for what positive integers $c$, with $c < 100$, does the following quadratic have rational roots? \[ 3x^2 20x c \]

Answer:

x ≥ 0

Step-by-step explanation:

The absolute value of x+8 equals itself, thus x must be a real number (0 or any positive number).

The value of x in |x+8|=x+8 is -8.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that;

|x+8|=x+8

Now,

To solve this equation, we need to consider two cases:

Case 1: x+8 is positive or zero. Then |x+8|=x+8 and we can solve for x by subtracting 8 from both sides:

|x+8|=x+8

x+8=x+8

x=x

This means that any value of x is a solution in this case.

Case 2: x+8 is negative. Then |x+8|=-(x+8) and we can solve for x by adding 8 to both sides and dividing by -2:

|x+8|=-(x+8)

x+8=-(x+8)

2x=-16

x=-8

Therefore, by the given equation the answer will be -8.

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Part a. Find the Laplace transform and inverse Laplace transform of Let+')} and L- [8 marks]Laplace transform of Let+')} is given as: L(et+')} = 1/s-(1/ s+2)Let's try to  this.1/s-(1/ s+2) = (s+2-s)/s(s+2) = 2/s(s+2)L-1{2/s(s+2)}= L-1{(1/s)-(1/s+2)} = e^(-2t) - 1

Part b. 18 = 1+k8-2+ 3+ 3k and 7 - 1 - 2k, obtain the following: i) ä. ax, ii) (ä xk), iii) 2:a)3 +34 i) 18 = 1+k8-2+ 3+ 3k

Let's simplify this as follows.18 = 12 + k + 3k - 2k + 3k-1 - 4k+1/218 = 12 - k + 2k + 2k + 3(1/k) - 4k+1/2a=12, b=-1, c=2 and d=2Therefore,ä. ax = ad-bc = 24 + 2 = 26ii) (ä xk) = (cd - bc)i + (ab - ad)j + (ad - bc)k = 1i - 2j + 24kiii) 2:a)3 +34 = 2(ad-bc) + 3(ab-ad) + 4(cd-bc) + 3(bd - ac) = 52
Part c. Find the point at which the plane 22 - 5y + z = 5 and the line Ft) - (+1) + (24+ 1)3+ (t+1)! (where t is a real number) intersect. [3 marks]. Let's substitute the given line in the plane equation. 2(1+4t) - 5(3+1t) + z = 5 solving for z, we get

z = 12t - 13

Substitute this z in line equation to get the point of intersection.(1+t, 4+2t, 12t-13)

Part d. Compute the curvature and principal unit normal vector for the curve rt) 2 sin(t)+ 2 con(e) { for t > 0. [6 marks]. Given curve r(t) = 2 sin(t) + 2 cos(t).

We need to find the first and second derivatives. r'(t) = 2 cos(t) - 2 sin(t)r''(t) = -2cos(t) - 2sin(t)

From these values, we get |r'(t)| = sqrt(8)K(t) = |r'(t)|/|r"(t)|^3/2K(t) = 2^(3/2)/8^(3/2)K(t) = 1/4^(1/2)K(t) = 1/2

Therefore the curvature is 1/2Now, let's find the principal unit normal vector. N(t) = r''(t)/|r"(t)|N(t) = <-1/sqrt(2),1/sqrt(2)>
Part e. For the two matrices A= 12 0 0-7 5 3 B= B=(- :) 0

Find i) AT, ii) BT, iii) B(AT) and iv) (AB)" [8 marks]

i) AT =Transpose of A = 1 -7 0 2 5 3

ii) BT =Transpose of B = 1 0 -3 0 2 1

iii) B(AT) =B(Transpose of A) = 1 -7 0 2 5 3(-1) 0 0 7 -5 -3= -1 7 0 -2 -5 -3

iv) (AB)" =(AB)^-1=Inverse of AB Let's calculate AB first. AB =12 0 0-7 5 3(-1) 0 0-5 2 -1= -1 0 0 1

Therefore, the inverse of AB is1 0 0-1

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Answer:

The ratio is [tex]\frac{2}{3}[/tex].

Step-by-step explanation:

The ratio of the perimeters of Quad ABCD to Quad WXYZ = [tex]\frac{perimeter of ABCD}{perimeter of WXYZ}[/tex]

But considering sides AB and WX,

representative factor for both figures = [tex]\frac{12}{8}[/tex]

So that;

WX = 12

XY = 1.5 x 6 = 9

YZ = 1.5 x 7 = 10.5

WZ = 1.5 x 7 = 10.5

Thus,

perimeter of Quad ABCD = 6 + 7 + 7 + 8

                                           = 28

perimeter of Quad WXYZ = 9 + 10.5 + 10.5 + 12

                                           = 42

The ratio of the perimeters of Quad ABCD to Quad WXYZ = [tex]\frac{28}{42}[/tex]

                                                         = [tex]\frac{2}{3}[/tex]

The sets A {1.2,3,4,6,12}, A{1,2,3,4,6,12,18,24}, and A{1,2,3,6,12} all yield a poset that is a total ordering.

In order for a partially ordered set (poset) to be a total order, every pair of elements must be comparable, i.e., for every pair of elements x, y in A, either x | y or y | x must be true.

Therefore, we should choose a set A that satisfies this condition.Let us consider each set in turn:(1, 4, 16, 64)This set contains powers of 4, which are not all divisible by each other.

For example, 16 | 64, but 16 does not divide 4.

Hence, this set is not a total order.{1.2,3, 4, 6, 12}In this set, 1 divides every other element, so it satisfies the condition for being a total order. Therefore, this set yields a poset that is a total order.

(1, 2, 3, 4, 6, 12, 18, 24)This set has the same elements as the previous set, plus some more. Hence, it also satisfies the condition for being a total order.

Therefore, this set yields a poset that is a total order.{1 , 2, 3, 6, 12}In this set, 1 divides every other element, 2 divides 6 and 12, and 3 divides 6 and 12.

Therefore, it satisfies the condition for being a total order.

Hence, this set yields a poset that is a total order.In conclusion, the sets A {1.2,3,4,6,12}, A{1,2,3,4,6,12,18,24}, and A{1,2,3,6,12} all yield a poset that is a total ordering.

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Answer:

The total sample list is 6

Step-by-step explanation:

The bag has following balls

Red - 1

Blue -1

White -1

Two balls are drawn from the bag without replacing the other -

The probability of drawing 1st ball of any color - 1/3

The probability of drawing 2nd ball of any color - 1/2

These two events are independent of each other

Hence, the probability of deriving two balls without replacement is 1/3*1/2 = 1/6

Hence, the total sample list is 6

The sample space is the list of possible outcomes of an experiment

The sample space is {rb, rw, br, bw, wr, wb}

The color of the three balls is represented as:

Red = r

Blue = b

White = w

Given that the selection is without replacement, the sample space would be:

rb, rw, br, bw, wr, wb

The count of the sample space represents the sample size.

Hence, the sample size of the experiment is 6, and the sample space is {rb, rw, br, bw, wr, wb}

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The probability that one is hired and one is not is 5/7.

Given that there are 7 people, including the husband and wife pair, apply for 6 sales positions. People are hired at random.The probability that one is hired and one is not is obtained as follows:

Total number of ways to choose 6 people out of 7 is given by, `n(S) = 7C6 = 7`

The number of ways in which the husband and wife pair will be selected and 4 other people will be selected out of remaining 5 is given by, `n(E) = 5C4 = 5`

Therefore, the probability that one is hired and one is not can be expressed as:

Probability = n(E) / n(S)

Probability = 5/7

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There are 7 people for 6 positions. We know that the husband and wife pair both want a job, so we can count them as a single "unit" for this calculation. So there are effectively 6 people for 6 positions.

The required probability is 2/3.

There are two possible outcomes for the husband-wife pair:

Either both are hired or both are not hired. For the probability that one is hired and one is not:

Find the probability that the husband-wife pair are hired and subtract that from 1 (to get the probability that one is hired and one is not). The probability that the husband-wife pair are hired is:

[tex]\frac {\binom{5}{4}}{\binom{6}{4}} = \frac{5}{15}[/tex]

[tex]= \frac{1}{3}[/tex]

So the probability that one is hired and one is not is:

[tex]1 - \frac{1}{3} = \frac{2}{3}[/tex]

The required probability is 2/3.

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Answer:

36+25= 61

61/600 x 100 = 10.1 %

Step-by-step explanation:   Hope This helped!!!!

Answer:

Step-by-step explanation:

1. b. Alt. Exterior angles

  a. 7x + 8 = 6x + 18

   c.    x + 8 = 18

          x = 10

   d. 6(10) + 18 = 60 + 18 = 78

       7(10) + 8 = 70 + 8 = 78

2. 15x + 10 + 12x + 8 = 180

     same side angles

   27x + 18 = 180

   27x = 162

   x = 6

15(6) + 10 = 90 + 10 = 100 degrees

12(6) + 8 = 72 + 8 = 80 degrees

3. 12x + 2 = 11x + 6

    x + 2 = 6

    x = 4

12(4) + 2 = 48 + 2 = 50 degrees

11(4) + 6 = 44 + 6 = 50 degrees

corresponding angles

To prove that x(dx/dg) - y(dg/dy) = 0, we'll start by finding the derivatives of the functions involved.

Given that g(x, y) = f(xy), we can find the partial derivatives of g with respect to x and y using the chain rule:

∂g/∂x = ∂f/∂u * ∂(xy)/∂x = y * ∂f/∂u

∂g/∂y = ∂f/∂u * ∂(xy)/∂y = x * ∂f/∂u

Now, let's differentiate the equation x(dx/dg) - y(dg/dy) = 0:

d/dg (x(dx/dg) - y(dg/dy)) = d/dg (x(dx/dg)) - d/dg (y(dg/dy))

Using the chain rule, we can rewrite the derivatives:

d/dg (x(dx/dg)) = d/dx (x(dx/dg)) * dx/dg = x * d/dx (dx/dg)

d/dg (y(dg/dy)) = d/dy (y(dg/dy)) * dg/dy = y * d/dy (dg/dy)

Substituting these expressions back into the equation, we have:

x * d/dx (dx/dg) - y * d/dy (dg/dy) = 0

Now, let's simplify the equation further. Since dx/dg represents the derivative of x with respect to g, it is essentially the reciprocal of dg/dx, which represents the derivative of g with respect to x:

dx/dg = 1 / (dg/dx)

Similarly, dg/dy represents the derivative of g with respect to y. Therefore, we can rewrite the equation as:

x * d/dx (1/(dg/dx)) - y * d/dy (dg/dy) = 0

Taking the derivatives with respect to x and y, we have:

[tex]x * (-1/(dg/dx)^2) * (d^2g/dx^2) - y * (d^2g/dy^2) = 0[/tex]

Since dg/dx and dg/dy are partial derivatives of g, we can simplify further:

x * (-1/(∂g/∂x)^2) * (∂^2g/∂x^2) - y * (∂^2g/∂y^2) = 0

Finally, using the expressions we found for the partial derivatives of g earlier, we can substitute them into the equation:

x * (-1/(y * ∂f/∂u)^2) * (∂^2f/∂u^2 [tex]* y^2[/tex]) - y * (∂^2f/∂u^2 * [tex]x^2[/tex]) = 0

Canceling out the common factors, we are left with:

∂^2f/∂u^2 * x + ∂^2f/∂u^2 * y = 0

Since ∂^2f/∂u^2 is a constant (it does not depend on x or y), we can factor it out:

∂^2f/∂u^2 * (y - x) = 0

For the equation to hold, we must have either ∂^2f/∂u^2 = 0 or (y - x) = 0. However, the second condition (y - x) = 0 implies that y = x, which is not a necessary condition for the given equation to be true.

Therefore, the only possibility is ∂^2f/∂u^2 = 0, which implies that the equation x(dx/dg) - y(dg/dy) = 0 holds.

In conclusion, we have shown that x(dx/dg) - y(dg/dy) = 0 under the assumption that f is a differentiable function of r and g(x, y) = f(xy).

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The 80% confidence interval for the mean length difference between two-year-old and one-year-old spotted flounder is [5.15, 7.83] millimeters.

For an 80% confidence interval, we need to find the critical value associated with a two-tailed test. Since the sample sizes are large, we can use the z-distribution. The critical value for an 80% confidence interval is approximately 1.282.

ME = 1.282 * 1.0466 ≈ 1.3426

Confidence interval = Point estimate ± Margin of error

Confidence interval = 6.49 ± 1.3426

Finally, rounding to at least two decimal places:

Confidence interval = [5.15, 7.83]

Therefore, the 80% confidence interval for the mean length difference between two-year-old and one-year-old spotted flounder is [5.15, 7.83] millimeters.

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The conclusions are as follows:

a. We reject the null hypothesis.

b. The p-value for this test is approximately 0.001.

To complete parts a and b, we can follow the steps for hypothesis testing.

a. The z-test statistic can be calculated using the formula:

z = ([tex]\bar{X}[/tex] - μ) / (σ / √n)

Given:

[tex]\bar{X}[/tex] = 49

σ = 11

n = 32

Substituting these values into the formula, we get:

z = (49 - 47) / (11 / √32) ≈ 2.90

The z-test statistic is approximately 2.90 (rounded to two decimal places).

To determine the critical z-score(s), we need to find the z-value that corresponds to the significance level α = 0.10. Since the alternative hypothesis is one-sided (μ > 47), we are performing a right-tailed test.

Using a standard normal distribution table or a calculator, the critical z-score for a right-tailed test at α = 0.10 is approximately 1.28 (rounded to two decimal places).

Because the test statistic z = 2.90 is greater than the critical z-score of 1.28, we reject the null hypothesis.

b. The p-value represents the probability of obtaining a test statistic as extreme as the observed value (or more extreme) assuming the null hypothesis is true. Since the alternative hypothesis is μ > 47, we are looking for the probability in the right tail of the distribution.

Using a standard normal distribution table or a calculator, we can find the p-value corresponding to the z-test statistic z = 2.90. The p-value is the area under the curve to the right of 2.90.

The p-value is approximately 0.001 (rounded to three decimal places).

Therefore, the conclusions are as follows:

a. We reject the null hypothesis.

b. The p-value for this test is approximately 0.001.

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Answer:

Zx = 131

Step-by-step explanation:

The angles will equal to 180, so therefore you will do 180-49=Zx

Answer:

I just learned about this, and if its wrong i am so so sorry

Step-by-step explanation:

a= 120

b= 60

w= 120

x= 120

r= 105

q= 105

p= 105

Answer:

a= 120

b= 60

w= 120

x= 120

r= 75

q= 105

p= 105

Step-by-step explanation:

The best approximation for the area of this circle is approximately 50.2 m².Option (c) is the correct answer.

To determine the best approximation for the area of this circle, we need to use the formula for the area of a circle, which is given by A = πr².

Here, we are given the value of π to be approximately equal to 3.14.

Now, we need to determine the radius of the circle.

From the diagram, we can see that the diameter of the circle is 8 meters.

Therefore, the radius is half of this, which is 4 meters.

Substituting the values of π and r into the formula, we get: A = πr²= 3.14 × 4²= 3.14 × 16= 50.24 (to two decimal places)

Therefore, the best approximation for the area of this circle is approximately 50.2 m².Option (c) is the correct answer.

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Answer:

B. 2 12

Step-by-step explanation:

maaf kalo salah ituh jawabbanya menurut guwah

As the lower bound of the 90% confidence interval is below 0, there is not enough evidence to conclude that  the proportion of overweight kids aged 6-11 among boys is greater than the proportion of overweight kids aged 6-11 among girls.

The sample proportions are given as follows:

The difference is then given as follows:

0.1367 - 0.1245 = 0.0122.

The standard error for each sample is given as follows:

Then the standard error for the distribution of differences is given as follows:

[tex]s = \sqrt{0.0153^2 + 0.0145^2}[/tex]

s = 0.0211.

The critical value for a 90% confidence interval is given as follows:

z = 1.645.

The lower bound of the interval is:

0.0122 - 1.645 x 0.0211 = -0.0225.

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Answer:5.987

Step-by-step explanation:

Answer:

22.7 km

Step-by-step explanation:

The Pythagorean Theorem is:

a² + b² = c²

where a and b are legs and c is the hypotenuse.

The hypotenuse is the longest side of a right triangle and can be identified as being across from the right angle. The legs are interchangeable between the variables a and b.

Because it's clear that x is the hypotenuse:

15² + 17² = x²

225 + 289 = x²

514 = x²

√514 = √x²

x = √514

Because we can't simplify √514 anymore, we can keep it as radical 514 or round it:

22.6715681 ≈ 22.7

Answer:

-1

Step-by-step explanation:

6 (y - 2) = -18

6y - 12 = -18

6y = -18 + 12

6y = -6

y = -1

1/4+1/5+1/6=1/x

LCM = 60

15/60+12/60+10/60=1/x

37/60=1/x

37x=60

x=60/37=1.62, round =1.6

1.6 HOURS

The number of hours they would take them all working together is around 1.6 hours.

A ratio is the divide of the two variables and the lower variable known as the denominator should not be zero.

Given that laine takes 4 hours to complete work

In 1 hour Laine will do 1/4 part of the work.

In 1 hour Leslie will do 1/5 part of the work.

In a 1-hour Lance will do 1/6 part of the work.

so let's suppose all done work by x hours then

1/4 + 1/5 + 1/6 = 1/x

x =1.6 so all together done the work by 1.6 hours.

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Using the Division Algorithm we have shown that the cube of any integer is of the form 9k, 9k + 1 or 9k + 8

To show that the cube of any integer is of the form 9k, 9k + 1, or 9k + 8, we will use the Division Algorithm. We will establish the result for the cases of 9q + 3 and 9q + 7.

Let's consider the case of 9q + 3, where q is an integer. We want to show that the cube of any integer of the form 9q + 3 is also of the form 9k, 9k + 1, or 9k + 8.

Let's choose an arbitrary integer, let's say n, such that n = 9q + 3.

Taking the cube of n:

n³ = (9q + 3)³

    = 729q³ + 243q² + 27q + 27

Now, let's express this in terms of 9k, 9k + 1, or 9k + 8:

n³ = 729q³ + 243q² + 27q + 27

    = 9(81q³ + 27q² + 3q + 3) + 18 + 9

    = 9(81q³ + 27q² + 3q + 3 + 2) + 7

We can see that n³ can be expressed in the form 9k + 7, where k = 81q³ + 27q² + 3q + 3 + 2.

Therefore, we have shown that for the case of 9q + 3, the cube of any integer of that form is of the form 9k + 7.

Now, let's consider the case of 9q + 7, where q is an integer. We want to show that the cube of any integer of the form 9q + 7 is also of the form 9k, 9k + 1, or 9k + 8.

Similar to the previous case, let's choose an arbitrary integer, let's say n, such that n = 9q + 7.

Taking the cube of n:

n³ = (9q + 7)³

    = 729q³ + 441q² + 147q + 49

Now, let's express this in terms of 9k, 9k + 1, or 9k + 8:

n³ = 729q³ + 441q² + 147q + 49

    = 9(81q³ + 49q² + 16q + 5) + 4

We can see that n³ can be expressed in the form 9k + 4, where k = 81q³ + 49q² + 16q + 5.

Therefore, we have shown that for the case of 9q + 7, the cube of any integer of that form is of the form 9k + 4.

By using the Division Algorithm and establishing the results for the cases of 9q + 3 and 9q + 7, we have shown that the cube of any integer is of the form 9k, 9k + 1, or 9k + 8.

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Answer:

the answer is 3,107.21

The answer to that question is that one

Answer:

Following are the responses to the given question:

Step-by-step explanation:

[tex]French \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Mathematics\\\\X= 85\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ X= 80\\\\\mu=72\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \mu =70\\\\\sigma=12 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sigma= 7.8\\\\[/tex]

Formula:

[tex]\bold{Z-Score=\frac{x-\mu}{\sigma}}\\\\French \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Mathematics\\\\Z=\frac{85-72}{12} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Z=\frac{80-70}{7.8}\\\\=1.0833 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =1.2820\\\\[/tex]

In the french exam Z value is 1.0833 and in the maths exam Z value is 1.2820 that's why we can say that  in maths exam, she does better than french exam.

the expression 2⁶ × (1/4)⁵ / (16)³ can be written as 4⁻⁸.

To express the given expression 2⁶ × (1/4)⁵ / (16)³ as a power with a base of 4, we can simplify the expression using the properties of exponents:

2⁶ × (1/4)⁵ / (16)³

First, we simplify the exponents:

2⁶ = 64 = 4³

(1/4)⁵ = 4⁻⁵

(16)³ = 4⁶

Now, we substitute these simplified values back into the expression:

4³ × 4⁻⁵/4⁶ = 4³ × 4⁻⁵ × 4⁻⁶

= 4³⁻⁵⁻⁶

= 4⁻⁸

Finally, we express the simplified expression as a power with a base of 4: 4⁻⁸

Therefore, the expression 2⁶ × (1/4)⁵ / (16)³ can be written as 4⁻⁸.

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Answer:

B.490

Step-by-step explanation:

Correct me if im wrong

Answer: 490

Step-by-step explanation:

Null and alternative hypothesis: The null hypothesis is that the mean weight of the diabetics insured by two employers is similar.

In contrast, the alternative hypothesis is that the mean weight of the diabetics insured by two employers is not equal. Level of significance: The level of significance

(α) is the probability of rejecting the null hypothesis when it is valid. The commonly used level of significance is 0.05.

Test statistic: Assuming the population variances are equal, the test statistic is the t-distribution.

Decision Rule: Reject H0 if the t-value is greater than 2.060 or less than -2.060 and accept H0 if the t-value is between 2.060 and -2.060.

State Output: Assuming equal variances, the p-value associated with a two-tailed t-test for equality of means is 0.2682.Statistical decision: Since the p-value is greater than 0.05, we accept the null hypothesis and conclude that the mean weight of diabetics insured by the two employers is equal.

Conclusion: Therefore, there is no considerable difference in the mean weight of diabetics insured by two employers in the City of Asheville and Mission-St. Joseph’s Health System. Linear regression model and interpretation (if necessary): A linear regression model was not necessary in this study.

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The trial balance provides a summary of Boilermaker House Painting Company's financial transactions for the month of September. The company engaged in several activities during the month, including providing painting services, purchasing equipment and office supplies, paying salaries, renting office space, and receiving cash from customers.

In the first transaction, the company painted houses for customers in the current month, generating service revenue of $16,000 on account. This resulted in an increase in the Accounts Receivable balance, representing the amount owed by customers.

The second transaction involved the purchase of painting equipment for $17,000 in cash. This expenditure was recorded as an increase in the Equipment account, which reflects the company's tangible assets.

Next, the company purchased office supplies on account for $2,700. This transaction increased the Supplies account and created an obligation in the form of an Accounts Payable.

The fourth transaction involved paying employee salaries of $3,400 for the current month. This expense was recorded in the Salaries Expense account, which represents the cost of labor incurred by the company.

In the fifth transaction, the company spent $1,100 in cash to purchase advertising, which was intended to appear in the current month. This expense was recorded in the Advertising Expense account.

The sixth transaction involved paying office rent of $4,600 for the current month. This expense was recorded in the Rent Expense account, representing the cost of utilizing office space.

In the seventh transaction, the company received $11,000 in cash from customers who had previously been billed for the painting services provided. This increased the Cash balance, reflecting the inflow of funds.

Lastly, the company received $5,200 in advance cash from a customer who planned to have their house painted in the following month. This created a liability in the form of Deferred Revenue, as the company had not yet provided the corresponding service.

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Answer:

180°

Step-by-step explanation:

cos(x) = - 1 has only 1 solution in the required interval , that is

x = [tex]cos^{-1}[/tex] (- 1) = 180°