or small a quantity is when compared to another
The ratio weight of clothing to the weight of dye will be:
For 21 and 3:
21:3 = 7: 1
For 42 and 9:
42:9 = 14: 3
For 84 and 12:
84:12 = 7: 1
For 105 and 15:
105:15 = 7: 1
Thus, 42 pounds is different from the other ratios
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Suppose that the scatterplot of log x and log y shows a strong positive correlation close to 1. Which of the following is true?
a. The variables x and y also have a correlation close to 1 b. A scatterplot of the variables log x andy shows a strong nonlinear pattern c. The residual plot of the variables and y shows a random pattern d. A scatterplot of the variables x andy shows a strong nonlinear pattern e. A residual plot of the variables log x and log y shows a nonrandom pattern
The correct options are;
a. The variables x and y also have a correlation close to 1 .
b. A scatterplot of the variables log x and y shows a strong nonlinear pattern .
The correlation is a measurement of a dependence between 2 variables. If the logarithm of the correlation function shows a linear tendency, it because the correlation between x and y shows a exponential tendency.
This mean that x and y are non linear correlated, but them are correlated.
For this type of data is used a non linear correlation technique know it as logarithm correlation.
Option c is incorrect because random patterns have a correlation value close to 0, which is not the case.
So ,
The correct options are;
a. The variables x and y also have a correlation close to 1
b. A scatterplot of the variables log x andy shows a strong nonlinear pattern
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9(4t+)+3t
Simplify
Explain please
Answer:
Step-by-step explanation:
1. Multiply 9 times 4t in parentheses
2. Once you get the answer you add it to 3t and that gives you 39t
Is this question any helpful enough for?
If numbers is a two-dimensional array, which of the following would give the length of row r?a. numbers[r].length[r]b. numbers.lengthc. numbers.length[r]d. numbers[r].length
If numbers is a two-dimensional array, which of the following would give the length of row r is d. numbers[r].length
A two-dimensional array is a data structure used to store data in a tabular format, consisting of rows and columns. Each element in the array is accessed by two indices, one for the row and one for the column. The length of a row in a two-dimensional array can be determined by accessing the array at the specified row and then returning the length of that row. To do this, the expression numbers[r].length can be used, where 'numbers' is the name of the two-dimensional array, and 'r' is the index of the row whose length is being determined.
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Select the correct answer from each drop-down menu. cos2x-cos4x/sin2x+sin4x cos2x+cos4x/sin2x-sin4x Select the correct answer from each drop-down menu_ 2821 Co841 sin2r + sin4j 0821 + co841 sin2t sin+I
The given trigonometric equations have the value tan x, -cot x.
Since the given trigonometric equations are: cos2x-cos4x/sin2x+sin4x and cos2x+cos4x/sin2x-sin4x. The problem is related to trigonometric Ratios, which are the ratios of the side of a right-angled triangle.Now for the equation (cos 2x - cos 4x )/(sin2x +sin4x)
since we know the formulas :
cos A + cos B = - sin (A+B)/2 sin(A-B)/2
sin A - sin B = sin( A+B)/2 cos (A-B)/2
so for the equation, we can
= (-sin 3x) sin ( -2x)/2)/( cos 3x cos x)
= sin 3x sin x/ (sin 3x) cos x
= tan x
for the second equation cos2x+cos4x/sin2x-sin4x
= cos 3x cosx/ cos3x sin(- x)
= - cot x
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when vector vector a is added to vector vector b, the resultant is a vector vector r such that vector r is equal to vector a plus vector b. this resultant vector has component rx
a. When vector is added to vector , the resultant is vector such that its magnitude and direction is proportional to the resultant magnitude and direction of the component vectors.
b. ∅ = (Rx/Ry)
Vectors are used to represent physical quantities in terms of magnitude and direction. Vectors can be added using the parallelogram method or the triangle addition method. The magnitude and direction of the resulting vector are generally proportional to the magnitude and direction of the component vectors.
I have every vector in 2D that has both vertical and horizontal components.
There are vectors say: A = xi + yj
and, B =zi + wj
For example, adding two vectors gives the result
R = (x +z)i + (y + w) j.
The - component has y +w as z and the y component as w. The sum has the horizontal component as x + z and the vertical component as y + w. So we get the y component of the resulting vector R = A+ y component of B
The direction of the angle is found as
tan∅ = Rx/Ry
∅ = (Rx/Ry)
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normally distributed population of test scores whose minimum was 51 points.
He then took a random sample of 6 tests and calculated the minimum of the sample. He replaced those tests
and repeated this process for a total of 40 trials. His results are summarized in the dotplot below, where each
dot represents the minimum score from a sample of 6 tests.
:
..
TATUS
50
70
75
55
60
65
Sample minimum
From the data we conclude that; (c) The sampling minimum appears to be biased estimator since it consistently over estimated the population minimum.
The sampling distribution of the sample minimum is given as 51 points
The number of tests in the sample = 6 tests
The results of the tests are summarized in the dot plot
In order to be an unbiased estimator the sampling distribution for the statistic has to be evenly distributed about the true parameter for the population .
and In this question , the true parameter for the population is that the sample minimum of the population is 99 points .
So , From sampling distribution of sample Minimum it is clear that distribution of sample maximum is unevenly distributed.
Hence , it is not an unbiased estimator that means it is an biased estimator which is overestimating the population minimum .
Therefore , the correct option is (c) .
-- The given question is incomplete , the complete question is
"Silas was curious if sample minimum was an unbiased estimator of population minimum. He started with a large normally distributed population of test scores whose minimum was 51 points. He then took a random sample of 6 tests and calculated the minimum of the sample. He replaced those tests and repeated this process for a total of 40 trials. His results are summarized in the dot plot , where each dot represents the minimum score from a sample of 6 tests.
50 , 70 , 75 , 55 , 60 , 65
(a) Sample minimum appears to be an unbiased estimator for the population minimum.
(b) Sample minimum appears to be an biased estimator since it consistently under estimates the population minimum.
(c) Sample minimum appears to be an biased estimator since it consistently over estimates the population minimum." --
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