all values of x
5 ( x + 10 )^2 − 30 = − 5
Plzzzz

The temperature of the sample of methane gas is 62.28°C

Mass of methane gas, CH4(g) = 45.63 g

Pressure, P = 1.24 atm

Volume, V = 34.16 L

We are supposed to calculate the temperature (in °C) of the sample of methane gas.

As per the Ideal Gas Law, PV = nRT

where P = Pressure of the gas

V = Volume of the gas

n = number of moles of the gas

R = Universal Gas Constant

T = Temperature of the gas

Given the mass of the gas and its molecular weight, we can calculate the number of moles as:

n = mass/molecular weight

Molecular weight of methane gas = 16.05 g/mol

So, the number of moles, n = 45.63/16.05 = 2.842 mol

Now, we can rearrange the Ideal Gas Law to get: T = PV/nR

Putting the given values in the above equation:

T = (1.24 atm) x (34.16 L) / (2.842 mol x 0.08206 L atm K⁻¹ mol⁻¹)T = 335.43 K

Convert to °C by subtracting 273.15°Celsius temperature = 335.43 K - 273.15 = 62.28°C

Therefore, the temperature of the sample of methane gas is 62.28°C.

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The new dimensions of the poster will be 5 in by 6 in.

In mathematics, scaling is the process of adjusting a geometric form or figure's size by a predetermined factor or ratio. With scaling, a shape's dimensions are all multiplied by the same quantity. Depending on whether the scaling factor is more than 1 or less than 1, respectively, scaling can either make the form larger or smaller. In addition to science, engineering, and computer graphics, scaling is frequently utilised in trigonometry, geometry, and other areas of mathematics.

Given that the scale factor = 1/3.

Thus, the new dimensions are:

New length = 15 in x (1/3) = 5 in

New width = 18 in x (1/3) = 6 in

Hence, the new dimensions of the poster will be 5 in by 6 in.

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The maximum value of the function is approximately 1.724 and the minimum value is approximately -1.724.

To find the maximum and minimum values of the function y = sin x + sin 2x, we can first take its derivative with respect to x:

y' = cos x + 2 cos 2x

Then, we can set y' equal to zero and solve for x:

cos x + 2 cos 2x = 0

We can use a graphing calculator to find the solutions to this equation, which are approximately x = 0.285 and x = 2.857. We can then evaluate the original function at these values to find the maximum and minimum values:

y(0.285) ≈ 1.724

y(2.857) ≈ -1.724

Therefore, the maximum value of the function is approximately 1.724 and the minimum value is approximately -1.724.

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Answer:

Step-by-step explanation:

perimeter P = 2L + 2W

where

Perimeter P = 56 m

Width W = L - 8 m

find:

length L

width W

solution:

just plugin the values into the formula:

P = 2L + 2W

56 = 2L + 2(L - 8)

56 = 2L + 2L - 16

56 + 16 = 4L

L = 72/4

L = 18 m

solve for W:

substitute L=18 back into the equation W=L-8

W = 18 - 8

W = 10 m

therefore:

length L = 18 m

Width W = 10 m

proof:

56 = 2(18) + 2(10)

56 = 36 + 20

56 = 56 ----- OK

Answer:

The family will save $896 on airfare by vacationing to Vancouver

Step-by-step explanation:

Tickets to Fairbanks - $958 each (4 total people)

Total cost - 958 times 4 = $3832

Tickets to Vancouver - $734 each (4 total people)

Total cost - 734 times 4 = $2936

$3832 - $2936 = $896

The future value of Tran Lee's savings after five years would be approximately $14,995.49.

To calculate the future value of Tran Lee's savings, we can use the formula for the future value of an ordinary annuity:

Future Value = Payment * [(1 + Interest Rate)^Number of Periods - 1] / Interest Rate

Given:

Payment (PMT) = $2,900 per year

Interest Rate (r) = 5% = 0.05 (decimal form)

Number of Periods (n) = 5 years

Substitute  these values into the formula, we get:

Future Value = $2,900 * [(1 + 0.05)^5 - 1] / 0.05

Calculating this expression, we find:

Future Value ≈ $14,995.49

Therefore, the future value of Tran Lee's savings after five years would be approximately $14,995.49.

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The future value of Tran Lee's savings after five years would be approximately $14,995.49.

To calculate the future value of Tran Lee's savings, we can use the formula for the future value of an ordinary annuity:

Future Value = Payment * [(1 + Interest Rate)^Number of Periods - 1] / Interest Rate

Given:

Payment (PMT) = $2,900 per year

Interest Rate (r) = 5% = 0.05 (decimal form)

Number of Periods (n) = 5 years

Substitute  these values into the formula, we get:

Future Value = $2,900 * [(1 + 0.05)^5 - 1] / 0.05

Calculating this expression, we find:

Future Value ≈ $14,995.49

Therefore, the future value of Tran Lee's savings after five years would be approximately $14,995.49.

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Answer:

186- none of those answers are correct, the right answer is one hundred eighty six miles

Step-by-step explanation:

623

-437

____

186

Answer:

The difference in the number of miles run by Kiki during practice is 186 miles.

Step-by-step explanation:

Given that Kiki runs 437 miles during the first week of track practice and she runs 623 miles during the second week of track practice.

The difference in miles will be:

= 623 - 437 = 186 miles.

81.3 marks is obtained by the student in psycology course

percentage of marks of  test that count for final marks =45 %

percentage of marks of quizzes that count for final marks =35 %

percentage of marks of papers that count for final marks =10 %

percentage of marks of final project that count for final marks =10 %

marks obtained by student in test = 75

marks obtained by student in quizzes = 85

marks obtained by student in papers =  88

marks obtained by student in final project = 90

Total marks obtained = \(\frac{45}{100} * 75 + \frac{35}{100} *85 + \frac{10}{100} * 88 +\frac{10}{100} *90\)

Total marks obtained = 33.75 + 29.75 + 8.8 + 9 = 81.3

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(A) The above linear system's least squares solutions are x₁  = 1/7 and x₂ = 22/21.

(b) [-3/7, 11/21, -22/21] is the least squares error vector, and the least squares error is roughly 0.8571.

We can express the linear system in matrix form to get the least squares solutions:

A * X = B

Where X is the column vector of variables (x₁ and x₂), A is the coefficient matrix, and B is the column vector of constants.

The following is a rewrite of the provided linear system:

| 3 -1 | | x1 | | 4 |

| 1 -2 | * | x2 | = | 3 |

| 2 3 | | 2 |

Finding X that minimizes the error (residuals) between A * X and B is required in order to get the least squares solution (a). The standard equation can be solved to obtain the least squares answer:

A^T * A * X = A^T * B

Where A^T is the transpose of matrix A.

First, let's calculate A^T * A:

= | 3 1 2 | | 3 -1 | | 33 + 11 + 22 3(-1) + 1*(-2) + 2*3 |

= | 1 -2 |

= | 2 3 |

= | 14 -4 |

= | -4 14 |

Next, let's calculate A^T * B:

= | 3 1 2 | | 4 |

= | 3 |

= | 2 |

= | 17 |

= | 7 |

Let's now resolve the standard equation:

| 14 -4 | | x1 | | 17 |

| -4 14 | * | x2 | = | 7 |

Simplifying, we have:

14×1 - 4×2 = 17

-4×1 + 14×2 = 7

Solving this system of equations, we find:

x1 = 1

x2 = 2

So, the least squares solution of the given linear system is x1 = 1 and x2 = 2.

Consequently, x1 = 1 and x2 = 2 are the least squares solutions for the given linear system.

(b) We may determine the residuals by deducting A * X from B in order to obtain the least squares error vector and least squares error:

Residuals = B - A * X

Substituting the values, we have:

| 4 | | 3 -1 | | 1 |

| 3 | - | 1 -2 | * | 2 |

| 2 | | 2 3 | |

| 4 | | 3 - (-1) | | 1 | | 5 |

| 3 | - | 1 - (-2) | * | 2 | = | 2 |

| 2 | | 2 - 3 | | -1 |

The least squares error vector is therefore [5, 2, -1].

The norm (magnitude) of the least squares error vector can be used to determine the least squares error:

Least squares error = ||Residuals||

We obtain the following by applying the Euclidean norm (2-norm): Least Squares Error = (5 + 2 + (-1) + 2) = (25 + 4 + 1) = 30.

As a result, the least squares error is roughly 30.

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The sum of the arithmetic series in this problem is given as follows:

S = -112.

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

The nth term of an arithmetic sequence is given by the explicit formula presented as follows:

\(a_n = a_1 + (n - 1)d\)

In which \(a_1\) is the first term of the arithmetic sequence.

The sum of the first n terms is given by the equation presented as follows:

\(S_n = \frac{n(a_1 + a_n)}{2}\)

The rule for this problem is given as follows:

\(a_n = 4 - 4n\)

The first and the last term are given as follows:

Hence the sum of the eight terms is given as follows:

S = 8 x (0 - 28)/2

S = -112.

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(a) The total amount of the nurse's annual salary that is not taxed is $6644. (b) His annual taxable salary is $22,226.8. (c) The tax he pays annually is $5856.7.

(a) To find the total amount of the nurse's annual salary that is not taxed, we need to add up all of the non-taxable allowances:

$37 x 12 (months) = $444 for national insurance

$3000 for personal allowance

$1800 for his wife

$1400 for his children

Total non-taxable allowances = $444 + $3000 + $1800 + $1400 = $6644

Therefore, the nurse's total non-taxable salary is $6644.

(b) To find the nurse's annual taxable salary, we need to subtract his non-taxable allowances from his gross salary:

Annual taxable salary = $29,460 - 2% x $29,460 - $6644

Annual taxable salary = $29,460 - $589.2 - $6644

Annual taxable salary = $22,226.8

Therefore, the nurse's annual taxable salary is $22,226.8.

(c) To calculate the nurse's annual tax, we need to apply the income tax rates:

Tax on first $4000 at 20% = $800

Tax on remainder at 25% = 0.25 x ($22,226.8 - $4000) = $5056.7

Total annual tax = $800 + $5056.7 = $5856.7

Therefore, the nurse pays an annual tax of $5856.7.

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Complete question is attached below

Step-by-step explanation:

15×2.25

pounds sold = 33.75

The value of the probability of choosing a green lollipop and a purple lollipop is, 8 / 45

We have to given that;

One bag contains 3 red lollipops and 2 green lollipops.

And, The other bag contains four purple lollipops and five blue lollipops.

Hence, The probability of choosing a green lollipop is,

P₁ = 2 / 5

And, The probability of choosing a purple lollipop is,

P₂ = 4 / 9

Thus, The value of the probability of choosing a green lollipop and a purple lollipop is,

P = P₁ ×  P₂

P = 2/5 × 4/9

P = 8/45

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So we got to evaluate:

To calculate this multiplication, we can first consider the numbers without the decimal digits:

Doing this multiplication, we got to:

Now, we count how many decimal places there ir in the initial numbers. We have 3 decimal places in 27.345 and also 3 decimal places in 4.335.

So we have a total of 6 decimal places. To get the result, we put the 6 rightmost digits in decimal places, so we get:

That is the result.

One way of checking it is by firts adding the digits of each number.

So we have 27345, the digits add to:

Since we still have 2 digits, we add them up:

Now, we do the same for 4335:

Now, we multiply this reduced numbers, 3 and 6:

And reduce it:

To check the result, 118540575, we do the same with it and compare:

So we also got to 9. This way, the result is probably right. This is a way of checking the result of a multiplication.

Answer:

they got -21 when they were supposted to get +21

and they also got +6x when they were supposted to get -6x

Step-by-step explanation:

that's because -3 and 2x are multiplied together and when you are multiplying negative and positive number you need to get negative result.

when you are multiplying negative with negative number, you will get positive number.

Answer:

d

Step-by-step explanation:

to find a discount you would multiply 50(0.20) whatever amount you get you would subtract that from 50

this is the same as 50(0.80)

In the collection, there are 11 nickels and 23 dimes. If each nickel is replaced with a quarter, the value of the collection becomes $5.05. So, C is correct. By writing them in the system of equations, we get the required value.

The given units are nickels, dimes, and quarters. Their conversion into dollars is as follows:

1 nickel = $0.05

1 dime = $0.10

1 quarter = $0.25

Given a collection of nickels and dimes is worth $2.85.

And there are 34 coins in the collection.

So, consider the number of nickel coins = n and the number of dime coins = d.

Then, the equation for the given collection is

n + d = 34...(1)

0.05n + 0.10d = 2.85...(2)

On simplifying (2), we get

5n + 10d = 2.85 × 100

⇒ 5n + 10d = 285

From (1), n = 34 - d, we get

5(34 - d) + 10d = 285

⇒ 170 - 5d + 10d = 285

⇒ 5d = 285 - 170 = 115

∴ d = 115/5 = 23

Thus, the number of dime coins is 23.

So, from (1), we get n + 23 = 34 ⇒ n = 34 - 23 = 11

∴ n = 11

Thus, the number of nickel coins is 11.

If each nickel coin in the collection is replaced with a quarter, then the value of the collection is

q + d = 34 and 0.25q + 0.10d = Y

Here q = 11; d = 23

So, we get

0.25(11) + 0.10(23) = Y

⇒ 2.75 + 2.3 = Y

⇒ 5.05 = Y

∴ Y = $5.05

The value of the new collection becomes $5.05.

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B. The statement is false. The transpose of the product of two matrices is the product of the transposes of the individual matrices in reverse order, or (AB)^T=B^TA^T.

Justification:
1. Let A and B be arbitrary matrices for which the product AB is defined.
2. To find the transpose of the product (AB)^T, we need to first understand the properties of transposes.
3. According to the property of transposes, (AB)^T is equal to the product of the transposes of the individual matrices in reverse order.
4. So, (AB)^T = B^TA^T, which contradicts the statement (AB)^T = A^TB^T.

Hence, the correct answer is option B.

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Each statement about integer is:

Statement A: If positive is subtracted from a negative integer, the difference is negative integer.

This statement is sometimes true.

If a positive integer is subtracted from a negative integer, the difference can be a negative integer or a positive integer. For example, if -5 is subtracted from -3, the difference is -8, which is a negative integer. However, if -3 is subtracted from -5, the difference is 2, which is a positive integer. The difference sign depends on which value is the bigger one.

Statement B: If a positive integer is subtracted from a positive integer, the difference is a positive integer.

This statement is sometimes true.

If a positive integer is subtracted from a positive integer, the difference can be a positive integer or a negative integer. For example, if 3 is subtracted from 5, the difference is 2, which is a positive integer. However, if 5 is subtracted from 3, the difference is -2, which is a negative integer.

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The actual ground speed = 2856.19 mph

And direction of the plane = -37.452 degree.

In navigation the angle of the course (on a compass) is counted clockwise from the North

So, the direction to the North is 0 degree, to the East is 90 degree,

to the South is 180 degree and to the West is 270 degree.

The North on most maps is a vertically up direction.

Angles are measured anticlockwise from the positive direction of the horizontal X-axis (the East on most maps) in coordinate Geometry and Trigonometry, which we will utilise.

Let us perform a basic transformation into Trigonometric standard, with the direction to the East serving as an X-axis:

310 degree on a compass is 90 degree + (360 - 310) = 140 degree

Now, counterclockwise from the X-axis:

330 degree on a compass is 90 + (360 −290) = 160

counterclockwise from the X-axis.

This is a two-vector addition issue. The amplitude and angle of direction of each are used to characterize it:

airplane (vector A) has amplitude 330 mph and angle 140 degree;

wind (vector W ) has amplitude 40 (mph) and angle 290 degree.

To add these two vectors, we describe them as sums of their X and Y components:

AX = 330 cos(140 degree)

AY = 330 sin (140 degree)

WX = 40 cos ( 290 degree)

WY = 40 sin(290 degree)

Both X-components behave in the same direction, as do both Y-components. As a result, we can add X-components to obtain an X-component of the resulting movement, and we can add Y-components to obtain a Y-component of the resulting movement..

(A+W)X =A X + WX= 330 cos(140 degree)+40 cos ( 290 degree)

                               = -227.22

(A+W)Y = AY+WY= 330 sin (140 degree) + 40 sin(290 degree)

                            = 174.66

Knowing two components of the resulting vector of movement, we can simply calculate its amplitude |A+W| and direction (A+W):

|A+W| = √[(A+W)² of x +(A+W)² of y]

          = 2856.19

∠(A+W) = arctan [ (A+W)y/(A+W)x]

            = arctan[-0.766]

            = -37.452 degree.

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Answer:

i think it's 100+y²

Step-by-step explanation:

look at the picture

Answer:

Distribute 2 to (x + 6) and 3 to (x – 4).

Step-by-step explanation:

While solving for:

2(x+6) = 3(x-4) + 5

Firstly, we need to open the parenthesis. For this, we've to distribute 2 to (x+6) and 3 to (x-4).

\(\rule[225]{225}{2}\)

Hope this helped!

To determine if a function has a vertical asymptote, you need to consider its behavior as the input approaches certain values.

A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. Here's how you can determine if a function has a vertical asymptote:

Check for restrictions in the domain: Look for values of the input variable where the function is undefined or has a division by zero. These can indicate potential vertical asymptotes.

Evaluate the limit as the input approaches the suspected values: Calculate the limit of the function as the input approaches the suspected values from both sides (approaching from the left and right). If the limit approaches positive or negative infinity, a vertical asymptote exists at that value.

For example, if a rational function has a denominator that becomes zero at a certain value, such as x = 2, evaluate the limits of the function as x approaches 2 from the left and right. If the limits are positive or negative infinity, then there is a vertical asymptote at x = 2.

In summary, to determine if a function has a vertical asymptote, check for restrictions in the domain and evaluate the limits as the input approaches suspected values. If the limits approach positive or negative infinity, there is a vertical asymptote at that value.

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i hope this helps! let me know if i got it wrong

Anton needs 3.75 lbs of sugar and 1.25 lbs of water to make 5 lbs of 75% sugar syrup.

To make a 75% sugar syrup, Anton will need 75% sugar and 25% water by weight. To find out how much sugar and how much water he needs, we can use the following formulas:

Sugar weight = 5lbs x 75% = 3.75lbs

Water weight = 5lbs x 25% = 1.25lbs

So Anton needs 3.75 lbs of sugar and 1.25 lbs of water to make 5 lbs of 75% sugar syrup.

It's important to note that syrup with 75% sugar content is heavy syrup, it is mostly used for preservation and not as a sweetener.

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Answer:

227 sides

Step-by-step explanation:

The sum of the interior angles of a convex polygon is S=180(n-2) where n is the number of sides. If S=40500, then we have our equation 40500=180(n-2) and we can solve for n:

40500 = 180(n-2)

225 = n-2

227 = n

Therefore, the number of sides in the regular polygon is 227.

Answer: He bought 20 ice cream bars and 14 popsicle

Step-by-step explanation:

To solve this I used the elimination method, you could use substitution as well

Here are our two equations

x+y=34 Because the total number of ice creams bought must be given to 34 children and no more

2x+5y=128 because that is the cost for each ice cream and the amount he spent

For the elimination method we have to cancel out one of the variables, I decided to cancel out the x, so I multiplied the top equation by -2. So i got -2x-2y=-68

2x+5y=128 Then we get

3y=60 so

y=20

Now we can go back to the first equation and plug in y.

x+20=34

  -20  -20

x=14

So he bought 14 popsicles and 20 ice cream bars.

The interval of continuity of the function is continuous given y = 2 (x + 4 ) 2 + 8 is (-∞, ∞).

A function is continuous at a point if the function value exists and is finite at that point, and the limit of the function as the input approaches that point from the left and right side is equal to the function value at that point. In other words, the function has no sudden jumps or discontinuities at that point.

In the case of the function y = 2(x + 4)² + 8, the function is defined and continuous for all real numbers x. There are no values of x for which the function is undefined or has a discontinuity, so the function is continuous for all values of x, meaning that the interval of continuity is (-∞, ∞).

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The binomial coefficient has several applications in combinatorics, probability theory, and algebra. The coefficient of x¹⁴y⁴ in the expansion of (x + y)¹⁸ is 3060.

The binomial coefficient, also known as a combination or choose symbol, is a mathematical function denoted by "n choose k" or written as "(nCk)" or "C(n, k)". It represents the number of ways to choose k elements from a set of n distinct elements without regard to their order. The binomial coefficient is defined using factorials and can be calculated using the following formula:

C(n, k) = n! / (k!(n-k)!)

Where:

n is a non-negative integer representing the total number of elements in the set.

k is a non-negative integer representing the number of elements to be chosen from the set.

n! (n factorial) is the product of all positive integers less than or equal to n.

It is commonly used in counting problems, such as determining the number of combinations, permutations, or possibilities in various situations. It also appears in the expansion of binomial expressions, binomial probability distributions, and the binomial theorem.

The coefficient of x¹⁴y⁴ in the expansion of (x + y)¹⁸ can be determined using the binomial theorem. The binomial theorem states that for any two numbers a and b, and any positive integer n, the coefficient of x^(n-k)yk in the expansion of (a + b)n is given by the formula:

C(n,k) * a(n-k) * bk

Where C(n,k) represents the binomial coefficient, which is the number of ways to choose k items from a set of n items. It can be calculated using the formula:

C(n,k) = n! / (k!(n-k)!)

In this case, a = x, b = y, n = 18, and k = 4. Let's calculate the coefficient step by step:

1. Calculate the binomial coefficient:
C(18,4) = 18! / (4!(18-4)!) = 18! / (4!14!) = (18*17*16*15) / (4*3*2*1) = 3060

2. Calculate the powers of a and b:
a(n-k) = x¹⁸⁻⁴ = x¹⁴
bk = y⁴

3. Multiply the binomial coefficient and the powers of a and b:
Coefficient = C(18,4) * a(n-k) * bk = 3060 * x¹⁴ * y⁴

Therefore, the coefficient of x¹⁴y⁴ in the expansion of (x + y)¹⁸ is 3060.

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