Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 15 people took the trip. She was able to purchase coach tickets for ​$220 and first class tickets for ​$910. She used her total budget for airfare for the​ trip, which was ​$8130. How many first class tickets did she​ buy? How many coach tickets did she​ buy?

In summary, to find the null spaces of the matrices given in exercises 9 and 10, use the Gauss-Jordan elimination method and refer to the Remarks that follow example 3 in section 4.2 of the text. This will give the dimension of the null space and the number of free variables.
In exercises 9 and 10, the null space of the given matrices can be found by solving the homogeneous linear system of equations. In order to do this, use the Gauss-Jordan elimination method. Refer to example 3 in section 4.2 of the text for a detailed explanation. Afterwards, use the Remarks that follow the example to determine the dimension of the null space and the number of free variables.

The null space of a matrix is the set of all vectors that produce a zero vector when the matrix is multiplied by the vector. Therefore, to find the null space of a matrix, the homogeneous linear system of equations needs to be solved. The Gauss-Jordan elimination method involves adding multiples of one row to another to get a row with all zeroes. After this is done for all the rows, the equations can be solved for the free variables. The number of free variables will determine the dimension of the null space. Refer to example 3 in section 4.2 of the text for more details.

The Remarks that follow the example are important when determining the dimension of the null space and the number of free variables. In the Remarks, it is mentioned that the number of free variables is equal to the number of columns with a zero row. Therefore, after using the Gauss-Jordan elimination method to get the row with all zeroes, the number of columns with a zero row can be counted. This will give the dimension of the null space and the number of free variables.

for such more questions on  Gauss-Jordan elimination

https://brainly.com/question/20536857

#SPJ11

The shortest interval that contains 95% of the debt values is $9,492.02 to $20,507.98

Given that a credit risk study found that an individual with good credit score has an average debt of $15,000 and the debt of an individual with good credit score is normally distributed with standard deviation $3,000.

Then the 95% confidence interval can be calculated as follows:

Upper limit: µ + Zσ

Lower limit: µ - Zσ

Where

The z-score corresponding to a 95% confidence interval can be found using the standard normal distribution table.

The area to the left of the z-score is 0.4750 and the area to the right is also 0.4750.

The z-score corresponding to 0.4750 can be found using the standard normal distribution table as follows:z = 1.96Therefore

Upper limit: µ + Zσ= $15,000 + 1.96($3,000) = $20,880

Lower limit: µ - Zσ= $15,000 - 1.96($3,000) = $9,120.02

The shortest interval that contains 95% of the debt values is $9,492.02 to $20,507.98.

See more about confidence interval at: https://brainly.com/question/15712887

#SPJ11

we have

13x+6y=−30------------- > 6y=-30-13x--------------- > y=(-30-13x)/6

x−2y=−4-- > 2y=x+4-------- > y=(x+4)/2

Using a graphing tool---------- > see attached figure

the solution of the system is the point (-2.625,0688)

the best estimate pair for the solution to the system is (−2.5, 0.75)

Answer:

(2, 0) and (-1, 0)

Step-by-step explanation:

[tex]4x^2 - 4x - 8 = 0 \text{ // Divide by 4} \\x^2 - x - 2 = 0\\\\x_{1, 2} = \frac{-(-1) \pm \sqrt{(-1)^2 - 4 \times 1 \times (-2)}}{2\times1}\\\\x_{1, 2} = \frac{1 \pm \sqrt{1 + 8}}2\\\\x_{1, 2} = \frac{1 \pm \sqrt9}2\\\\x_{1, 2} = \frac{1 \pm 3}2\\\\x_1 = \frac{1 + 3}2 = \frac42 = 2\\\\x_2 = \frac{1 - 3}2 = \frac{-2}2 = -1[/tex]

Therefore, the zeroes are (2, 0) and (-1, 0).

Answer:

"9 more than A" is a verbal expression.

Therefore, Person A is approximately 95.17 miles away from the building.

To find out how far person A is from the building, we'll need to use trigonometry. The diagram below shows the situation.

Given that Person A's angle of elevation to the building is 35 degrees, we'll let angle BAC be 35 degrees.

Similarly, since Person B's angle of elevation is 77 degrees, we'll let angle ABC be 77 degrees. We'll also let AB be x, the distance from Person A to the building, and BC be 8 miles, the distance from Person B to the building.

First, we'll use the tangent function to find the height of the building. In triangle ABC, tan(77) = height/8. Solving for the height, we get:

height = 8tan(77) ≈ 61.23 miles.

Next, we'll use the tangent function again to find x. In triangle ABC, tan(35) = height/x + 8. Solving for x, we get:

x = (height)/(tan(35)) - 8
≈ 103.17 miles - 8
≈ 95.17 miles.
for such more questions on  elevation

https://brainly.com/question/25748640

#SPJ11

Answer:

Point-Slope Form: y - 1 = -1/2(x - 4) or Standard Form: y = -1/2x + 3

Step-by-step explanation:

For a line to be perpendicular, you take the negative inverse of the slope of 2x - y = 4. To do this, rearrange the y to one side and you get y = 2x - 4. The slope of the line is 2. So, taking the negative inverse would be -1/m (with m being slope of the the equation given in the problem. This would give you -1/2.

Using point slope formula, y - y1 = m(x - x1), you can plug in the point given, (4,1) and the slope you found to get y - 1 = -1/2(x - 4). For standard form, isolating the y gets you y = -1/2x + 3.

You can check your answer by using Desmos by putting in the line 2x - y = 4, the point (4,1), and the equation you got as your answer. You will see that the equation is perpendicular to 2x - y = 4 and passes through point (4,1). Your equation of the line is y - 1 = -1/2(x - 4) or y = -1/2x + 3

The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.

We have,

To find the work required to pump all the water out of the rectangular swimming pool, we can use the concept of work as the force multiplied by the distance.

First, let's calculate the weight of the water in the pool.

The weight of an object is given by the formula:

Weight = mass x gravitational acceleration

Since the density of water is given as 1 lb/ft³, we need to find the volume of water in the pool.

The volume of the pool is given by the formula:

Volume = length x width x depth

Volume = 50 ft x 30 ft x 6 ft = 9000 ft³

Now, let's calculate the weight of the water:

Weight = density x volume x gravitational acceleration

Weight = 1 lb/ft³ x 9000 ft³ x 32.2 ft/s² ≈ 290,400 lb

To pump all the water out over the top, we need to raise it to the height of the pool, which is 8 ft.

The work required to pump the water out is given by the formula:

Work = weight x height

Work = 290,400 lb x 8 ft = 2,323,200 ft-lb

Therefore,

The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.

Learn more about rectangles here:

https://brainly.com/question/15019502

#SPJ12

The approximate area of the surface formed by revolving the polar equation over the given interval about the polar axis is 67.59 square units.

To solve the question, we can use the integration capabilities of a graphing utility to approximate to two decimal places the area of the surface formed by revolving the polar equation over the given interval about the polar axis. Polar curve is a type of curve that is made up of points that represent polar coordinates (r, θ) instead of Cartesian coordinates.

A polar curve can be represented in parametric form, but it is often more convenient to use the polar equation for a curve. According to the question, r = 7 cos(20), [0, Phi/4] is the polar equation and we need to find the approximate area of the surface formed by revolving the polar equation over the given interval about the polar axis.

To solve the problem, follow these steps: Convert the polar equation to a rectangular equation. The polar equation r = 7 cos(20) is converted to a rectangular equation using the following formulas: x = r cos θ, y = r sin θx = 7 cos (20°) cos θ, y = 7 cos (20°) sin θx = 7 cos (θ - 20°) cos 20°, y = 7 cos (θ - 20°) sin 20°

Sketch the curve in the plane. We can sketch the curve of r = 7 cos(20) by plotting the points (r, θ) and then drawing the curve through these points. Use the polar equation to set up the integral for the volume of the solid of revolution.

The volume of the solid of revolution is given by the formula: V = ∫a b πf2(x) dx where f(x) = r, a = 0, and b = Φ/4.We can find the volume of the solid of revolution using the polar equation: r = 7 cos(20) => r2 = 49 cos2(20) => x2 + y2 = 49 cos2(20)Thus, f(x) = √(49 cos2(20) - x2) = 7 cos(20°) sin(θ - 20°)

So, V = ∫a b πf2(x) dx = ∫0 Φ/4 π(7 cos(20°) sin(θ - 20°))2 dθStep 4: Use a graphing utility to evaluate the integral to two decimal places. Using a graphing utility to evaluate the integral, we get V ≈ 67.59.

Learn more about Interval

brainly.com/question/30486507

#SPJ11

The slopes are,

1) 7/6

2)7/2

3) -1

4) -2

5) 10/9

What is slope?

Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined. The difference between the line's y and x coordinate changes is known as the slope of the line.Any two distinct places along the line can be used to determine the slope of any line.

1) The given points , [tex](x_1,y_1) =(0,1)[/tex] and [tex](x_2,y_2) = (6,8)[/tex] then,

=> slope  = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = [tex]\frac{8-1}{6-0} = \frac{7}{6}[/tex]

2) The given points [tex](x_1,y_1) =(-1,10)[/tex] and [tex](x_2,y_2) = (-5,-4)[/tex] then,

=> Slope = [tex]\frac{-4-10}{-5+1} = \frac{-14}{-4}=\frac{7}{2}[/tex]

3)  The given points [tex](x_1,y_1) =(-10,2)[/tex] and [tex](x_2,y_2) = (-3,-5)[/tex] then,

=> slope = [tex]\frac{-5-2}{-3+10} = \frac{-7}{7}=-1[/tex]

4)  The given points [tex](x_1,y_1) =(-3,-4)[/tex] and [tex](x_2,y_2) = (-1,-8)[/tex] then,

=> slope = [tex]\frac{-8+4}{-1+3} = \frac{-4}{2}=-2[/tex]

5)The given points [tex](x_1,y_1) =(0,1)[/tex] and [tex](x_2,y_2) = (-9,-9)[/tex] then,

=> slope = [tex]\frac{-9-1}{-9+0} = \frac{-10}{-9}=\frac{10}{9}[/tex]

Hence the slopes are,

1) 7/6

2)7/2

3) -1

4) -2

5) 10/9

To learn more about slope refer the below link

https://brainly.com/question/16949303

#SPJ1

16h^(10/2) *remove the root sign

16h^5 *simplify the exponent

Answer: 16h^5

Step-by-step explanation: im correct

Answer:

X

Step-by-step explanation:

We first must check the total amount of breakfast. Y happens to have 130 instead of 125. Now, we see that W and Z have a majority on strawberries with oatmeal, which is not what we are looking for. The last answer we have is X, where there is a majority of oatmeal + blueberries and there is a total of 125 breakfasts.

Hope this helps!

Answer:

-21

Step-by-step explanation:

y^2 + 8y - 9                       y = -6

(-6)² + 8(-6) - 9

36 - 48 - 9

-21

So, the answer is -21

Answer:y=\frac{7}{12}-i\frac{\sqrt{167}}{12},\:y=\frac{7}{12}+i\frac{\sqrt{167}}{12}

Step-by-step explanation:y=\frac{7}{12}-i\frac{\sqrt{167}}{12},\:y=\frac{7}{12}+i\frac{\sqrt{167}}{12}

Answer: 46.0 ft

Step-by-step explanation:

[tex]\text{sin} \ 24^o=\dfrac{x}{105}[/tex]

[tex]x=105 \ \text{sin 24}^o[/tex]

So, the distance above the ground is [tex]\text{105 sin} \ 24^o+3.25\thickapprox \boxed{46.0 \ \text{ft}}[/tex]

The probability that an 18-year-old man selected at random is between 70 and 72 inches tall is approximately 0.0793 and the probability that the mean height of a sample of eight 18-year-old men is between 70 and 72 inches is approximately 0.9057 and the probability in part (b) is much higher because the standard deviation is smaller for the x distribution.

What do you mean by normally distributed data?

In statistics, a normal distribution is a probability distribution of a continuous random variable. It is also known as a Gaussian distribution, named after the mathematician Carl Friedrich Gauss. The normal distribution is a symmetric, bell-shaped curve that is defined by its mean and standard deviation.

Data that is normally distributed follows the pattern of the normal distribution curve. In a normal distribution, the majority of the data is clustered around the mean, with progressively fewer data points further away from the mean. The mean, median, and mode are all the same in a perfectly normal distribution.

Calculating the given probabilities :
(a) The probability that an 18-year-old man selected at random is between 70 and 72 inches tall can be found by standardizing the values and using the standard normal distribution table. First, we find the z-scores for 70 and 72 inches:

[tex]z-1 = (70 - 71) / 5 = -0.2[/tex]

[tex]z-2 = (72 - 71) / 5 = 0.2[/tex]

Then, we use the table to find the area between these two z-scores:

[tex]P(-0.2 < Z < 0.2) = 0.0793[/tex]

So the probability that an 18-year-old man selected at random is between 70 and 72 inches tall is approximately 0.0793.

(b) The mean height of a sample of eight 18-year-old men can be considered a random variable with a normal distribution. The mean of this distribution will still be 71 inches, but the standard deviation will be smaller, equal to the population standard deviation divided by the square root of the sample size:

[tex]\sigma_x = \sigma / \sqrt{n} = 5 / \sqrt{8} \approx 1.7678[/tex]

To find the probability that the sample mean height is between 70 and 72 inches, we standardize the values using the sample standard deviation:

[tex]z_1 = (70 - 71) / (5 / \sqrt{8}) \approx -1.7889[/tex]

[tex]z_2 = (72 - 71) / (5 / \sqrt{8}) \approx 1.7889[/tex]

Then, we use the standard normal distribution table to find the area between these two z-scores:

[tex]P(-1.7889 < Z < 1.7889) \approx 0.9057[/tex]

So the probability that the mean height of a sample of eight 18-year-old men is between 70 and 72 inches is approximately 0.9057.

(c) The probability in part (b) is much higher because the standard deviation is smaller for the x distribution. When we take a sample of eight individuals, the variability in their heights is reduced compared to the variability in the population as a whole. This reduction in variability results in a narrower distribution of sample means, with less probability in the tails and more probability around the mean. As a result, it becomes more likely that the sample mean falls within a given interval, such as between 70 and 72 inches.

To know more about normal distribution visit :

brainly.com/question/29509087

#SPJ1

An assignment of probabilities to events in a sample space must obey all of the following: They must obey the addition rule for disjoint events, They must sum to 1 when adding over all events in the sample space, and The probability of any event must be a number between 0 and 1, inclusive. Hence, the correct option is All of the above.

Probability is the branch of mathematics that deals with the likelihood of a random event occurring. Probability is concerned with quantifying the probability of different results in a certain event.

The possibility that a specific event will occur is calculated using probability. Probability is calculated using several methods in mathematics, including axioms, probability spaces, events, random variables, and expectation values.

Learn more about Probability here: https://brainly.com/question/25839839

#SPJ11

Answer:

169 - 144p²

Step-by-step explanation:

(13 - 12p) × (13 + 12p)

each term in the second factor is multiplied by each term in the first factor

13(13 + 12p) - 12p(13 + 12p) ← distribute parenthesis

= 169 + 156p - 156p - 144p² ← collect like terms

= 169 - 144p²

By using  Bayes' theorem in probability.

a) The probability that isaac would not become a hurricane but remain a tropical storm when it reached the gulf of mexico is 0.31.

b) P(H|c) = 0.4493

c) It can be observed that the likelihood of a tropical storm developing into a hurricane decreases slightly when it passes over Cuba. This can be inferred from the fact that the conditional probability of a hurricane forming given that the storm has passed over Cuba (P(H|c) = 0.4493) is lower than the initial probability of 0.69.

a) The probability that Isaac would not become a hurricane but remain a tropical storm when it reached the Gulf of Mexico is:

P(not hurricane) = 1 - P(hurricane) = 1 - 0.69 = 0.31

So the probability is 0.31 (to 2 decimals).

b) We need to use Bayes' theorem to calculate the probabilities:

P(c|H) = P(H|c) * P(c) / P(H)

P(c|T) = P(T|c) * P(c) / P(T)

where c denotes passing over Cuba, H denotes becoming a hurricane, and T denotes remaining a tropical storm.

From the problem, we have:

P(H) = 0.69

P(T) = 1 - P(H) = 0.31

P(c|H) = 0.08

P(c|T) = 0.20

To calculate P(c), we need to use the law of total probability:

P(c) = P(c|H) * P(H) + P(c|T) * P(T)

= 0.08 * 0.69 + 0.20 * 0.31

= 0.1228

Now we can calculate P(c|H) and P(c|T):

P(c|H) = 0.08 * 0.69 / 0.1228

= 0.4493 (to 2 decimals)

P(c|T) = 0.20 * 0.31 / 0.1228

= 0.5065 (to 2 decimals)

To calculate P(H|c), we use Bayes' theorem again:

P(H|c) = P(c|H) * P(H) / P(c)

= 0.08 * 0.69 / 0.1228

= 0.4493 (to 4 decimals)

c) Passing over a landmass such as Cuba can alter the probability of becoming a hurricane because it can either enhance or weaken the storm. In this case, we can see that the probability of becoming a hurricane is actually slightly lower when a tropical storm passes over Cuba, as P(H|c) = 0.4493 is lower than the initial probability of 0.69. However, it is important to note that this is just one example and the effect of passing over a landmass can vary depending on many factors.

To know about "Bayes' theorem": https://brainly.com/question/14989160

#SPJ11

Random sampling 50 batteries throughout the day and testing to see if they would provide most valid results.

A sample is described as a smaller, more manageable representation of a larger group. A smaller population with characteristics of a larger one. A sample is used in statistical analysis when the population size is too large to include all participants or observations in the test.

The sample may be biased if it is taken from the first 25 batteries made each day or the last 25 batteries made each day.

The first and last battery made each day could not be an accurate representation of the total quality of the batteries produced that day if the battery manufacturing process is not consistent thought the day.

Although the battery quality can change during the day, sampling the first 50 batteries produced each day may also add bias into the sample.

The ideal course of action is to randomly select 50 batteries throughout the day, since this helps to ensure that the sample is reflective of the general calibre of batteries manufactured that day.

A more accurate image of the quality of the batteries manufactured can be obtained using this method, which is also more likely to capture any variations in battery quality over the day.

To know more about Random sampling go through:-

https://brainly.com/question/13219833

#SPJ4

Answer:

The answer to 1 + 1 is 2.

Very complicated problem, please mark brainliest!

Answer:

1+1 = 2

Or, 1=2-1

1=1

we know value of one is one

so,

1+1=11

Answer:

a=1/3

Step-by-step explanation:

First, expand the brackets by doing multiplication:

2+6a+3=3a+6

Then, move the unknown to the left and the numbers to the right:

3a=6-5

3a=1

a=1/3

The solution to the given equation is -1.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The given equation is 2+3(2a+1)=3(a+2)

2+6a+3=3a+2

6a+5=3a+2

6a-3a=2-5

3a=-3

a=-1

Therefore, the solution to the given equation is -1.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ2

The distribution is skewed to the right.

If the median is to the left of the center of the box and the right whisker is substantially longer than the left whisker in a box plot, then the distribution is skewed to the right.

This means that the majority of the data is clustered on the left side of the box plot and there are some extreme values on the right side that are causing the right whisker to be longer.

The median being to the left of the center of the box indicates that the data is not symmetric and is pulled to the left by the majority of the values.

Learn more about skewed distribution

brainly.com/question/1604092

#SPJ11

Answer: The given equation 2x + 5y = 10 can be rewritten in slope-intercept form (y = mx + b) by solving for y:

2x + 5y = 10

5y = -2x + 10

y = (-2/5)x + 2

where the slope is -2/5.

Since we want to find the equation of a line parallel to this one, the slope of the new line will also be -2/5. We can use the point-slope form of the equation of a line to find the equation of the new line, using the point (0,-3):

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the given point.

Substituting m = -2/5, x1 = 0, and y1 = -3, we get:

y - (-3) = (-2/5)(x - 0)

y + 3 = (-2/5)x

y = (-2/5)x - 3

Therefore, the equation of the line parallel to 2x + 5y = 10 which passes through (0,-3) is y = (-2/5)x - 3.

Step-by-step explanation:

Answer:

2x + 5y = - 15

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

2x + 5y = 10 ( subtract 2x from both sides )

5y = - 2x + 10 ( divide through by 5 )

y = - [tex]\frac{2}{5}[/tex] x + 2 ← in slope- intercept form

with slope m = - [tex]\frac{2}{5}[/tex]

• Parallel lines have equal slopes , then

y = - [tex]\frac{2}{5}[/tex] x + c

the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3

y = - [tex]\frac{2}{5}[/tex] x - 3 ← equation of parallel line in slope- intercept form

multiply through by 5 to clear the fraction

5y = - 2x - 15 ( add 2x to both sides )

2x + 5y = - 15 ← in standard form

Answer:

operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.

Answer:

operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.

Step-by-step explanation:

Based on the given data, The shape's whole surface area is about 252 mm².

Based on the image, the shape appears to be a set of rectangles with different lengths and widths.

To find the area of this shape, we can break it down into smaller rectangles and add up their areas.

Starting from the bottom, we can see that the first rectangle has a length of 6 mm and a width of 4 mm. Its area is:

Area1

= 6 mm × 4 mm

= 24 mm²

Moving up to the second rectangle, we see that it has a length of 6 mm and a width of 3 mm. Its area is:

Area2

= 6 mm × 3 mm

= 18 mm²

The third rectangle has a length of 6 mm and a width of 5 mm. Its area is:

Area3

= 6 mm × 5 mm

= 30 mm²

The fourth rectangle has a length of 6 mm and a width of 3 mm. Its area is:

Area4

= 6 mm × 3 mm

= 18 mm²

The fifth rectangle has a length of 6 mm and a width of 15 mm. Its area is:

Area5

= 6 mm × 15 mm

= 90 mm²

The sixth rectangle has a length of 3 mm and a width of 9 mm. Its area is:

Area6

= 3 mm × 9 mm

= 27 mm²

Finally, the seventh rectangle has a length of 5 mm and a width of 9 mm. Its area is:

Area7

= 5 mm × 9 mm

= 45 mm²

To find the total area of the shape, we can add up the areas of all seven rectangles:

Total Area

= Area1 + Area2 + Area3 + Area4 + Area5 + Area6 + Area7

= 24 mm² + 18 mm² + 30 mm² + 18 mm² + 90 mm² + 27 mm² + 45 mm²

= 252 mm²

Therefore, the total area of the shape is approximately 252 mm².

To learn more about area click here

brainly.com/question/27683633

#SPJ4

The measure of ∠J in ΔJKL is approximately 57.5 degrees.

The measure of ∠J in ΔJKL can be found using the trigonometric function tangent, which is defined as the ratio of the opposite side to the adjacent side.

The straight line that "just touches" the plane curve at a given point is called the tangent line in geometry. It was defined by Leibniz as the line that passes through two infinitely close points on the curve.

tan(∠J) = JK/KL

tan(∠J) = 7.3/4.7

∠J = arctan(7.3/4.7)

∠J = 57.5 degrees (rounded to the nearest tenth of a degree)

Therefore, the measure of ∠J in ΔJKL is approximately 57.5 degrees.

Learn more about Triangles

https://brainly.com/question/27996834

#SPJ4

The missing amounts for Walco Corporation and Gunther Enterprises assuming  all changes in stockholders equity are due to changes in retained earnings are
(a) Walco Corporation Total Stockholders' Equity =  $54,000
(b) Walco Corporation Total Assets = $182,000
(c) Walco Corporation Dividends = $47,100
(d) Gunther Enterprises Total Liabilities = $140,000
(e) Gunther Enterprises Total Stockholders' Equity = $91,500
(f) Gunther Enterprises Total Revenues =  $135,100

A balance sheet is a financial statement that reports a company's assets, liabilities, and stockholder equity on a specific date. Assets are resources a company owns that have monetary value, liabilities are obligations that must be paid in the future, and stockholder equity is the difference between a company's assets and liabilities. To calculate the missing amounts, you need to subtract the beginning of year figures from the end of year figures.

a) Total liabilities + Total stockholders' equity = Total assets

Total liabilities + $54,000 = $100,000

Total liabilities = $46,000

(b) Total assets = Total liabilities + Total stockholders' equity

Total assets = $128,000 + $54,000

Total assets = $182,000

(c) Changes during year in retained earnings = Total revenues - Total expenses - Dividends

Changes during year in retained earnings = $219,000 - $167,000 - $4,900

Changes during year in retained earnings = $47,100

The missing values for Gunther Enterprises:

(d) Total liabilities + Total stockholders' equity = Total assets

$67,500 + $(e) = $159,000

$(e) = $91,500

(f) Changes during year in retained earnings = Total revenues - Total expenses - Dividends

Changes during year in retained earnings = $(f) - $79,000 - $4,900

Changes during year in retained earnings = $(f) - $83,900

Using the balance sheet equation, we can find the missing values:

(d) Total liabilities = Total assets - Total stockholders' equity

Total liabilities = $159,000 - $67,500

Total liabilities = $91,500

(e) Total stockholders' equity = Total assets - Total liabilities

Total stockholders' equity = $190,000 - $50,000

Total stockholders' equity = $140,000

(f) Changes during year in retained earnings = Total revenues - Total expenses - Dividends

Changes during year in retained earnings = $219,000 - $79,000 - $4,900

Changes during year in retained earnings = $135,100

Therefore, the missing amounts are:

(a) Walco Corporation Total Stockholders' Equity =  $54,000
(b) Walco Corporation Total Assets = $182,000
(c) Walco Corporation Dividends = $47,100
(d) Gunther Enterprises Total Liabilities = $140,000
(e) Gunther Enterprises Total Stockholders' Equity = $91,500
(f) Gunther Enterprises Total Revenues =  $135,100

To learn more about the 'balance sheet':

https://brainly.com/question/1113933

#SPJ11

The triangle LMN, with vertices L(6, −8), M(4, −4), and N(−12, 2), dilated with respect to the origin by a scale factor of 1/2, results in triangle L'M'N', with vertices L'(3, -4), M'(2, -2), and N'(-6, 1)

To dilate a triangle with respect to the origin, we need to multiply the coordinates of each vertex by the scale factor. In this case, the scale factor is 1/2, so we multiply each coordinate by 1/2.

The coordinates of L' are obtained by multiplying the coordinates of L by 1/2:

L'((1/2)6, (1/2)(-8)) = (3, -4)

The coordinates of M' are obtained by multiplying the coordinates of M by 1/2:

M'((1/2)4, (1/2)(-4)) = (2, -2)

The coordinates of N' are obtained by multiplying the coordinates of N by scale factor 1/2:

N'((1/2)×(-12), (1/2)×2) = (-6, 1)

Learn more about dilation here

brainly.com/question/26155897

#SPJ4

The given question is incomplete, the complete question is:

Triangle LMN with vertices L(6, −8), M(4, −4), and N(−12, 2) is dilated with respect to origin by a scale factor of 2 to obtain triangle L′M′N′. What are the new coordinates of  L′M′N′ ?

Answer:

Step-by-step explanation:

i think you have to times it

Answer:

To find the equation of the line passing through the points (5,-12) and (0,-2), we first need to find the slope of the line:

slope = (change in y) / (change in x)

slope = (-2 - (-12)) / (0 - 5)

slope = 10 / (-5)

slope = -2

Now that we have the slope, we can use the point-slope form of the line equation to find the equation of the line:

y - y1 = m(x - x1)

where m is the slope, and (x1, y1) is one of the given points on the line.

Let's use the point (5,-12):

y - (-12) = -2(x - 5)

y + 12 = -2x + 10

y = -2x - 2

Therefore, the equation of the line passing through the points (5,-12) and (0,-2) is y = -2x - 2.