The circumference of a circle can be found using the
formula C = 2rer.
Which is an equivalent equation solved for
r = CT
Or= C(20)
O
ra
2T
2m
re
쯘

The positive solution to the equation \(-x^{2} +2x+1=0\) is \(x=1+\sqrt{2}\).

Given quadratic equation is:

\(-x^{2} +2x+1=0\)

The general form of a quadratic equation is \(ax^{2} +bx+c=0\) and \(a\neq 0\).

On comparing with general form of quadratic equation

a = -1

b = 2

c = 1

So, from the Shreedharacharya formula,

\(x = \frac{-b+-\sqrt{b^{2} -4ac} }{2a}\)

\(x = \frac{-2+-\sqrt{2^{2} -4(-1)(1)} }{2*(-1)}\)

\(x = 1-\sqrt{2} \\x=1+\sqrt{2}\)

as \(x = 1-\sqrt{2}\) is negative

So, the positive solution is \(x=1+\sqrt{2}\)

Therefore, the positive solution to the equation \(-x^{2} +2x+1=0\) is \(x=1+\sqrt{2}\).

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Answer:  x = 2 + √2. x = 2 - √2 ·

Step-by-step explanation:

- x² + 2x + 1 = 0. x² - 2x - 1 = 0. Here,. a = 1. b = - 2. c = - 1

Answer:

Step-by-step explanation:

2 kilograms equals 2,000 grams

2,000 divided by 20 equals 100

Answer:100 cookies

Answer:

7) A    8) C

Step-by-step explanation:

number 7 tells us that y=x+1

so we just basically plug it in

2x+3(x+1)=4  Answer: A

to eliminate x's in number 8, we have to multiply one of the equations by -1

let's multiply the second one

4x+3y=6

4x ·-1-y·1=2·-1

4x+3y=6

-4x+y=-2

x's eliminate

4y=4, meaning that the answer is C

the worker's total biweekly earnings would be $1277.55.

To calculate the worker's total biweekly earnings, we need to consider the regular pay for the hours worked up to 40 hours per week, as well as any overtime pay for the additional hours worked.

Let's break down the calculation:

Regular pay for the first week:

Regular workweek: 40 hours

Hours worked in the first week: 47 hours

Overtime hours: 47 - 40 = 7 hours

Regular pay for the first week: 40 hours * $13.66/hour = $546.40

Overtime pay for the first week: 7 hours * $13.66/hour * 1.5 = $143.71

Total earnings for the first week: $546.40 + $143.71 = $690.11

Regular pay for the second week:

Regular workweek: 40 hours

Hours worked in the second week: 42 hours

Overtime hours: 42 - 40 = 2 hours

Regular pay for the second week: 40 hours * $13.66/hour = $546.40

Overtime pay for the second week: 2 hours * $13.66/hour * 1.5 = $41.04

Total earnings for the second week: $546.40 + $41.04 = $587.44

Total biweekly earnings: $690.11 + $587.44 = $1277.55

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Answer:

46 degrees

Step-by-step explanation:

if you look at it closely u can see that the 120 degrees is reflected to the opposite side so if the 120 degrees is reflected then the 46 degrees would be reflected too

Answer:

5

Step-by-step explanation:

Change in Y / Change in X = Slope

5/1 = 5

When sampling with replacement is used, an element that has already been chosen is put back into the sample frame and given the chance to be chosen again.

In the case of sampling without replacement, an element is eliminated from the sample frame after it has been chosen.

In this question, we are supposed to state the differences between sampling with replacement and sampling without replacement.

Generally speaking, sampling without replacement is more effective than producing representative samples using replacement sampling. It prevents the inclusion of the same population element in the sample several times.

By "drawing from a hat" or by using a computer program that simulates the same process, you select the sample at random using the lottery method.

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The length of the legs of the right triangle are 2.83 units.

A right tangle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the legs of the triangle can be found using trigonometric ratios.

Hence,

sin 45 = opposite / hypotenuse

sin 45 = a / 4

cross multiply

a = 4 × 0.70710678118

a = 2.83 units

Therefore,

cos 45 = b / 4

cross multiply

b = 0.70710678118 × 4

b = 2.82842712475

b = 2.83 units

Therefore, the legs are 2,83 units

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Answer:

Step-by-step explanation:

Her average speed for the first lap is 8m per second. Her speed for the second lap is about 7.6m per second. So her total time for the two laps is 1 minute and 42 seconds.

The total amount required to pay off the loan at the end of 8 years would be $37,784.09.

To calculate the total amount required to pay off a loan of $16,000 with an interest rate of 14% per annum compounded half-yearly over 8 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the total amount, P is the principal (or loan amount), r is the interest rate per annum, n is the number of times the interest is compounded per year, and t is the time period in years.

In this case, P = $16,000, r = 14%, n = 2 (since the interest is compounded half-yearly), and t = 8 years.

Plugging in the values, we get:

A = $16,000(1 + 0.14/2)^(2*8)

= $37,784.09

Therefore, the total amount required to pay off the loan at the end of 8 years would be $37,784.09, including the principal amount of $16,000 and the accumulated interest.

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Answer:mhmm cool b

Step-by-step explanation:

Answer:

(0,0) represents the cost of 0 bags of candy.

where (1,2) tells us that 1 bag of candy costs $2....(2,4) and 2 bags of candy costs $4.....(3,6) and 3 bags of candy cost $6

Step-by-step explanation:

Answer:

The top right net would

Hope this helps!

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

The net in option A represents the rectangular prism.

Option A is the correct answer.

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

The rectangular prism has 6 faces.

The net in option A represents the rectangular prism.

Thus,

The net in option A represents the rectangular prism.

Option A is the correct answer.

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Answer:

its e

Step-by-step explanation:

(a) To calculate the permeate composition, yp, we can use the formula:

yp = (P * x * (Ph - p₁) * t * 0) / (q * (Ph - p₁) + P * x * t * 0)

Given:

x = 0.5 (mole fraction of gas A)

Ph = 80 cm Hg (feed-side pressure)

p₁ = 20 cm Hg (permeate-side pressure)

P = 400 x 10^(-10) cm³(STP) cm/(s cm² cm Hg) (permeability)

t = 2 x 10³ cm (membrane thickness)

0 = 0.25 (fraction of feed permeated)

q = feed flow rate (to be determined)

Substituting the given values into the formula:

yp = (400 x 10^(-10) * 0.5 * (80 - 20) * 2 x 10³ * 0) / (q * (80 - 20) + 400 x 10^(-10) * 0.5 * 2 x 10³ * 0)

Since 0 * anything equals zero, we can simplify the formula to:

yp = 0

Therefore, the permeate composition, yp, is zero.

(b) To calculate the reject composition, xo, we can use the formula:

xo = 1 - yp

Since we found in part (a) that yp = 0, we can conclude that:

xo = 1 - 0

xo = 1

Therefore, the reject composition, xo, is 1.

(c) To calculate the feed flow rate, q, we can rearrange the formula from part (a) and solve for q:

q = (P * x * (Ph - p₁) * t * 0) / (yp * (Ph - p₁) + P * x * t * 0)

Substituting the given values into the formula:

q = (400 x 10^(-10) * 0.5 * (80 - 20) * 2 x 10³ * 0) / (0 * (80 - 20) + 400 x 10^(-10) * 0.5 * 2 x 10³ * 0)

Again, since 0 * anything equals zero, we can simplify the formula to:

q = 0

Therefore, the feed flow rate, q, is zero.

In conclusion:

(a) The permeate composition, yp, is zero.

(b) The reject composition, xo, is 1.

(c) The feed flow rate, q, is zero.

Please note that the calculations resulted in a feed flow rate of zero, which may suggest an inconsistency in the given values or equations. Double-checking the values and equations is recommended to ensure accuracy.

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Answer:

10 x^3 - x^2 - 29 x - 30 = (10 x + 9)(x^2 - x - 2) + -12

Step-by-step explanation:

Compute (10 x^3 - x^2 - 29 x - 30) ÷ (x^2 - x - 2) using polynomial long division:

x^2 - x - 2 | 10 x^3 | - | x^2 | - | 29 x | - | 30

To eliminate the leading term of the numerator, 10 x^3, multiply x^2 - x - 2 by 10 x to get 10 x^3 - 10 x^2 - 20 x. Write 10 x on top of the division bracket and subtract 10 x^3 - 10 x^2 - 20 x from 10 x^3 - x^2 - 29 x - 30 to get 9 x^2 - 9 x - 30:

| | | | | 10 x | |

x^2 - x - 2 | 10 x^3 | - | x^2 | - | 29 x | - | 30

| -(10 x^3 | - | 10 x^2 | - | 20 x) | |

| | | 9 x^2 | - | 9 x | - | 30

To eliminate the leading term of the remainder of the previous step, 9 x^2, multiply x^2 - x - 2 by 9 to get 9 x^2 - 9 x - 18. Write 9 on top of the division bracket and subtract 9 x^2 - 9 x - 18 from 9 x^2 - 9 x - 30 to get -12:

| | | | | 10 x | + | 9

x^2 - x - 2 | 10 x^3 | - | x^2 | - | 29 x | - | 30

| -(10 x^3 | - | 10 x^2 | - | 20 x) | |

| | | 9 x^2 | - | 9 x | - | 30

| | | -(9 x^2 | - | 9 x | - | 18)

| | | | | | | -12

The quotient of (10 x^3 - x^2 - 29 x - 30)/(x^2 - x - 2) is the sum of the terms on top of the division bracket. The remainder is the expression that remains after the final subtraction step.

| | | | | 10 x | + | 9 | (quotient)

x^2 - x - 2 | 10 x^3 | - | x^2 | - | 29 x | - | 30 |

| -(10 x^3 | - | 10 x^2 | - | 20 x) | | |

| | | 9 x^2 | - | 9 x | - | 30 |

| | | -(9 x^2 | - | 9 x | - | 18) |

| | | | | | | -12 | (remainder) invisible comma

(10 x^3 - x^2 - 29 x - 30)/(x^2 - x - 2) = (10 x + 9) - 12/(x^2 - x - 2)

Write the result in quotient and remainder form:

Answer: 10 x^3 - x^2 - 29 x - 30 = (10 x + 9)(x^2 - x - 2) + -12

In both cases, pumping s leads to a string that does not follow the pattern defined by L2. Therefore, L2 cannot be regular.

To prove that a language is not regular, we can use the pumping lemma for regular languages.

1. The language L = {\(a^2n b^n : n ≥ 1\)}.

To prove that L is not regular, we assume that L is regular and apply the pumping lemma. Let p be the pumping length given by the pumping lemma.

We choose the string s = \(a^2p b^p\). According to the pumping lemma, s can be divided into three parts, s = xyz, such that:

1) |xy| ≤ p,

2) |y| > 0, and

3) for all i ≥ 0, \(xy^iz\) ∈ L.

Now, consider pumping up by setting i = 2. The resulting string \(xy^2z\) will have more a's than b's, violating the condition that the number of a's should be twice the number of b's. Therefore, the string \(xy^2z\) is not in L, contradicting the pumping lemma. This implies that L is not regular.

2. The language L = {y_i : i ≥ 0}, where y_0 = ϵ, y_i = y_i−1 \(a^i\) if i is an odd positive integer, and y_i = y_i−1 \(b^i\) if i is an even positive integer. To prove that L is not regular, we again assume that L is regular and use the pumping lemma.

Let p be the pumping length given by the pumping lemma. We choose the string s = y_p, which is \(y_p = y_p−1 a^p\) if p is odd, and y_p = \(y_p−1 b^p\) if p is even.

Now, consider pumping up by setting i = 2. The resulting string \(y_p^2\) will have more a's or more b's than the original string y_p, depending on whether p is odd or even.

This violates the condition that the number of a's and b's should be equal in each string y_i. Therefore, the string \(y_p^2\) is not in L, contradicting the pumping lemma. This implies that L is not regular.

In both cases, we have shown that the given languages cannot be regular by using the pumping lemma. Therefore, the first language L = {\(a^2n b^n\) : n ≥ 1} and the second language L = {y_i : i ≥ 0} are not regular.

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Answer:

equation is 2x - 18 = 81

Step-by-step explanation:

(x - 9)2 = 81

(2x - 18) = 81

taking the square root of both sides

\((\sqrt{2x - 18} ) = \sqrt{81}\)

\((\sqrt{2x - 18})^2 = 81\)

2x - 18 = 81

2x = 81 + 18

2x = 99

x = 99/2

x = 49.5

If the value of x was 40, then it would make the equation true.

\(x = 40\)

____________________________________________________

To solve for x, we need to simplify both sides of the equation, then isolate the variable. In this case, the x variable being 40.

Hope this helps!

9514 1404 393

Answer:

  XL = 13 cm, m∠L = 29°

  AC = 21 cm, m∠C = 29°

  PC = 13 cm, m∠Y = ??  (there is no angle Y in the figure)

Step-by-step explanation:

The figure on the right shows the triangles are isosceles, with XL = XN. That means also PA = PC. Those side lengths are all the same: 13 cm.

  PA = PC = XL = XN = 13 cm

In the same fashion, ...

  LN = AC = 21 cm

__

Of course, the angles have a similar relationship:

  ∠A = ∠C = ∠L = ∠N = 29°

The two base angles in the triangle add to 58°, so the third angle is ...

  180° -58° = 122°

  ∠P =∠X = 122°

_____

Additional comment

As is often the case in over-specified problems, the numbers shown are not consistent The attached figures show the length LN is actually incorrect for the angle and side specified for triangle ACP, or the angles are incorrect for the side lengths specified. What this means is that the answers you get will depend on how you work the problem. Above, we have taken the given numbers and relationships at face value, even though we know they are incorrect.

The minimum length of the third side must be greater than 16 feet.

The minimum length of the third side can be determined using the Triangle inequality theorem. This theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. The Triangle Inequality Theorem can be expressed by the following inequality: a + b > c, where a, b, and c are the lengths of the three sides of the triangle. In this case, we have two sides of 4 feet and 12 feet, so the inequality can be written as 4 + 12 > c, which simplifies to 16 > c. Solving for c yields c > 16, which means that the minimum length of the third side must be greater than 16 feet.

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Answer: 28/42 as a fraction simplified is 2/3

Hope this helped

When Tracey pours all the water from the smaller 5-inch cube container into the larger 7-inch cube container, the water will be approximately 7 inches deep in the larger container.

To find out how deep the water will be in the larger container, we need to consider the volume of water transferred from the smaller container. Since both containers are cube-shaped, the volume of each container is equal to the length of one side cubed.

The volume of the smaller container is 5 inches * 5 inches * 5 inches = 125 cubic inches.

When Tracey pours all the water from the smaller container into the larger container, the water completely fills the larger container. The volume of the larger container is 7 inches * 7 inches * 7 inches = 343 cubic inches.

Since the water fills the larger container completely, the depth of the water in the larger container will be equal to the height of the larger container. Since all sides of the larger container have the same length, the height of the larger container is 7 inches.

Therefore, the water will be approximately 7 inches deep in the larger container.

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Answer:

0 years: $0

5 years: $460

10 years: $520

15 years: $580

20 years: $640

Step-by-step explanation:

The results from the observational study can only be classified as correlational or associative, but not causal.

This is because an observational study does not have the same level of control over variables as a double-blind experiment, making it difficult to establish a cause-and-effect relationship between the variables being studied. A double-blind experiment, on the other hand, allows for more rigorous control over variables and can establish a causal relationship between them. Therefore, the results from the observational study should be interpreted with caution and may require further investigation using a double-blind experiment to confirm any causal relationship.

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The definition of slope-intercept form y=mx+b is given below.

A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.

In geometry, there are two types of lines: straight and curved. Vertical and horizontal straight lines are further divided into categories. Parallel, intersecting, and perpendicular lines are further types of lines.

In the given question:-

The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope may be determined using a variety of approaches.

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Answer: 9,030$

8400 * 0.075 = 630

630 + 8400 = 9030$

Answer: $630 increase, $9030 in total

Step-by-step explanation: Using the formula Prt (Principal x Rate x Time)

Scott started with 8400 and %7.5 rate and 1 year, so (8400)(0.075)(1) = $630 in interest and 8400 + 630 = $9030 in Scott's account.

It is established that P → (Q ∧ R) is logically equivalent to (-P ∨ Q) ∧ (-P ∨ R) using the truth table.

To establish the logical equivalence between P → (Q ∧ R) and (-P ∨ Q) ∧ (-P ∨ R), we can use a truth table. Let's construct a truth table that includes all possible truth value combinations for the variables P, Q, and R, and evaluate the given expressions for each combination.

By comparing the truth values in the last two columns, we can see that for every combination of truth values, P → (Q ∧ R) and (-P ∨ Q) ∧ (-P ∨ R) have the same truth value. In other words, the two expressions are logically equivalent.

Therefore, we have established that P → (Q ∧ R) is logically equivalent to (-P ∨ Q) ∧ (-P ∨ R) using the truth table.

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