A company was formed with $61,100 cash contributed by its owners in exchange for common stock. The company borrowed $31,100 from a bank. The company purchased $11,100 of inventory and paid cash for it. The company also purchased $71,100 of equipment by paying $10,000 in cash and issuing a note for the remainder.

What is the amount of the total liabilities to be reported on the balance sheet?

Answer:

C) (-6,0)(2,0)

For x-intercept, f(x) = 0:

\({ \tt{ {x}^{2} + 4x - 12 = 0 }} \\ { \tt{(x - 2)(x + 6) = 0}} \)

Answer:

C) (-6,0)(2,0)

Step-by-step explanation:

f(x)= x²+4x-12

(x-2)(x+6)=0

x=2

x=-6

The number of turns the wheel makes is 1.93 ≈ 2.

What is Turns?

This is referred to as a cycle. It is a unit of plane angle measurement that is equivalent to 2π radians, 360 degrees, or 400 gradians.

formular for calculating Turns:

Turns =         Lenght

              Circumference

Circumference of a circle, C= πD

Where,

Diameter=D

            π =22/7

Calculating Circumference;

C= 22  * 66

            7

    =207.4

From the question:

D= 66cm

L  =400m

Calculating Turns:

Turns =  Lenght

              Circumference

          =   400m

               207.4

      Turns =1.93

Turns =1.93≈ 2

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Answer:

Step-by-step explanation:

a) To find the average life of the ten batteries, we need to calculate the mean, which is the sum of all the values divided by the number of values.Sum of all values = 10.8 + 10.6 + 11.4 + 8.9 + 10.1 + 10.6 + 9.9 + 12.6 + 10.5 + 11.9 = 106.2

Number of values = 10

Average life = Sum of all values / Number of values = 106.3 / 10 ≈ 10.63

Therefore, the average life of the ten batteries, rounded to the nearest tenth of an hour, is approximately 10.6 hours.

b) Comparing the two advertisements:

i) The first advertisement claims that Atlas batteries are guaranteed to last 10 hours. This means that all Atlas batteries are expected to last at least 10 hours. However, based on the data provided, we can see that the average life of the batteries is approximately 10.6 hours, which is higher than the guaranteed 10-hour minimum

ii) The second advertisement claims that Atlas batteries have an average life of over 10 hours. This statement aligns with the data we have, as the average life of the batteries is indeed over 10 hours.

Based on the information provided, the second advertisement claiming that Atlas batteries have an average life of over 10 hours is more accurate, as the average life calculated from the given data is 10.6 hours.

In summary, the average life of the ten batteries is approximately 10.6 hours, and the second advertisement stating an average life of over 10 hours is more accurate based on the data provided.

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The maximum revenue possible in this situation is 15625/A dollars, where A is the coefficient in the quadratic equation.

To find the maximum revenue possible in this situation, we can use the concept of vertex or the vertex form of a quadratic equation.

The revenue equation is given by R = -Ax^2 + 250x, where A is a constant coefficient.

The maximum revenue occurs at the vertex of the parabolic curve represented by the equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.

In this case, a = -A and b = 250. Plugging in these values, we get:

x = -250 / (2 * (-A))

= 125 / A

To find the maximum revenue, we substitute this value of x into the revenue equation:

R = -A * (125 / A)^2 + 250 * (125 / A)

= -A * (15625 / A^2) + (31250 / A)

= -15625 / A + 31250 / A

= 15625 / A

The maximum revenue is given by 15625 / A. The value of A is not specified in the question, so we cannot determine the exact maximum revenue without knowing the value of A. However, we can say that the maximum revenue increases as A decreases.

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Part (a)

\(R(1)=\frac{2000(1)^2}{1^2+4}=400\)

Part (b)

\(R(2)=\frac{2000(2)^2}{2^2+4}=1000\)

Answer:

(a) 400

(b) 1000

Answer:

Center ( -8, 1 )

Radius ( 13 )

Answer:

24

Step-by-step explanation:

For this problem, you need to find the greatest common factor because you need to divide all of the materials equally into identical sets.

If you factor out the numbers 48, 72, and 120, (same # of blue, green, and yellow crayons) you'll get the GCF of 24.

48 - 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

72 - 1, 2, 3, 4, 18, 6, 8, 9, 12, 24, 36, 72

120 - 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

The greatest common factor in all of these lists is 24.

Therefore, the largest number of identical sets is 24.

(2 blue crayons, 2 green crayons, 2 yellow crayons, 3 red crayons, 5 colored pictures)

Answer:

24

Step-by-step explanation:

The length of the side c, to the nearest integer is 12.

Cosine law is a formula relating the length of the sides of a triangle to the cosine of one angle of the triangle.

u² = s² + t² - 2(s)(t)·cos U

In ΔABC, m < C = 50* , a = 14 and b = 15.

We can solve for the length of side a to the nearest whole number using the Laws of Cosines

c² = b² + a²- 2ba CosC

Solving for the value of a, we have:

c² = 15² + 14²- 2(15)(14)cos50°

c² = 225 + 196 - 269.97

c² = 151.029

c = 12.28

Hence, The length of the side c, to the nearest integer is 12.

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Answer:

22ax

Step-by-step explanation:

(5x)(2a) + (3x)(4a) = 10ax + 12 ax = 22ax

Answer:

the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).

Step-by-step explanation:

To solve this equation for "a", you need to simplify and rearrange the terms so that all the "a" terms are on one side of the equation and all the constant terms are on the other side. Here are the steps:

Start by combining the "a" terms on the left side of the equation: -2a - 6a = -8a. The equation now becomes: -8a - 9 = -9 - 6a - 2a.

Combine the constant terms on the right side of the equation: -9 - 2a - 6a = -9 - 8a. The equation now becomes: -8a - 9 = -9 - 8a.

Notice that the "a" terms cancel out on both sides of the equation. This means that the equation is true for any value of "a". Therefore, the solution is all real numbers, or in interval notation: (-∞, +∞).

In summary, the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).

Answer:

     y = 94

Step-by-step explanation:

Linear Pair:

The two adjacent angles whose non common arms form a straight line is called linear pair. They add up to 180

2x + 36 = 180 {linear pair}

       2x  = 180 - 36

       2x = 144

Sum of all angles of a n-sided polygon = (n-2)*180

                                                                 = ( 6-2)*180

                                                                 = 4 * 180

                                                                  = 720

y + 144 + 111 + 105 + 165 + 101 = 720

                                  y + 626  = 720

                                             y = 720 - 626

                                            \(\sf \boxed{y = 94^ \circ}\)

Answer:

94°

Step-by-step explanation:

2x + 36 = 180 (angles on a straight line)

2x = 180 - 36

2x = 144

2x = 144°

Sum of all angles of a n-sided polygon = (n-2)×180 = ( 6-2)×180

= 4 × 180

= 720

y + 144 + 111 + 105 + 165 + 101 = 720

y + 626 = 720

y = 720 - 626

y=94 °

The first function is a reflective function and the other one is translative

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The given function is f(x) = -(x+3)²-8

f(x) = -(x+3)²-8 is a reflective function.

f(x) = |x+5|+4 is a translative.

Let us solve these two functions by plotting some points from two functions.

In the given attachment we have given the graphs.

Hence, the first function is a reflective function and the other one is translative

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The solution of the linear equation  is determined as x = -4.

The solution of the linear equation is calculated by applying the following method as follows;

The given linear equation;

2/x+3 - 1/x = -4/x² +3x

We can start by simplifying the equation and getting rid of the fractions.

Multiplying every term by x will help us achieve that:

2 + 3x - 1 = -4/x + 3x²

Simplifying further:

2 + 3x - 1 = (-4 + 3x²) / x

Combining like terms:

3x + 1 = (-4 + 3x²) / x

(x)(3x + 1) = -4 + 3x²

3x² + x = -4 + 3x²

We can subtract 3x² from both sides:

x = -4

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Answer:

0.04

Step-by-step explanation:

1. 9/10 = 0.9 and 13/15 = 0.86

2. Subtract 0.9 and 0.86

3. You should end up with 0.04

Remember when a number goes like 0.86666666666 to use 0.86 or if it has 0.86666666667 to use 0.87 because you would be simplifying it.

To calculate the final amount of money at the end of the period, considering that the interest is compounded continuously you have to use the following formula:

Where

A is the accrued amount at the end of the given time

P is the principal amount

r is the annual nomial interes expressed as a decimal value

t is the time period in years

For this investment, the initial value is P= $200

The interest rate is 6%, divide it by 6 to express it as a decimal value

The time is t= 20 years

After 20 years, the amount of money in the account will be $664.02

The only equation given that represents the Exponent Property of Logs is; Option A: log(A^r) = r*log(A)

The  exponent property of logarithm says that the log of a power is the exponent times the logarithm of the base of the power. For example;

logₐ(MN) = logₐM + logₐN

logₐ(M/N) = logₐM - logₐN

logₐ(3²) = 2logₐ3

The first example above shows the product rule of logarithms

The second example shows the quotient rule of logarithms

The third rule shows the power rule

Now, looking at the options, the only one that shows the correct pattern of exponent property of logarithm is;

Option A: log(A^r) = r*log(A)

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Answer:

  D.)  because it cannot be expressed as a ratio of integers

Step-by-step explanation:

The root of any integer that is not a perfect square is irrational. 5 is not a perfect square, so is irrational—it cannot be expressed as the ratio of integers.

__

Proof

Suppose √5 = p/q, where p and q are mutually prime. Then p² = 5q².

If p is even, then q² must be even. We know that √2 is irrational, so the only way for q² to be even is for q to be even—contradicting our requirement on p and q.

If p is odd, then both p² and q² will be odd. We can say p = 2n+1, and q = 2m+1, so we have ...

  p² = 5q²

  (2n+1)² = 5(2m+1)²

  4n² +4n +1 = 20m² +20m +5

  4n² +4n = 4(4m² +4m +1)

  n(n+1) = (2m+1)²

The expression on the left will be even for any integer n; the expression on the right will be odd for any integer m. This equation cannot be satisfied for any integers m and n, so contradicting our assumption √5 = p/q.

We have shown using "proof by contradiction" that √5 cannot be the ratio of integers.

By applying the supplementary angle theorem, the magnitude of angle B (m<B) is equal to 38°.

A supplementary angle can be defined as two (2) angles or arc whose sum is equal to 180 degrees.

Mathematically, a supplementary angle can be calculated by using this formula:

Q + R = 180

Where:

Q and R are measure of the angles subtended.

m<ADC = 180° - 110°

m<ADC = 70°

Substituting the given parameters into the formula, we have;

m<ADC + m<DAC + m<ACB = 180

70 + 46 + m<ACB = 180

116 + m<ACB = 180

m<ACB = 180 - 116

m<ACB = 64°

Now, we can determine the magnitude of angle B (m<B) based on the given diagram:

m<B = 180 - (m<CAB + m<ACB)

m<B = 180 - (78 + 64)

m<B = 180 - 142

m<B = 38°

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Answer:

B) approximately normal with mean 2.3 and standard deviation 2

Step-by-step explanation:

Given the following :

Mean crimes per day = 2.3

Standard deviation = 2

Number of samples = 100

Sampling distribution of the mean:

According to the central limit theorem:

Sample mean = population mean

2.3 = 2.3

The standard deviation of the sample (s) : ratio of the population standard deviation and square root of the sample size.

s = population standard deviation / √sample size

s = 2 / √100

s = 2 / 10

s = 0.2

The central limit theorem also posits that once ths sample size is large enough, the sampling of the sample mean will be approximately normal.

Hence, the distribution is approximately normal, with mean of 2.3 and standard deviation of 0.2

Answer:

Assuming you mean (2^3)3, the answer is 24

Step-by-step explanation:

using pemdas you do 2 to the third power first

2x2=4 4x2=8

then you mutiply by the number not in parenthesis; 3

8x3 = 24

Area of the yard = 30*45 = 1350 square feet

Company A

Area of the roll of sod: 2*5 = 10 square feet

Number of roll of sod needed: 1350/10 = 135 roll of sod

Cost: 3.9*135 = $526.5

Company B

Number of pallets needed: 1350/450 = 3

Cost: 150*3 + 45 = $495

The better deal is Company B

He will save $526.5 - $495 = $31.5

The translation used to create the image of the second polygon is A, 7 units to the right.

To determine the translation used to create the image of the second polygon (A' B' C' D') from the original polygon (ABCD), compare the corresponding vertices.

Original polygon (ABCD):

A (-2, -1)

B (0, -4)

C (4, -4)

D (2, -1)

Image polygon (A' B' C' D'):

A' (5, -1)

B' (7, -4)

C' (11, -4)

D' (9, -1)

To find the translation, calculate the horizontal and vertical differences between the corresponding vertices.

Horizontal difference:

For point A: A'x - Ax = 5 - (-2) = 7

For point B: B'x - Bx = 7 - 0 = 7

For point C: C'x - Cx = 11 - 4 = 7

For point D: D'x - Dx = 9 - 2 = 7

Vertical difference:

For point A: A'y - Ay = -1 - (-1) = 0

For point B: B'y - By = -4 - (-4) = 0

For point C: C'y - Cy = -4 - (-4) = 0

For point D: D'y - Dy = -1 - (-1) = 0

From the calculations, see that the horizontal difference is 7 units for all the corresponding vertices, while the vertical difference is 0 units for all the corresponding vertices.

Therefore, the translation used to create the image of the second polygon is 7 units to the right.

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Mathematical form of the question:

Use the graph to answer the question.

Graph of polygon ABCD with vertices at A (-2, -1), B (0, -4), C (4, -4), D (2, -1). A second polygon A' (5, -1), B' (7, -4), C' (11, -4), D' (9, -1).

Determine the translation used to create the image.

7 units to the right

3 units to the right

7 units to the left

3 units to the left

Answer:

37  r10                  

explanation                                              

   0 3 7

2 3   L 8 6 1

 − 0    

   8 6  

 − 6 9  

   1 7 1

 − 1 6 1

     1 0

Answer:

252 cupcakes were mocha flavored

Step-by-step explanation:

(63*400)/100 = 25200/100 = 252

Answer:

252 cupcakes were mocha flavored.

Step-by-step explanation:

Average Minutes Per Night Spent On Homework

0 20

48 60

190

Average Minutes Per Night Spent Watching TV

0 10

20 30

50

11. What is the median for TV time?

12. What is the range of times that the middle 50% of the sophomores spend on TV per night?

13. What percent of the sophomores spend more than 30 minutes per night watc

Answer:

n = 3

Step-by-step explanation:

Hello!

p = 2n - 3

the question asks for when p is equal to 3 so we put 3 in for p

3 = 2n - 3

Now we can solve this

3 = 2n - 3

Add 3 to both sides

6 = 2n

Divide both sides by 2

3 = n

The answer is n = 3

Hope this Helps!