Answer:
\(15.0118^o\)
Step-by-step explanation:
\(\mathrm{We\ use\ the\ sine\ law\ to\ solve\ this\ question.}\\\mathrm{\frac{a}{sinA}=\frac{c}{sinC}}\\\\\mathrm{or,\ \frac{31}{sin138^o}=\frac{12}{sinC}}\\\\\mathrm{or,\ sinC=\frac{12}{31}sin138^o}\\\mathrm{or,\ sinC = 0.259}\\\mathrm{or,\ C=sin^{-1}0.259=15.0118^o}\)
. Write a number in which the value of
the 6 is one tenth the value of the 6 ir
35,629.
The required value is 60 where the value of 6 in the number is one-tenth the value of 6 in the 35, 629.
Given that,
To determine a number in which the value of the 6 is one-tenth the value of the 6 in 35,629.
A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.
Here,
The value of 6 in 35, 629, is 600
A number in which the value of the 6 is one-tenth the value of the 6 in 35,629.
= 1 / 10 * 600
= 60
Thus, the required value is 60 where the value of 6 in the number is one-tenth the value of 6 in the 35, 629.
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Please if anyone help i would be greatly grateful
Answer:
A
Step-by-step explanation:
a and b have to be same cause of isosceles triangle
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total $44,714, and the variable costs will be $11.50 per book. With the other method, the one-time fixed costs will total $17,174, and the variable costs will be $20 per book. For how many books produced will the costs from the two methods be the same?
The number of books published by a small publishing company is 3240.
Given that, a small publishing company is planning to publish a new book. The production costs will include one-time fixed costs and variable costs.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of books be x.
With one method, the one-time fixed costs will total $44,714, and the variable costs will be $11.50 per book.
That is, 44,714+11.50x
With the other method, the one-time fixed costs will total $17,174, and the variable costs will be $20 per book.
That is, 17,174+20x
Now, the number of books produced will the costs from the two methods be the same.
So, 44,714+11.50x=17,174+20x
⇒ 44,714-17,174=20x-11.50x
⇒ 8.5x = 27540
⇒ x=3,240
Therefore, the number of books published by a small publishing company is 3240.
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after 24.0 days, 2.00 milligrams of an original 128.0 milligram sample remain. how many half lives have occurred?
After 24.0 days, 2.00 milligrams of an original 128.0-milligram sample remain, and 6 half-lives have occurred.
To determine the number of half-lives that occurred, we must use the half-life formula:
Final amount = Initial amount x (1/2)^(number of half-lives)Here, the initial amount of the sample is 128.0 milligrams, and the final amount is 2.0 milligrams.
Putting these values in the formula, we get:
\(2.0 = 128.0 x (1/2)^(number of half-lives)2.0/128.0 = (1/2)^(number of half-lives)log(2.0/128.0) = number of half-lives x log(1/2)log(2.0/128.0) = number of half-lives x (-0.3010)Number of half-lives = log(2.0/128.0) ÷ (-0.3010)Number of half-lives ≈ 6.13 ≈ 6\)
Therefore, 6 half-lives have occurred.
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Classify the following numbers as rational
or irrational.
3.1415926535... 0 V1 7.4 15 V3
pls helpp
Answer: 2.5.02
Step-by-step explanation:
2(c+1)=10 HELP PLSSSSSSSS
Answer:
c=4
Will venus1234 delete the c4?
Step-by-step explanation:
You simplify by distributive property
2c+2=10
Then you can use subtraction property of equality to subtract 2 from both sides to get
2c=8
Then do division property of equality to get the unit rate of c.
You end up with
c=4
4
4
4
4
4
4
4
Hope this helps!
Answer: c=4
Step-by-step explanation:
2÷2=c+1
10÷2=5
5-1
c=4
What is 14 x 14 x 14 is exponet form
Answer:
14^3
Step-by-step explanation:
Y>x-3, y<-x+3? I need a graph:(
Answer:
Then make one
Step-by-step explanation:
hey could someone help me with this. i’ll mark u brainiest if u don’t leave a link.
Answer:
10,000
Step-by-step explanation:
10 to the power of 4 is equal to 10x10x10x10 which is 10,000! I hope this helps
Answer:
the answer will be 10000!
Step-by-step explanation:
10 x 10 x 10 x 10 = 10000
or...
10 x 10 = 100
100 x 100 = 10000
or...
jusr simply add 4 zero to 1!
Testing more properties of the Cobb-Douglas utility function Check if the Cobb-Douglas utility function u(x
1
,x
2
)=x
i
α
x
2
β
, where α,β>0, satisfies the following properties: (a) local nonsatiation, (b) decreasing marginal utility for both goods 1 and 2, (c) quasi-concavity, and (d) homotheticity.
The Cobb-Douglas utility function satisfies the properties of local non-satiation, decreasing marginal utility for both goods, quasi-concavity, and homotheticity.
The Cobb-Douglas utility function u(x1, x2) = xi^(α) * x2^(β), where α and β are both greater than zero, satisfies the following properties:
(a) Local non-satiation:
This property states that at each point of the consumption set, there is always another bundle that is arbitrarily close and strictly preferred. Thus, the function has local non-satiation.
(b) Decreasing marginal utility for both goods 1 and 2: The marginal utility of a good measures the utility obtained by consuming one more unit of it. The marginal utility of x1 can be obtained as:
MU1 = α * xi^(α−1) * x2^(β)
The marginal utility of x2 can be obtained as:
MU2 = β * xi^(α) * x2^(β−1)
Therefore, both marginal utilities are decreasing in x1 and x2, satisfying this property.
(c) Quasi-concavity:
The Cobb-Douglas function is quasi-concave. This means that the upper contour set of any level set of the function is convex. This can be proved by taking the second partial derivative of the function and checking whether it is negative or not.
(d) Homotheticity:
The Cobb-Douglas function is homothetic. This means that its shape is independent of the total level of utility. The proof can be achieved by checking whether the function is homogeneous of degree one or not. This is true, since multiplying the inputs by any positive scalar λ leads to a proportional increase in the output.
In conclusion, the Cobb-Douglas utility function satisfies all four properties - local non-satiation, decreasing marginal utility for both goods 1 and 2, quasi-concavity, and homotheticity.
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Please Help quickly!
compute (r) and (x) for (a) the ground state, (b) the first excited state, and (c) the second excited state of the harmonic oscillator.
To compute the values of (r) and (x) for the different states of the harmonic oscillator, we need to consider the wavefunction solutions for each state.
The wavefunctions for the harmonic oscillator are given by Hermite polynomials multiplied by a Gaussian factor. The energy eigenvalues for the harmonic oscillator are given by (n + 1/2) * h * ω, where n is the quantum number and ω is the angular frequency of the oscillator. (a) Ground State: The ground state of the harmonic oscillator corresponds to n = 0. The wavefunction for the ground state is: ψ₀(x) = (mω/πħ)^(1/4) * exp(-mωx²/2ħ), where m is the mass of the oscillator. In this state, the energy (E₀) is equal to 1/2 * h * ω. Therefore, for the ground state: (r) = 0 (since n = 0). (x) = √(ħ/(2mω)). (b) First Excited State:The first excited state corresponds to n = 1. The wavefunction for the first excited state is: ψ₁(x) = (mω/πħ)^(1/4) * √2 * (mωx/ħ) * exp(-mωx²/2ħ), where m is the mass of the oscillator. In this state, the energy (E₁) is equal to 3/2 * h * ω. Therefore, for the first excited state: . (r) = 1. (x) = √(ħ/(mω)). (c) Second Excited State:The second excited state corresponds to n = 2. The wavefunction for the second excited state is: ψ₂(x) = (mω/πħ)^(1/4) * (2(mωx/ħ)^2 - 1) * exp(-mωx²/2ħ) where m is the mass of the oscillator. In this state, the energy (E₂) is equal to 5/2 * h * ω.
Therefore, for the second excited state: (r) = 2. (x) = √(ħ/(2mω)). In summary: (a) Ground State: (r) = 0, (x) = √(ħ/(2mω)). (b) First Excited State: (r) = 1, (x) = √(ħ/(mω)). (c) Second Excited State: (r) = 2, (x) = √(ħ/(2mω)).
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the graph of F(x) = |x| is shown below. if you horizontally shift this function right 7 units, what is the equation of the new function?
ANSWER:
C. G(x) = |x - 7|
STEP-BY-STEP EXPLANATION:
An absolute value function has the following form:
\(y=|x-a|+b\)Where (a, b) is the origin, if we want to move 7 units to the right, we must add 7 units on the x-axis, that is, in a, therefore, the function would be:
\(\begin{gathered} G\left(x\right)=\left|x-+7\right| \\ \\ G(x)=\lvert x-7\rvert \end{gathered}\)So the correct answer is C. G(x) = |x - 7|
37 of the 998 digital video recorders (dvrs) in an inventory are known to be defective. what is the probability that a randomly selected item is defective?
The probability that a randomly selection of 998 digital video recorders in a inventory one of them is defective is 3.71%
To solve this exercise the formula and the procedure that we have to use for probability is:
% probability= (achieving success / possible outcomes) * 100
Information about the problem:
Achieving success = 37Possible outcomes = 998Applying the formula to calculate the probability we get:
% probability= (achieving success / possible outcomes) * 100
% probability= (37/ 998) * 100
% probability= (0.0371) * 100
% probability= 3.71%
What is probability?Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.
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Which expression correctly represents "ten times the difference of a number and six"?
Answer:
10*(n-6)
Step-by-step explanation:
Break up the equation above and use words. ex.
10 (times) n (minus) 6
^
this is the difference
This model represents an equation.
Which value of x makes the equation true?
A.
B.
C.
D.
Evaluate the limit :lim h- 0 ((1/(x+h)^2)-(1/x^2))/h
The limit lim h→0 ((1/(x+h)^2)-(1/x^2))/h = -1/(x^2). To evaluate the limit lim h→0 ((1/(x+h)^2)-(1/x^2))/h, we first need to simplify the expression inside the limit.
Starting with ((1/(x+h)^2)-(1/x^2))/h, we can use the difference of squares formula to simplify the numerator:
((1/(x+h)^2)-(1/x^2))/h = ((1/(x+h)-1/x)(1/(x+h)+1/x))/h
Next, we can simplify the first factor using the common denominator (x(x+h)):
((1/(x+h)-1/x)(1/(x+h)+1/x))/h = ((x-x-h)/(x(x+h)) * 1/(x+h)+1/x)/h
Simplifying further, we get:
((x-x-h)/(x(x+h)) * 1/(x+h)+1/x)/h = (-h/(x(x+h)) * 1/(x+h)+1/x)/h
Now, we can cancel out the h's in the numerator and denominator:
(-1/(x(x+h)) * 1/(x+h)+1/x)/1 = -1/(x(x+h)) * 1/(x+h)+1/x
Taking the limit as h approaches 0, we get:
lim h→0 -1/(x(x+h)) * 1/(x+h)+1/x = -1/(x^2)
Therefore, the limit lim h→0 ((1/(x+h)^2)-(1/x^2))/h = -1/(x^2).
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the radius of a circle is 4 inches
r=4
Answer:
Step-by-step explanation:
Use SD and determine relationship
of polynomial and linear expression.
x³ + 9x²-16x-144 (division symbol) x +9
The polynomial expression x³ + 9x² - 16x - 144 can be factored as (x + 9)(x² - x - 16) with a remainder of -288 when divided by the linear expression x + 9.
To determine the relationship between the polynomial expression x³ + 9x² - 16x - 144 and the linear expression x + 9, we can use synthetic division (SD) to divide the polynomial expression by the linear expression.
The polynomial expression can be rewritten as:
x³ + 9x² - 16x - 144 = (x + 9)(x² - x - 16)
Using synthetic division, we divide the polynomial expression by x + 9:
-9 | 1 9 -16 -144
---------------------
1 0 -16 -288
The result of the division is 1x² + 0x - 16 with a remainder of -288.
Therefore, the relationship between the polynomial expression x³ + 9x² - 16x - 144 and the linear expression x + 9 is that the polynomial expression can be factored as (x + 9)(x² - x - 16) with a remainder of -288.
This means that the polynomial expression can be written as the product of the linear expression x + 9 and the quadratic expression x² - x - 16. The remainder -288 indicates that there is no perfect division, and there is a leftover term of -288.
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Solve the equation for exact solutions over the interval [0, 2x). 3 cotx+4=7 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The solution set is.
To solve the equation for exact solutions over the interval [0, 2x), we need to follow these steps: according to the solving, The solution set is {45°}.
Step 1: Subtract 4 from both sides of the equation.3 cot x = 7 - 4 ⇒ 3 cot x = 3
Step 2: Divide both sides by 3cot x = 1
Step 3: Find the angle whose cotangent is 1.
The angle whose cotangent is 1 is 45°
Step 4: To obtain the solution set, we can add 2πn to the solution of x = cot-1 (1) over the given interval [0, 2x).∴ x = cot-1(1) + πn, n ∈ Z
For x = cot-1(1),
we know that cot45° = 1.
So, x = 45° + π n, n ∈ Z
Since the given interval is [0, 2x), we have to solve x = 45° + π n, n ∈ Z for x in the interval [0, 90°).n = 0 ⇒ x = 45° lies in the interval [0, 90°).
n = 1 ⇒ x = 45° + π lies outside the interval [0, 90°).n = -1 ⇒ x = 45° - π lies outside the interval [0, 90°).
Hence, the solution set is {45°} for the given interval [0, 2x).
Answer: The solution set is {45°}.
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what the answer to 24/3/7/5=
Answer:24/3/7/5 = 8/ 35 ≅ 0.2285714
Step-by-step explanation:
Divide: 24/3: 7 = 24/3· 1/7
= 24 · 1/3 · 7
= 24/21
= 3 · 8/3 · 7= 8/7
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 7/1 is 1/7) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 3 gives 8/
7
.
In other words - twenty-four thirds divided by seven = eight sevenths.
Divide: the result of step No. 1 : 5 = 8/7 : 5 = 8/7 · 1/5
= 8 · 1/7 · 5
= 8/35
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 5/1
is 1/5
) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - eight-sevenths divided by five = eight thirty-fifths.
[3 points] implement (i.e get the truth table, then the boolean function, and finally draw the logic diagram) of the following functions using and, or, and not logic gates. assume a and b are the inputs and f is the output. a. f has the value of 1 only if: i. a has the value 0 and b has the value 0. ii. a has the value 0 and b has the value 1.
The truth table is attached in the image and the logic diagram is also attached.
What is the equivalent expression?
Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
To implement the given function using AND, OR, and NOT logic gates, let's go through each step:
a. f has the value of 1 only if:
i. a has the value 0 and b has the value 0.
ii. a has the value 0 and b has the value 1.
We can create a truth table to represent the function:
The truth table is attached in thee image.
From the truth table, we can observe that f is equal to 1 when (a = 0 and b = 0) or (a = 0 and b = 1).
We can express this using logical operators as:
f = (a AND b') OR (a' AND b)
the logic diagram to implement this function is attached.
In the logic diagram, the inputs a and b are connected to the AND gate, and its complement (NOT) is connected to the other input of the AND gate.
The outputs of the AND gate are connected to the inputs of the OR gate. The output of the OR gate represents the output f.
This logic diagram represents the implementation of the boolean function f using AND, OR, and NOT logic gates based on the given conditions.
Hence, The truth table is attached in the image and the logic diagram is also attached.
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Estimate the conditional probabilities for Pr(A = 1|+) ..., Pr(B = 1|+) ..., Pr(C = 1|+)...
Question:
Estimate the conditional probabilities for
_____,
_____,
_____,
_____,
_____, and
_____;
Instance A B C Class
1 0 0 1 -
2 1 0 1 +
3 0 1 0 -
4 1 0 0 -
5 1 0 1 +
6 0 0 1 +
7 1 1 0 -
8 0 0 0 -
9 0 1 0 +
10 1 1 1 +
To estimate the conditional probabilities for Pr(A = 1|+), Pr(B = 1|+), and Pr(C = 1|+), we need to calculate the probabilities of each event occurring given that the class is positive (+).
Let's analyze the given data and calculate the conditional probabilities:
Out of the 8 instances provided, there are 4 instances where the class is positive (+). Let's denote these instances as +1, +2, +5, and +6.
For Pr(A = 1|+), we calculate the proportion of instances among the positive class where A = 1. Out of the four positive instances, +2 and +5 have A = 1. Therefore, Pr(A = 1|+) = 2/4 = 0.5.
For Pr(B = 1|+), we calculate the proportion of instances among the positive class where B = 1. Out of the four positive instances, +5 has B = 1. Therefore, Pr(B = 1|+) = 1/4 = 0.25.
For Pr(C = 1|+), we calculate the proportion of instances among the positive class where C = 1. Out of the four positive instances, +5 and +6 have C = 1. Therefore, Pr(C = 1|+) = 2/4 = 0.5.
To summarize:
- Pr(A = 1|+) = 0.5
- Pr(B = 1|+) = 0.25
- Pr(C = 1|+) = 0.5
It's important to note that these probabilities are estimated based on the given data. Depending on the context and the underlying distribution of the data, these probabilities might not be accurate representations in other scenarios.
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Find the common factors of the following
25x2y. 30xy2
Plz the 2 is square2
Answer:
5xy is the answer
Step-by-step explanation:
plz check it
Can the two triangles be proven congruent by SAS? Explain.
A) No, there's only one pair of congruent angles, ∠B ≅ ∠D, and one pair of congruent sides, ≅ .
B) No, because the two triangles share a side.
C) Yes, because ≅ , ∠B ≅ ∠D, and and are parallel.
D) Yes, because ≅ , ∠B ≅ ∠D, and and are parallel
Answer:
The correct option is;
Yes because AC ≅ AC, ∠B ≅ ∠D, and AD and BC are parallel.
Step-by-step explanation:
Based on the the given information
The number of congruent sides = One which is AC is congruent to AC which is the reflexive property
The number of given congruent angles = One which is angle ∠ABC is congruent to ∠ADC
However, where angle ∠ABC is congruent to ∠ADC, we have AD is parallel to BC, therefore, ∠BAC is congruent to ∠DCB, and BA is parallel to CD, therefore AD is congruent to BC and DC is congruent to AB
Therefore the correct option is yes because AC ≅ AC, ∠B ≅ ∠D, and AD and BC are parallel.
what’s the simplified value of 12.4x(-6.3)
Answer:
-78.12
Step-by-step explanation:
Answer: u just divide the small number to the big number and add and get ur answer that is -78.12
Step-by-step explanation:
cut all 6 colored sections as well as non colored sections. connect each section in an opposite section, what shape is formed?
The shape that is formed when the sections are cut is a triangle.
What is a triangle?A triangle is a flat geometric figure that has three sides and three angles.
In this case, we can see that each section is triangular. The sum of the angles of a triangle is always 180 degrees.
Therefore, the shape that is formed when the sections are cut is a triangle.
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Can someone help me with part b?
Answer: x^2+3x+5
Step-by-step explanation:
Substitute (x+4) in so that you get f(x)=(x+4)^2-5(x+4)+9. Then expand so you get x^2+8x+16-5x-20+9. Now simplify and you get x^2+3x+5. That is your final answer.
Find the coordinates of a point on a circle with radius 20 corresponding to an angle of 120° (x,y) = (_____,_____)
Round your answers to three decimal places.
To find the coordinates of a point on a circle with a radius of 20 corresponding to an angle of 120°, we can use trigonometry.
In a circle, the x-coordinate of a point is given by the formula x = r * cos(θ), and the y-coordinate is given by y = r * sin(θ), where r is the radius and θ is the angle.
Substituting the given values, we have x = 20 * cos(120°) and y = 20 * sin(120°).
Using a calculator, we can evaluate cos(120°) ≈ -0.5 and sin(120°) ≈ 0.866.
Therefore, the coordinates of the point on the circle are (20 * (-0.5), 20 * 0.866), which simplifies to (-10, 17.32) when rounded to three decimal places.
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To find the coordinates of a point on a circle with a radius of 20 corresponding to an angle of 120°, we can use trigonometry.
In a circle, the x-coordinate of a point is given by the formula x = r * cos(θ), and the y-coordinate is given by y = r * sin(θ), where r is the radius and θ is the angle.
Substituting the given values, we have x = 20 * cos(120°) and y = 20 * sin(120°).
Using a calculator, we can evaluate cos(120°) ≈ -0.5 and sin(120°) ≈ 0.866.
Therefore, the coordinates of the point on the circle are (20 * (-0.5), 20 * 0.866), which simplifies to (-10, 17.32) when rounded to three decimal places.
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Find the missing side. Round to the nearest tenth. (ITS DUE IN THE MORNING PLEASE HELP)
24.
A) 14.2
C) 13.8
B) 9.2
D) 15.7.
25.
A) 37.6
B)30.8
C) 45.1
D)5.5
Answer:
24. A)14.2
25. D)5.5
Step-by-step explanation:
I hope it help for you keep safe