the side of a triangle blowers extended a form and exterior angle of 144 degrees. find a value of x

Answer:

\(9 \sqrt{2} \)

Step-by-step explanation:

\(3 \sqrt{6} \times \sqrt{3} \\ 3 \times \sqrt{2} \sqrt{3} \times \sqrt{3} \\ 3 \times 3 \sqrt{2} \\ 9 \sqrt{2} \)

The total amount of money Mark earns after taxes have been deducted,

during a 4-week period is  $1256.

The first step is to detemine his total earnings in 4 weeks:

Total earnings = 4 (earnings per hour x total hour worked per week)

4 x 8.75 x 40 = $1400

The second step is to determine the total taxes for 4 weeks

4 x 36 = $144

Now subtract $144 from $1400

$1400-  $144 = $1256

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Answer:

Ali has 1528. She has 1146 more cards than Max. In total, there are 1910 cards.

Step-by-step explanation:

382 x 4 = 1528

1528 - 382 = 1146

1528 + 382 = 1910

Answer:

correct answer is snow in march

Answer:

32nd of March

Step-by-step explanation:

Maximum number of days to ever exist in March is 31. That will not change. The only changing month is February

Answer:

0.03

Step-by-step explanation:

Given the following :

Instructor __no of failure __prop (failure /100)

A ________ 13__________0.13

B ________0___________0

C________11___________0.11

D________16__________0.16

Prof. B adds no proportion to the data and hence excluded in the estimation.

Mean(m) = 0.13 + 0.11 + 0.16) / 3

= 0.4 / 3

= 0.1333

Standard deviation :

Σ(X - m)² / N - 1

Σ(0.13 - 0.1333)² + (0.11 × 0.1333)² + ( 0.16 - 0.1333)² = 0.0012668689

= 0.0012668689 / 2

= 0.00063343445

√0.00063343445

= 0.0251681

= 0.03 To 2 decimal places

Answer and Step-by-step explanation:

The Word form is:

Six hundred, seventy-two thousand, eight hundred and twenty nine.

The Expanded form is:

600,000 + 70,000 + 2,000 + 800 + 20 + 9

The Unit form is:

6 one hundred thousands, 7 ten thousands, 2 thousands, 8 hundreds, 2 tens and 9 ones.

#teamtrees #PAW (Plant And Water)

Step-by-step explanation:

Starting with the equation E = mgh, we can solve for h in terms of E, m, and g as follows:

E = mgh

Divide both sides by mg:

E/mg = h

Therefore, h = E/mg.

So the solution for h in terms of E, m, and g is h = E/mg.

Taking into account the scientific notation, the result of the sum is 2.56197×10¹⁹.

Scientific notation is a quick way to represent a number using powers of base ten.

The numbers are written as a product:

a×10ⁿ

where:

You want to add the following two numbers in scientific notation:

When the numbers to be added do not have the same base 10 exponent, the base 10 power with the highest exponent must be found. In this case, the highest exponent is 19.

Then all the values ​​are expressed as a function of the base 10 exponent with the highest exponent. In this case: 3.197×10¹⁷= 0.03197×10¹⁹

Taking the quantities to the same exponent, all you have to do is add what was previously called the number "a". In this case:

2.53×10¹⁹ + 0.03197×10¹⁹= (2.53 + 0.03197)×10¹⁹= 2.56197×10¹⁹

Finally, the result of the sum is 2.56197×10¹⁹.

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The domain of the function f(x) = -3x + 2 is (-∞, +∞), representing all real numbers, and the range is (-∞, 2], representing all real numbers less than or equal to 2.

The function f(x) = -3x + 2 is a linear function defined by a straight line. To determine the domain of this function, we need to identify the range of values for which the function is defined.

The domain of a linear function is typically all real numbers unless there are any restrictions. In this case, there is no explicit restriction mentioned, so we can assume that the function is defined for all real numbers.

Therefore, the domain of the function f(x) = -3x + 2 is (-∞, +∞), which represents all real numbers.

Now, let's analyze the range of the function. The range of a linear function can be determined by observing the slope of the line. In this case, the slope of the line is -3, which means that as x increases, the function values will decrease.

Since the slope is negative, the range of the function f(x) = -3x + 2 will be all real numbers less than or equal to the y-intercept, which is 2.

Therefore, the range of the function is (-∞, 2] since the function values cannot exceed 2.

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Answer:

Bargain Busters shop sells the cheapest soup

Step-by-step explanation:

Bargain Busters sell 4 cans of soup for £3.76

Bargain Busters sell 1 cans of soup for

3.76÷4

=0.94

cost cutters sell 3 cans of soup for £2.85

cost cutters sell 1 cans of soup for 2.85÷3

=0.95

so

Bargain Busters<cost cutters

0.94<0.95

therefore

Bargain Busters shop sells the cheapest soup

True

One from of the linear function is Y =  mx + b where b is the y intercept.

The y intercept is where x is 0 so it would be at (0,6)

The statement that "σ(n) < 2n holds true for all n of the form n = p²" has been proved.

Let p be any prime number, and let σ(n) be the sum of all positive divisors of the integer n.

As p is a prime number, and 2 is the smallest prime number, so, p\(\geq\)2

So, the positive divisors of the integer n are: 1,p,p².

As σ(n) represents the sum of all positive divisors of the integer n.

σ(n)=1+p+p²

In order to prove that σ(n) < 2n,for all n of the form n = p².

1+p+p²<2p²

p²-p-1>0

It is know that, p\(\geq\)2.

So, p²-p-1\(\geq\)1

Thus, σ(n) < 2n holds true for all n of the form n = p².

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\(~~\text{L.H.S}\\\\=\dfrac{\sin x}{1-\cos x}\\\\\\=\dfrac{\sin x(1+ \cos x)}{(1 -\cos x)(1+ \cos x)}\\\\\\=\dfrac{\sin x + \sin x \cos x}{1- \cos^2 x}\\\\\\=\dfrac{\sin x+ \sin x \cos x}{\sin^2 x}\\\\\\=\dfrac{\sin x}{ \sin^2 x}+ \dfrac{\sin x \cos x}{ \sin^2 x}\\\\\\=\dfrac{1}{ \sin x} + \dfrac{\cos x}{ \sin x}\\\\\\=\csc x + \cot x\\\\\\=\text{R.H.S}\\\\\text{Proved.}\)

9514 1404 393

Answer:

Step-by-step explanation:

The order of operations tells you to evaluate parentheses first.

Step 1: simplify (12+1) and (4+15)

  39÷13 -2×19

Then it tells you to do multiplication and division, left to right.

Step 2: divide 39÷13

  3 -2×19

Step 3: multiply 2×19

  3 -38

Finally, addition and subtraction are done, left to right.

Step 4: subtract 38 from 3

  -35

Answer: C

Step-by-step explanation:

Answer:

The Answer Is B

Step-by-step explanation:

3, x, x+6 are the first 3 terms of G.P

common ratio is x/3=x+6/x

so we cross multiply x×x=3×x+6

ײ= 3x+18 so we have x²-3x-18

(x-6)(x+3)=0

the possible value of x are 6 and -3

b) tenth term of the seauence

first of all the possible sequence are 3, 6, 12 and 3, -3, 3

but we need only the positive GP

so the common ratio of.the GP r is 6/3=2

the 10th term of a GP sequence is ar^10-1=ar^9

where a = first time

3×2^9=3×512=1536

the 10th term is 1536

Answer: 18, 28, 38, 48, 58

Step-by-step explanation:

Answer:

18, 28, 38, 48, 58

Step-by-step explanation:

I think this is pretty self explanatory.

Answer:

(a) \(y = \frac{4}{x^2}\)

(b) \(x = \frac{2}{5}\)

Step-by-step explanation:

Given

Variation: Inverse proportional.

This is represented as:

\(y\ \alpha\ \frac{1}{x^2}\)

See attachment for table

Solving (a):

First convert variation to equation

\(y = k\frac{1}{x^2}\)

From the table:

\((x,y) = (1,4)\)

So, we have:

\(4 = k * \frac{1}{1^2}\)

\(4 = k * \frac{1}{1}\)

\(4 = k * 1\)

\(4 = k\)

\(k = 4\)

Substitute 4 for k in \(y = k\frac{1}{x^2}\)

\(y = 4 * \frac{1}{x^2}\)

\(y = \frac{4}{x^2}\)

Solving (b): x when y = 25.

Substitute 25 for y in \(y = \frac{4}{x^2}\)

\(25 = \frac{4}{x^2}\)

Cross Multiply

\(25 * x^2 = 4\)

Divide through by 25

\(x^2 = \frac{4}{25}\)

Take positive square roots of both sides

\(x = \sqrt{\frac{4}{25}\)

\(x = \frac{2}{5}\)

Answer:

To solve the linear programming problem, we need to first graph the feasible region determined by the constraints, and then evaluate the objective function at each corner point of the feasible region to find the maximum value of z.

Plotting the lines corresponding to the inequalities, we get:

Graph of the feasible region:

The feasible region is the shaded polygon in the graph. We can see that the vertices of the feasible region are (2, 9), (2, 12), (4, 7), and (8, 2).

Next, we evaluate the objective function at each of these vertices to find the maximum value of z.

At (2, 9): z = 7x + 2y = 7(2) + 2(9) = 23

At (2, 12): z = 7x + 2y = 7(2) + 2(12) = 31

At (4, 7): z = 7x + 2y = 7(4) + 2(7) = 35

At (8, 2): z = 7x + 2y = 7(8) + 2(2) = 58

Therefore, the maximum value of z is 58, which occurs at the point (8, 2).

Hence, the answer is: the maximum value of z is 58.

using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

(A) Between 1995 and 2003, there was a change at an annual rate of -0.1463

(B) Between 1995 and 2003, a change occurred at a rate of -14.63% per year.

(C) The automobile would be worth $5,844.24 in 2007.

Depreciation is an annual income tax deduction that enables you to recoup the purchase price or other basis of a specific item over the course of its use.

It is a provision for the property's normal wear and tear, degeneration, or obsolescence.

As the years pass, the car's value drops.

This process is known as depreciation.

Depreciation is the decrease in asset value brought on by normal wear and tear.

Use this formula to calculate the annual rate of change:

g = (FV/PV)¹⁾ⁿ - 1

Now, using the formula calculate as follows:

(11000/3900)¹⁾⁸ - 1

-0.1463 = -14.63%

The following formula can be used to estimate a car's worth in 7 years:

FV = P (1 + g)ⁿ

$39,000 x (1 - 0.1463)¹²

$39,000 x 0.8537¹² = $5,844.24

Therefore, (A) between 1995 and 2003, there was a change at an annual rate of -0.1463

(B) Between 1995 and 2003, a change occurred at a rate of -14.63% per year.

(C) The automobile would be worth $5,844.24 in 2007.

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Correct question:

A car was valued at $39,000 in the year 1995. The value depreciated to $11,000 by the year 2003.

A)What was the annual rate of change between 1995 and 2003? (Round to 4 decimal places)

B)What is the correct answer to part A written in percentage form?

C)Assume that the car value continues to drop by the same percentage. What will the value be in the year 2007?

The quadratic equation that describes the function is  

f(x) = x² + 4x + 1

A quadratic equation is a equation that is of the form -

y = f{x} = ax² + bx + c

Given is the table that describes the quadratic function h(x) as follows -

{x}                h{x}

−3               −2

−2               −3

−1                −2

0                  1

1                   6

2                  13

3                  22

The quadratic equation is of the form given -

y = ax² + bx + c

For the point (0, 1), we can write -

1 = c                                                      ..... Eq{1}

For the point (1, 6), we can write -

6 = a + b + 1

a + b = 5                                               ...... Eq{2}

For the point (2, 13), we can write -

13 = 4a + 2b + 1

4a + 2b = 12                                               ...... Eq{3}

From Eq{2}, we can write -

a = 5 - b

So, the equation 3 can be written as -

4(5 - b) + 2b = 12

20 - 4b + 2b = 12

20 - 2b = 12

2b = 8

b = 4                                    ...... Eq{4}

then

a = 1                                ...... Eq{5}

So, we can write the quadratic equation as -

f(x) = x² + 4x + 1

Therefore, the quadratic equation that describes the function is  

f(x) = x² + 4x + 1

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After simplifying an equation the value of x is x = 3.

What is solving an equation?

Unifying Principle for Equation Solving

By deleting parenthesis and grouping like terms, each side of the equation can be made simpler.

The variable term on one side of the equation can be separated using addition or subtraction.

To find the variable, use multiplication or division.

Consider, the given equation

     5(2x - 4) = 10

      10x - 20 = 10                                  Removing parenthesis

10x -20 + 20 = 10 + 20                         Adding 20 on both sides

              10x = 30                                 Simplifying

                  x = 3                                    Dividing both sides by 10

Hence, the value of x is, x = 3.

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Note: ^ is for Start of the line, $ is for end of the line ,* means 0 or more, + means 1 or more, [ab] means either a or b and {} is for specific number of times, () is for grouping.

A task in which it is necessary to create regular expressions to define five different languages. The alphabet used is A = {a, b}. The languages ​​are:

L1, which has exactly one "a" but any number of "bs".

L2, which has an odd number of "as" and an even number of "bs".

L3, which contains exactly two "as" or exactly two "bs", although not necessarily adjacent.

L4, which has all "bs" appearing before any "a" or all "as" appearing before any "b".

L5, where there can be any number of "as", but the number of "bs" must be even, although the "bs" need not be adjacent.

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The algebraic property illustrated is the commutative property of multiplication

The properties of algebra are those properties mostly used in simplifying algebraic expressions.

Algebraic properties are:

From the expression given we have

4/5 • 5/4 = 1

= 4/ 5 × 5/ 4

= 1

Thus, the algebraic property illustrated is the commutative property of multiplication

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Answer:

a

 \(\frac{\alpha }{2} = 2.5 \%\)

b

  \(N = 25\)

Step-by-step explanation:

From the question we are told that

   The number of bootstrap samples is  n =  1000

From the question we are told the confidence level is  95% , hence the level of significance is    

      \(\alpha = (100 - 95 ) \%\)

=>   \(\alpha = 0.05\)

Generally the percentage of values that must be chopped off from each tail  for a 95% confidence interval is mathematically evaluated as

      \(\frac{\alpha }{2} = \frac{0.05}{2} = 0.025 = 2.5 \%\)

=>    \(\frac{\alpha }{2} = 2.5 \%\)

Generally the number of the bootstrap sample that must be chopped off to produce a 95% confidence interval is

      \(N = 1000 * \frac{\alpha }{2}\)

=>   \(N = 1000 * 0.025\)

=>   \(N = 25\)

Answer:

Step-by-step explanation:

Hey

Answer: Choice A

\(x \le 5\)

========================================

Explanation:

Any point in the shaded purple region has an x coordinate that is 5 or smaller. So we go for \(x \le 5\). Either x = 5 or x < 5. The boundary line is solid to indicate that points on the boundary are included in the solution set.

Answer:

1/729

Step-by-step explanation:

a negative exponent is fractioned like 1/9^3. Which can be simplified as 1/729 ans 9^3 = 729