The point P = (1/7, y) lies on the unit circle shown below. What is the value of y in
simplest form?

The area of the shaded section is approximately equal to 219.711 square meters.

In this problem we find the case of a shaded section, whose area must be determined. This can be realized by finding the area of rhombus OPQR and subtract the circular section OPR from it. All missing lengths of the triangles from the rhombus can be found by trigonometric functions.

The formula to determine the area of the shaded area is:

A = 2 · 0.5 · OR · RQ - (140 /360) · π · OR²

RQ = OR · tan 70°

If we know that OR = 12 m, then the area of the shaded section is:

RQ = 12 · tan 70°

RQ = 32.970

A = 2 · 0.5 · OR · RQ - (140 /360) · π · OR²

A = OR · RQ - (7π / 18) · OR²

A = 12 · 32.970 - (7π / 18) · 12²

A ≈ 219.711 m²

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the factored form of 36x² - 16 is (6x + 4)(6x - 4).this is final answer.

To factor the expression 36x² - 16 as a difference of two squares, we need to identify the perfect squares and apply the formula:

a² - b² = (a + b)(a - b)

In this case, we have 36x² as a perfect square of (6x)², and 16 as a perfect square of 4². So we can rewrite the expression as:

36x² - 16 = (6x)² - 4²

Now we can apply the formula:

(6x)² - 4² = (6x + 4)(6x - 4)

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capacity of bucket to hold water = 6liters or 6000 milliliters

capacity of jug= 500 milliliters

numbers of jug need to use in order to fill the empty bucket= 6000/500

=12 jugs of water

Answer:

12 jugs

Step-by-step explanation:

A unit can be used for measurement and is commonly found in mathematics to describe length, size, etc.

Let's get to know these units.

To convert 6 liters into milliliters, we can use this equation:

Therefore, the empty bucket can hold 6000 milliliters.

To solve for the number of jugs Megan will need, we can use this equation:

Therefore, to fill the bucket, Megan will need 12 jugs.

Answer:

13.85$

Step-by-step explanation:

105$-8$=97$

97$/7$=13.85$

Answer: About $13.86

Step-by-step explanation: To find how much the cost of the forks is, we need to subtract the value of the lunch box from the total cost, because we don't need to find the value of the lunch box. So:

105 - 8 = 97

So, now since he bought 7 forks, we need to divide 7 by 97. So:

97 / 7 = 13.857142857142858

So, we need to round to the nearest cent. So, the 7 is greater than 5, so we round up. So, we have $13.86 each. So, check, we do:

13.86(7) + 8

97.02 + 8

= 105.02

This is the closest he can buy for each fork is ABOUT $13.86. I hope this helps ;)

Muscular strength can be measured based on the amount of weight lifted.

Muscular strength can be measured based on the amount of weight lifted. The upper-body and lower-body strength are measured separately. Muscular strength is typically measured which is known as a One Rep Max (1RM).

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Answer:

12

Steps:

−3x+5y=2

9x−15y=6

Solve −3x+5y=2 for x

= −3x+5y+−5y=2+−5y

= −3x=−5y+2

= −3x/-3 = (−5y+2) /-3

x = 5/3y + −2/3

Substitute 5/3y + −2/3 for x in 9x−15y=6

9x−15y=6

=9 (5/3y + −2/3) )−15y=6

= −6 = 6

= −6+6=6+6

= 12

The number of possible permutations of the three letters C, D, and E is d.6

A permutation is an arrangement of objects in a specific order. In this case, we are looking at the number of possible arrangements of the three letters C, D, and E. To find the number of permutations, we can use the formula:

n! = n x (n-1) x (n-2) x ... x 3 x 2 x 1

where "n" is the number of distinct objects to be permuted.

So for our problem, we have three distinct objects (C, D, and E). Therefore, we can plug in n=3 to get:

3! = 3 x 2 x 1 = 6

This means there are 6 possible ways to arrange the letters C, D, and E in different orders. We can list all of these permutations as follows:

CDE

CED

DCE

DEC

ECD

EDC

So the answer to the question is 6, as given in option (d).

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Answer:

Step-by-step explanation:

\( \mathsf{ 12 {p}^{2} q - 9 {q}^{2} }\)

In such an expression, the factor which is present in all terms of the expression is taken out as common and each term of the expression should be divided by the common factor to get another factor.

Factor out 3q from the expression

\( \mathsf{ = 3q(4 {p}^{2} - 3q)}\)

Hope I helped!

Best regards!

Factorization of 12p²q-9q² is  3q(4p²-3q).

Factorization is defined as breaking an entity into a product of another entity, or factors, which when multiplied together give the original number.

Here, given expression is,   12p²q-9q²

Now, by factorizing this we get,

3q(4p²-3q)

Hence, required factorization is 3q(4p²-3q)

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The probability of observing the expected value for the distribution of a binomial (100, 0.20) is 0.20 (or 20%).

The probability of observing the expected value for a binomial distribution can be calculated using the following formula:

Probability = (n C r) p^r (1-p)^(n-r)

where n = number of trials,

r = expected value,

p = probability of success

For the given distribution, binomial (100, 0.20), we know that n = 100 and p = 0.20.

The expected value is given by:E(X) = np = 100 * 0.20 = 20

So, to find the probability of observing the expected value of 20, we need to plug in the values of n, r, and p into the formula:

Probability = (n C r) p^r (1-p)^(n-r)=

(100 C 20) (0.20)^20 (0.80)^80≈

0.1875 ≈ 0.20 (rounded to two decimal places)

Therefore, the probability of observing the expected value for the distribution of binomial (100, 0.20) is approximately 0.20 (or 20%).

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Answer:

19.63 inches

Step-by-step explanation:

The area of a circle is found by using the formula

A = πr²

r is the radius of the circle, which is the diameter divided by two.

D = 5 in so r = D ÷2

5 ÷ 2 = 2.5 inches for the radius.

A = π (2.5)²

A = π (6.25)

A = (3.14)(6.25)

A = 19.625 inches

The inverse property of multiplication states that if you multiply a number by its reciprocal, also called the multiplicative inverse, the product will be 1.

So the reciprocal of 2 is 1/2 because 2*1/2=1

Total fixed cost is $6. The value of AFC is $6 / Q. Productive efficiency is greatest at Q = 4.5. Diminishing returns begin when Q = 3. The total fixed cost (TFC) does not change because it is fixed.

a) Total fixed cost is $6

b) We can obtain the average fixed cost function (AFC) from the total fixed cost (TFC) by dividing it by output (Q) as follows: AFC = TFC / Q. So, the value of AFC is $6 / Q.

c) The AVC function is calculated by dividing total variable cost (TVC) by output (Q).

STC = TFC + TVC6 + 9Q - 3Q2 + (1/3)Q3TVC = 9Q - 3Q2 + (1/3)Q3AVC = TVC / QAVC = (9Q - 3Q2 + (1/3)Q3) / QAVC = 9 - 3Q + (1/3)Q2

d) The MC function is derived by taking the first derivative of the STC function with respect to output (Q). The derivative of the STC function is: MC = dSTC / dQMC = 9 - 6Q + Q2

e) As Q approaches infinity, the denominator of AFC becomes larger and larger. So, AFC approaches zero as Q gets very large. This implies that fixed costs per unit decrease as production quantities get larger.

f) We can find the value of Q at which AVC is a minimum by taking the first derivative of the AVC function and setting it equal to zero. The first derivative of AVC is: AVC = 9 - 3Q + (1/3)Q2

dAVC / dQ = -3 + (2/3)Q= 0

Q = 4.5

g) Productive efficiency is greatest when AVC is at its minimum. Therefore, productive efficiency is greatest at Q = 4.5.

h) We can demonstrate that the value of SMC equals the value of AVC at the value of Q where AVC is a minimum by plugging Q = 4.5 into both the AVC and MC functions. AVC = 9 - 3(4.5) + (1/3)(4.5)2AVC = 7.125MC = 9 - 6(4.5) + 4.52MC = 7.125

Since SMC = MC, we can conclude that SMC equals AVC at the value of Q where AVC is a minimum.

i) In the short run, the total fixed cost (TFC) does not change because it is fixed. Therefore, the derivative of the STC function with respect to output (Q) is equal to the derivative of the TVC function with respect to output (Q). This means that dSTC / dQ = dTVC / dQ.

j) Increasing returns to scale cease when the marginal cost (MC) is equal to average total cost (ATC). Diminishing returns to scale begins when MC exceeds ATC. ATC is calculated by dividing the total cost (TC) by output (Q). TC is calculated by adding total fixed cost (TFC) and total variable cost (TVC).

ATC = TC / QATC = (6 + 9Q - 3Q2 + (1/3)Q3) / Q

Now, we can find the level of Q where increasing returns to scale cease by calculating the first derivative of ATC and setting it equal to zero.

ATC = (6 + 9Q - 3Q2 + (1/3)Q3) / QdATC / dQ = (6 - 6Q + Q2) / Q2= 0

Q = 3

Now, we can calculate the marginal cost function and find the level of Q where diminishing returns begins. We know that diminishing returns begin where the marginal cost is at its minimum.

MC = 9 - 6Q + Q2MC = 9 - 6(3) + 32MC = 3

So, diminishing returns begin when Q = 3.

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Answer:

c is the answers for the question

Step-by-step explanation:

please give me brainlest

Answer:

x =(-2-√-116)/-10=(1+i√ 29 )/5= 0.2000-1.0770i

x =(-2+√-116)/-10=(1-i√ 29 )/5= 0.2000+1.0770i

Step-by-step explanation:

Answer:

its 80ft

Step-by-step explanation:

Teresa would need to work 10 weeks in order to earn the same total amount as the second job.

Assuming Teresa takes the first job, she would need to work for 10 weeks in order to earn the same total amount as the alternate job. The total amount earned from the first job can be calculated by (400 x 10) + 200 = 6000. The total amount earned from the second job can be calculated by (420 x 10) = 4200. Thus, in order to earn the same amount from the total of both jobs, Teresa would need to work 10 weeks at the first job. This can be expressed by the following formula: (400 x n) + 200 = 420 x n, working for n is the number of weeks. Solving for n gives n = 10.

Thus, Teresa would need to work 10 weeks in order to earn the same total amount as the second job.

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Answer:

y * ( 6*5)

Step-by-step explanation:

(y x 6) x 5

We can change the order of multiplication by changing where the parentheses are placed using the associative property

y * ( 6*5)

Answer:

The answer will be Y*(6*5)

Step-by-step explanation:

this is the answer because while doing the associative property you switch the parenthesis to the different numbers or the other side in this case were 6 and 5

The graph of of the quadratic function f(x) = -x² + 2 is attached below

The graph of a quadratic function is called a parabola and has a curved shape.  One of the main points of a parabola is its vertex.  It is the highest or the lowest point on its graph.  You can think of like an endpoint of a parabola. The graph of a quadratic function is a U-shaped curve called a parabola. One important feature of the graph is that it has an extreme point, called the vertex. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value. In either case, the vertex is a turning point on the graph. The graph is also symmetric with a vertical line drawn through the vertex, called the axis of symmetry.

In the given function

f(x) = -x² + 2, this can be represented on a graph below;

The characteristic of this graph are;

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Answer:

1/10, 0.9, 3/10

Step-by-step explanation:

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Answer:

its purple

Step-by-step explanation:

Answer:

y = x/4 + 5

Step-by-step explanation:

Solve for y:

20 - 4 y = -x

Hint: | Isolate terms with y to the left-hand side.

Subtract 20 from both sides:

-4 y = -x - 20

Hint: | Solve for y.

Divide both sides by -4:

Answer: y = x/4 + 5

Answer:

y=1/4x+5

Step-by-step explanation:

The remainder r in the division algorithm is often referred to as a residue.

This is because it represents the leftover value after the divisor has been subtracted as many times as possible from the dividend. The residue can be useful in a variety of mathematical applications, including modular arithmetic and the Chinese Remainder Theorem.

An algorithm is a set of instructions for carrying out a specific task or solving a problem. In number theory, algorithms can be used for a variety of purposes, such as finding the greatest common divisor of two numbers or determining whether a number is prime.

In modular arithmetic, the notation a mod n represents the residue when the integer a is divided by the positive integer n. This concept is important in cryptography, computer science, and many other fields that rely on modular arithmetic.

An nth-degree polynomial is said to be a monic polynomial if its leading coefficient is 1. Monic polynomials have several useful properties, including the fact that their roots can be easily found using the Rational Root Theorem. Additionally, monic polynomials are often used in applications such as finite fields and coding theory.

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The congruent triangles in this problem are given as follows:

Triangles A and B.

Two figures are classified as congruent if their side lengths are the same.

If we rotate triangle B 180º over it's base, we have that it will have a similar format to triangle A, and also with the same side lengths.

Hence the congruent triangles in this problem are given as follows:

Triangles A and B.

With triangle C, no rotation would make it like A and B, with the same side lengths, hence it is not congruent to any of the triangles in this problem.

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The coordinates of the function y = x are related in that for every input value of x, there is a corresponding output value of y. This creates a set of ordered pairs (x,y), where the x-coordinate represents the input value and the y-coordinate represents the output value.

ii. Not all functions have inverse relations. For a function to have an inverse relation, it must be a one-to-one function, which means that each input value maps to a unique output value. If the function is not one-to-one, then multiple input values may map to the same output value, making it impossible to find a unique inverse for the function.

iii. If a function is one-to-one, then its inverse relation will also be a function. The inverse function is defined as the reflection of the original function across the line y = x, and since the line y = x passes the vertical line test, the inverse function will also pass the vertical line test and be a function.

iv. Two functions that are their own inverses are y = -x and y = 1/x.

For y = -x, the inverse function is obtained by switching the x and y variables: x = -y, which can be rewritten as y = -x. Therefore, y = -x is its own inverse.

For y = 1/x, the inverse function is obtained by switching the x and y variables and solving for y: x = 1/y, which can be rewritten as y = 1/x. Therefore, y = 1/x is also its own inverse.

v. A function is its own inverse if its inverse function is identical to the original function, which means that applying the function twice in succession results in the same input value. This can be expressed mathematically as f(f(x)) = x, where f(x) is the function and x is the input value. In other words, the composition of the function with itself results in the identity function.

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The distance along the unit circle between any two successive 8th roots of 1 is c) π/4.

To find the distance along the unit circle between any two successive 8th roots of 1, we can consider the concept of angular displacement.

Each 8th root of 1 represents a point on the unit circle that is evenly spaced by an angle of 2π/8 = π/4 radians.

Starting from the point corresponding to 1 on the unit circle, we can move π/4 radians to reach the first 8th root of 1. Moving π/4 radians further will bring us to the second 8th root of 1, and so on.

Since we are moving by π/4 radians for each successive 8th root of 1, the distance between any two successive 8th roots of 1 is π/4 radians.

Therefore, the correct answer is option c. π/4.

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Answer: x=11/36

Step-by-step explanation:

Step One-Subtract 1/6 from both sides.

2x+1/6-1/6=7/9-1/6

2x=11/18

Step Two-Divide both sides by 2.

2x/2=11/18/2

x=11/36.

My math might not be correct, sorry if it is. In addition, my explanation is a bit confusing, so sorry about that too.

It is true that the A shift is a type of permutation where elements in a sequence or set are moved to the right or left by a certain number of positions.

For example, shifting the sequence (1,2,3,4,5) to the right by 2 positions would result in the sequence (4,5,1,2,3). This can be represented mathematically as (1,2,3,4,5) → (4,5,1,2,3), which is a permutation of the original sequence. Shifts can be useful in various applications, such as cryptography or data compression, where rearranging elements in a sequence can improve efficiency or security.

True. A shift is a specific type of permutation. In general, a permutation refers to the arrangement of objects in a particular order. A shift, also known as a cyclic permutation, involves moving elements of a set in a fixed direction, such that the order is maintained, but the elements change positions. In a shift, the first element moves to the last position, while all other elements move one position forward. This maintains the relative order of the elements and results in a new arrangement. Therefore, a shift is a type of permutation, as it represents an altered ordering of the elements in a set.

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Answer:

it is a rational number

Step-by-step explanation:

In the graph, we have four points: A=(-2,2), B=(-1,1), C=(2,0) and D=(7,-1)

At the segment AB, we have the function f(x). Its slope is (1 - 2)/[-1 -(-2)] = -1

Then, it can be expressed in the form f(x) = -x + b

Replacing x with -1, we got: 1 = 1 + b, which implies b = 0

Therefore, f(x) = -x

At the segment BC, we have the function f'(x). Its slope is (0 -1)/[2 -(-1)] = -1/3.

From this, we have: f'(x) = -x/3 + b

Replacing x with 2, we got -2/3 + b = 0, which implies b = 2/3

Therefore, function f'(x) = -x/3 + 2/3 is the function f(x) turned left with an angle of arctan(1/3) and turned up by 2/3 units.

From the segment CD, we have the function f''(x). Its slope is -1/(7-2) = -1/5

Then, it can be expressed in the form f''(x) = -x/5 + b

Replacing x with 2, we got -2/5 + b = 0, which implies b = 2/5

Therefore, the function f''(x) = -x/5 + 2/5 is the function f(x) turned left with an angle of arctan(1/