At December 31, the records of Nortech Corporation provided the following selected and incomplete data:
Common stock (par $1; no changes during the current year).
Shares authorized, 500,000.
Shares issued, 2; issue price $12 per share.
Common Stock account, $100,000.
Shares held as treasury stock, 2,000 shares, cost $10 per share.
Net income for the current year, $24,500.
Dividends declared and paid during the current year, $14,700.
Retained Earnings balance, beginning of the year, $145,000.
Required:
Complete the following: TIP: To determine the number of shares issued, divide the balance in the Common Stock account by the par
value per share. (Round "per share" answers to 2 decimal places.)
1-a. Shares authorized
1-b. Shares issued
1-c. Shares outstanding
2. The balance in Additional Paid-in Capital would be
3. Earnings per share is
4. Dividends paid per share of common stock is
5. Treasury stock should be reported in the stockholders' equity section of the balance
sheet in the amount of
6. Assume that the board of directors approved a 2-for-1 stock split. After the stock split,
the par value per share will be
500,000
290,000

The probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 8/25 or 0.32 (rounded to the nearest millionth).

1. Calculate the total number of students on the Student Government Board by summing up the numbers in the table:

  Total Students = 2 + 2 + 2 + 4 + 0 + 3 + 4 + 2 = 19

2. Calculate the total number of graduate students on the Student Government Board:

  Total Graduate Students = 2 + 0 = 2

3. Calculate the total number of students living in on-campus housing:

  Total On-Campus Housing = 2 + 2 + 0 + 4 + 2 = 10

4. Calculate the probability of selecting a graduate student from the Student Government Board by dividing the total number of graduate students by the total number of students:

  Probability of Graduate Student = Total Graduate Students / Total Students = 2 / 19

5. Calculate the probability of selecting a student living in on-campus housing by dividing the total number of students in on-campus housing by the total number of students:

  Probability of On-Campus Housing = Total On-Campus Housing / Total Students = 10 / 19

6. Calculate the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing by summing up the probabilities from steps 4 and 5:

  Probability = Probability of Graduate Student + Probability of On-Campus Housing = 2 / 19 + 10 / 19

7. Simplify the fraction if necessary. In this case, the fraction cannot be simplified further, so the final probability is 2 / 19 + 10 / 19 = 12 / 19.

8. Convert the fraction to a decimal by dividing the numerator by the denominator: 12 / 19 ≈ 0.631578947, which rounds to 0.632 (rounded to the nearest thousandth).

9. Finally, express the probability as a fraction in lowest terms: 12 / 19 is already in lowest terms.

Therefore, the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 12/19 or approximately 0.632 (rounded to the nearest thousandth).

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Answer:

D

Step-by-step explanation:

median because it indicates the expected range of gas prices

Answer:

\(n=2\frac{1}{3}\)

Step-by-step explanation:

Im assuming you mean

\(11-2n=4-5n\)

Solve

\(11-2n=4-5n\)

add \(5n\) to both sides

\(11+3n=4\)

subtract \(11\) from both sides

\(3n=-7\)

divide both sides by 3

\(n=2\frac{1}{3}\)

Answer:

Below

Step-by-step explanation:

Find unit rate (since it starts at 0,0)

at 45 seconds  it is 900 bottles

             900 bottles / 45 seconds = 20 bottle / sec

20 bottles / sec * 80 sec = 1600 bottles

In order to calculate the value of 2x + 5 if x=10, we would need to substitute in the expression 2x + 5 the variable x with the number 10.

Therefore, 2x + 5 if x=10 would be equal to:

2(10)+5=20+5=25

Therefore, the value of 2×+5​ if x=10 would be 25

Answer:

10 shirts, 6 pants

Step-by-step explanation:

Let y = the number of shirts

Let x = the number of pants

y + 2 = 2x

x + y = 16

y = 2x - 2

x + (2x - 2) = 16

3x = 18

x = 6

y + 6 = 16

y =  10

Answer:

\(\textsf{A.} \quad \begin{cases}y=2x-2\\x+y=16\end{cases}\)

\(\textsf{B. \quad 6 pants and 10 shirts}\)

Step-by-step explanation:

Given variables:

If the number of shirts Sylvia packed was 2 fewer than twice the number of pants she packed:

\(\implies y=2x-2\)

If the total number of pairs of pants and shirts was 16:

\(\implies x+y=16\)

Therefore, the system of equations that represents the problem is:

\(\begin{cases}y=2x-2\\x+y=16\end{cases}\)

System of equations:

\(\begin{cases}y=2x-2\\x+y=16\end{cases}\)

Substitute the first equation into the second equation and solve for x:

\(\implies x+2x-2=16\)

\(\implies 3x-2=16\)

\(\implies 3x=18\)

\(\implies x=6\)

Substitute the found value of x into the first equation and solve for y:

\(\implies y=2(6)-2\)

\(\implies y=12-2\)

\(\implies y=10\)

Therefore, Sylvia packed:

I can't see the diagram sorry.

Step-by-step explanation:

Is there supposed to be a picture attached?

The final answer is (f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

To find the composite functions (f o g)(x) and (g o f)(x), we need to substitute one function into the other.

(f o g)(x):

To find (f o g)(x), we substitute g(x) into f(x):

(f o g)(x) = f(g(x))

Let's substitute g(x) = x^2 - 8 into f(x) = x^2 + 8:

(f o g)(x) = f(g(x)) = f(x^2 - 8)

Now we replace x in f(x^2 - 8) with x^2 - 8:

(f o g)(x) = (x^2 - 8)^2 + 8

Simplifying further:

(f o g)(x) = x^4 - 16x^2 + 64 + 8

(f o g)(x) = x^4 - 16x^2 + 72

Therefore, (f o g)(x) = x^4 - 16x^2 + 72.

(g o f)(x):

To find (g o f)(x), we substitute f(x) into g(x):

(g o f)(x) = g(f(x))

Let's substitute f(x) = x^2 + 8 into g(x) = x^2 - 8:

(g o f)(x) = g(f(x)) = g(x^2 + 8)

Now we replace x in g(x^2 + 8) with x^2 + 8:

(g o f)(x) = (x^2 + 8)^2 - 8

Simplifying further:

(g o f)(x) = x^4 + 16x^2 + 64 - 8

(g o f)(x) = x^4 + 16x^2 + 56

Therefore, (g o f)(x) = x^4 + 16x^2 + 56.

(f o g)(2):

To find (f o g)(2), we substitute x = 2 into the expression (f o g)(x) = x^4 - 16x^2 + 72:

(f o g)(2) = 2^4 - 16(2)^2 + 72

(f o g)(2) = 16 - 64 + 72

(f o g)(2) = 24

Therefore, (f o g)(2) = 24.

In summary:

(f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

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The solution to the system of equations is x = -3 and y = -4.

To solve the system of equations:

Equation 1: 2x - y = -10

Equation 2: 3x + 2y = -1

We can use the method of substitution or elimination to find the values of x and y.

Let's use the method of elimination:

Multiply Equation 1 by 2 to make the coefficients of y in both equations equal:

2(2x - y) = 2(-10)

4x - 2y = -20

Now, we can eliminate y by adding Equation 2 and the modified Equation 1:

(3x + 2y) + (4x - 2y) = -1 + (-20)

7x = -21

x = -3

Substitute the value of x into Equation 1 to solve for y:

2(-3) - y = -10

-6 - y = -10

y = -10 + 6

y = -4

Therefore, the solution to the system of equations is x = -3 and y = -4.

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Answer:

-3

Step-by-step explanation:

Answer: The slope whould be 3

Step-by-step explanation:

Graph the line using the slope and y-intercept, or two points.

Slope: 3

y-intercept:

(0,0)

x|y

----

0|0

1|3

The total centimeters that the plants grew in all was 200 centimeters or 2.00 centimeters when written as a decimal.

Centimetres (cm) is a unit of length in the metric system, equal to one-hundredth of a metre. It is commonly used in everyday life, for example when measuring the height of a person or the size of a room. Centimetres are also used in scientific and engineering measurements, such as the size of an object or the distance between two points. Centimetres are divided into millimetres, which are one-thousandth of a metre.

This can be written as a decimal as 2.00 centimeters.

To determine the total centimeters, we simply add the individual centimeter measurements of the two plants.

Daysha's plant grew 100 centimeters and India's plant grew 100 centimeters.

Therefore, the total centimeters that the plants grew in all was 200 centimeters, or 2.00 centimeters when written as a decimal.

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Answer:

c

Step-by-step explanation:

thats the answerrrrrrrr

Answer:

c

Step-by-step explanation:

edg 2021

Answer:

Corresponding Angles

Step-by-step explanation:

9514 1404 393

Answer:

  n(t) = 20,000/(1 +99e^(-0.7033t))

Step-by-step explanation:

One way to write the logistic function is ...

  n(t) = L/(1 +a·e^(-kt))

where L is the maximum value and parameters 'a' and k depend on boundary conditions.

Here, we have n(∞) = L = 20,000 and n(0) = L/(1+a) = 200. We also have n(1) = L/(1+a·e^-k) = 400.

Solving for 'a', we get ...

  n(0) = 20000/(1+a) = 200

  20000/200 -1 = a = 99

Solving for k, we get ...

  n(1) = 20000/(1 +99e^-k) = 400

  20000/400 -1 = 99e^-k = 49

  e^-k = 49/99

  k = -ln(49/99) ≈ 0.7033

So, the desired function is ...

  n(t) = 20000/(1 +99e^(-0.7033t))

Answer:

Joint probability table :

_____ A _____ A'

_ Y_ 0.45 ___ 0.30

_ Y'_ 0.05___ 0.20

No

No

Step-by-step explanation:

Given :

Sample, size n = 500

A = driver is under the influence of alcohol :

Y = driver is less than 30 years old

P(A) = 275 / 500 = 0.55

P(Y) = 375 / 500 = 0.75

P(AnY) = 225 / 500 = 0.45

P(YnA') = (1 - 225/375)*0.75 = 0.4 * 0.75 = 0.30

Joint probability table :

_____ A _____ A'

_ Y_ 0.45 ___ 0.30

_ Y'_ 0.05___ 0.20

To determine if it is mutually exclusive : P(AnY) = 0

P(AnY) = 0.45 ; hence, it is not mutually exclusive

For A and Y to be independent ; P(A|Y) = P(A) ;

P(A|Y) = P(AnY) / P(Y)

P(A|Y) = 0.45 / 0.75 = 0.6

Hence, A and Y are not independent.

Answer:

(2.5, -3.25)

Step-by-step explanation:

In relictions, only one value in the coordinate changes, either the x or y value depending on the type of reflection

First, reflect the coordinate over the x-axis.

Reflections across the x-axis is basically folding the graph across the x-axis. If you fold the graph across the x-axis, you notice that only the y-value is changing to be the opposite sign.

Basically in a reflection of the x-axis, the coordinates (x, y) change to (x, -y)

Therefore, (-2.5, -(3.25)) turns into (-2.5, -3.25)

Next, reflect the coordinate (-2.5, -3.25) across the y-axis. Similarly as above, reflections across the y-axis is like folding the graph on its y-axis. If you do so, you notice that only the x-value changes while the y-values stays the same.

Therefore (x,y) turns into (-x, y)

So, (-2.5, -3.25) = (-(-2.5), -3.25) = (2.5, -3.25)

Answer:

\((2.5 , -3.25)\)

When you do a reflection, the negative values turn positive and the positive values turn negative.

Currently in the graph, the ordered pair is (-2.5, 3.25).

So, we will flip the two around.

Now, we will put them into an ordered pair again.

Our new ordered pair will be (2.5, -3.25)

Best of Luck!

The values of a and b are a = -3 and b = 42. The solutions for x can be written as:

x = -3 - √42

x = -3 + √42

To solve the quadratic equation 2x² + 12x = 66 by completing the square, we need to follow these steps:

Step 1: Move the constant term to the right side:

2x² + 12x - 66 = 0

Step 2: Divide the equation by the leading coefficient (2):

x² + 6x - 33 = 0

Step 3: To complete the square, we take half of the coefficient of x, square it, and add it to both sides of the equation:

x² + 6x + (6/2)² = 33 + (6/2)²

x² + 6x + 9 = 33 + 9

x² + 6x + 9 = 42

Step 4: Rewrite the left side as a perfect square:

(x + 3)² = 42

Step 5: Take the square root of both sides:

√(x + 3)² = ±√42

x + 3 = ±√42

Step 6: Solve for x:

x = -3 ± √42.

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Step-by-step explanation:

i am very sorry but I don't know the answer

Answer:

\(16\sqrt{2}\)

Step-by-step explanation:

The given triangle shown is a 45-45-90. We can use this picture attached to figure out BC.

n in this case is 16ft

Based on the picture, we can get BC's length, which is n\(\sqrt{2}\)

BC = \(16\sqrt{2}\)

Answer:

3+4x

7-12

2x+14=18

four times a number

four times a number is added to seven

Step-by-step explanation:

Step-by-step explanation:

x + y = -8

x = 12

so,

12 + y = -8

y = -20

Answer:

Step-by-step explanation:

x can be one number while z can be an other one

so x+z=-8

we have on value so

12+z=-8

so now lets crack the question

z=-8-12

so - - =+ so it will be -20 please support worked really hard

Compound amount is:

Initial amount (p) = 350000.

Time (t) = 7

n = 4 (quarterly)

r (interest rate) = 16%

Answer:

look at the photo........................

To find the point (0,_), evaluate g(0):

Hence, the point is (0,2)

In the same way, for the point (1 , _ ), evaluate g(1):

Hence, the point is (1,-1)

Answer:

x = 1, x = 5

Step-by-step explanation:

Solutions to a graph are where x=0 or where the function crosses the x axis. It is difficult to see the numbers but if we assume it goes up one number for each line we find that the line crosses the x axis at 1 and 5.

Answer: 162000

Step-by-step explanation:

Reduce the expression, if possible, by cancelling the common factors.

162000

\(\displaystyle\\Answer:\ (\frac{6}{125})^4\)

Step-by-step explanation:

\(\displaystyle\\(\frac{125}{6} )^{-4}=\\\\(\frac{6}{125})^{-(-4)}= \\\\(\frac{6}{125})^4\)

The complete table will be;

 Statement                                                   Reason

1. Y is the midpoint of UW and VX                   Given

2. UY = WY ,                                              Definition of midpoint

3. VY = XY                                                Definition of midpoint

4. ∠UYX ≅ ∠VYW                                      Vertical angle theorem

5. ΔUYX ≅ ΔVYW                                     Side Angle Side (SAS)    

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Y is the midpoint of UW and VX.

Now,

Since, Y is the midpoint of UW and VX.

So, We get;

UY = WY

And, VY = XY

Hence, The complete table will be;

 Statement                                                   Reason

1. Y is the midpoint of UW and VX                   Given

2. UY = WY ,                                              Definition of midpoint

3. VY = XY                                                Definition of midpoint

4. ∠UYX ≅ ∠VYW                                      Vertical angle theorem

5. ΔUYX ≅ ΔVYW                                     Side Angle Side (SAS)    

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Step-by-step explanation:

c = number of cars used

v = number of vans used

5c + 12v = 60

as the sum of all students in cars and vans must be 60.

but this does not consider solutions with partly filled cars or vans.

Answer:

A, D, G, H

Step-by-step explanation:

Look at the pink(or purple) lines. R and F both have 4 lines, so they're congruent. S and G both have 1 line, so those are congruent too.

-hope it helps

Answer:

1st option: ∠S ≅ ∠G

4th option: ∠T ≅ ∠H

7th option: ∠Q ≅ ∠E

8th option: ∠R ≅ ∠F

Step-by-step explanation:

Side lengths are unnecessary you just look at those loop things. Angles with the same number of "loops" are congruent like how ∠Q and ∠E both have 3 "loops", this means those angles are congruent.

(b) The probability that the call is not for medical assistance = 0.37

(c) The probability that two successive calls will both be for medical assistance = 0.3969

(d) The probability that the first is for medical assistance and the second is not for medical assistance = 0.2331

(e) The probability that exactly one of the next two calls is going to be for medical assistance = 0.4662

The probability of an event is the proportion of favourable outcomes to all other possible outcomes. The symbol x can be used to denote how many successful outcomes there were in an experiment with 'n' outcomes. The formula below can be used to determine a given event's probability:

Probability (Event) = Positive Results/Total Results

                                 = x/n

Given P (call for medical assistance) = 0.63

This means that out of all incoming calls to the fire station, the probability that the call is for medical assistance is 0.63 or 63%. The complement of this event, which is the probability that an incoming call is NOT for medical assistance, is:

P (Not Medical Assistance) = 1 - P (Medical Assistance)

                                            = 1 - 0.63

                                            = 0.37

Now, assuming that successive calls are independent of one another, the probability that two successive calls will both be for medical assistance will be:

P (2 calls for medical assistance)

= 0.63 × 0.63

= 0.3969

The probability that the first is for medical assistance and the second is not for medical assistance will be:

P (1st for medical assistance × 2nd for not medical assistance)

= 0.63 × 0.37

= 0.2331

The probability that exactly one of the next two calls is going to be for medical assistance will be:

P (Exactly 1 call for medical assistance)

= (0.63×0.37) + (0.63×0.37)

= 0.2331 + 0.2331

= 0.4662

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