10% of ivy tech students are dual credit students. If there are 13,129 dual credit students, how many Ivy Tech students are there?

Answer:

153.94 square centimeters.

Step-by-step explanation:

To calculate the area of a circle when the circumference is given, you can use the formula:

Circumference = 2 * pi * r, where pi is approximately equal to 3.14 and r is the radius of the circle.

We can rearrange this formula to solve for the radius:

r = Circumference / (2 * pi)

Substituting the given value of circumference:

r = 44 cm / (2 * 3.14) = 7.006 cm (rounded to three decimal places)

Now that we have the radius, we can calculate the area of the circle using the formula:

Area = pi * r^2

Substituting the value of r:

Area = 3.14 * 7.006^2 = 153.94 cm^2 (rounded to two decimal places)

Therefore, the area of the circle is approximately 153.94 square centimeters.

The total distance traveled by the car between t = 0 and t = 3 is given as follows:

c. 15 mi.

The velocity function is given as follows:

v(t) = 20 - 10t.

The distance function is the integral of the velocity function, hence it is given as follows:

d(t) = 20t - 5t².

The distance at t = 0 is given as follows:

d(0) = 20(0) - 5(0)²

d(0) = 0.

The distance at t = 3 is given as follows:

d(3) = 20(3) - 5(3)²

d(3) = 15.

Hence the total distance is given as follows:

15 - 0 = 15 mi.

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The requried inverse function is [tex]f^{-1}(y) = (y + 3)/2[/tex].

To find the inverse of y = 2x - 3, we need to solve for x in terms of y.

Starting with y = 2x - 3:

Add 3 to both sides: y + 3 = 2x

Divide both sides by 2: (y + 3)/2 = x

Therefore, the inverse of y = 2x - 3 is:

x = (y + 3)/2

We can also express this as:

[tex]f^{-1}(y) = (y + 3)/2[/tex]

Thus, the inverse function is [tex]f^{-1}(y) = (y + 3)/2[/tex]

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The item is an inelastic good at a price of 6 because it is negative and have a demand of -0.71.

The formula for elasticity of demand is Elasticity of demand = (% change in quantity demanded) / (% change in price)

The initial quantity demanded at a price of 6 and the quantity demanded at a slightly different price must be know.

Let say Initial quantity demanded is:

x = -0.7(6) + 10

x = 5.8

Assume price changes slightly to 6.01, which gives us a new quantity demanded of x:

= -0.7(6.01) + 10

= 5.793

The % change in quantity demanded will be:

= [(new quantity demanded - initial quantity demanded) / initial quantity demanded] x 100%

= [(5.793 - 5.8) / 5.8] x 100%

= -0.12%

As price has changed from 6 to 6.01, we can calculate the percentage change as follows:

% change in price = [(new price - initial price) / initial price] x 100%

= [(6.01 - 6) / 6] x 100%

= 0.17%

Elasticity of demand = (% change in quantity demanded) / (% change in price)

= (-0.12% / 0.17%)

= -0.71

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Answer:

2013 - $880,000

2019 - $640,000

Step-by-step explanation:

The office building is being depreciated linearly over 25 years, which means the annual depreciation rate is:

Depreciation rate = (Cost - Scrap value) / Useful life = ($1,000,000 - $0) / 25 = $40,000 per year

To find the book value of the building in 2013, we need to determine how many years have elapsed since 2010. Since 2013 is three years after 2010, the building has been depreciated for three years. Therefore, the book value in 2013 is:

Book value in 2013 = Cost - Depreciation = $1,000,000 - ($40,000/year x 3 years) = $880,000

To find the book value of the building in 2019, we need to determine how many years have elapsed since 2010. Since 2019 is nine years after 2010, the building has been depreciated for nine years. Therefore, the book value in 2019 is:

Book value in 2019 = Cost - Depreciation = $1,000,000 - ($40,000/year x 9 years) = $640,000

Therefore, the book value of the building was $880,000 in 2013 and will be $640,000 in 2019.

The proportional relationship used to find B, the area of the base with a volume of V, is given as follows:

B = V/6.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

From the table given in the image at the end of the answer, we have that the base area is a sixth of the volume, hence the equation is:

B = V/6.

The table is given by the image presented at the end of the answer.

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Answer:

The inverse tangent of 3/1 can be found using a scientific calculator or graphing calculator by taking the arctan(3/1), which gives the angle in radians. To convert to degrees, we can multiply by 180/π. Rounding to the nearest degree gives:

arctan(3/1) = 71.57° ≈ 72°

Therefore, the answer is option C: 72°.

Answer:

The artist used 1680 colored squares of glass.

The graph that best shows `y=x^2` translated `2` units down is graph d

From the question, we have the following parameters that can be used in our computation:

y = x^2

When the function y=x^2` is translated `2` units down, we do the following

We subtract 2 from the function equation

So, we have

y = x^2 - 2

This means that the translated function is 2 units below the function y = x^2

From the list of options, this is represented with graph (d)

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Answer: 132 cubic cm

Step-by-step explanation: 6 x 5 x 3= 90 + 42

Kathy worked 9.14 hours for Job A and 18.86 hours for job B to make 186.10

Assuming hours of work for job A is x while that of job B is y

According to the given information, Kathy works a total of 28 hours per week

x + y = 28

Job A pays $6.10 per hour, and Job B pays $6.80 per hour, to make $184.10, we have the equation below

6.10x + 6.80y = 184

x + y = 28

6.10x + 6.80y = 184

solving simultaneously using calculator

x = job A = 9.143 = 9.14 (to 2 decimal places)

y = job B = 18.857 = 18.86 to 2 decimal places))

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Answer:2/3 or approximately 0.667.

Step-by-step explanation:

total number of outcomes =6

We can obtain a sum of 6: rolling a 1 and a 5, or rolling a 2 and a 4.

Therefore, the number of outcomes that do not result in a sum of 6 is:

6 - 2 = 4

So the probability of getting a sum that is not 6 is:

P(sum is not 6) = number of outcomes that do not result in a sum of 6 / total number of possible outcomes

P(sum is not 6) = 4 / 6

P(sum is not 6) = 2 / 3

The possible first mistake Noah made in the evaluation of the sine and cosine of the acute angles of a right triangle is that the acute angles are complementary and are not always congruent. The correct option is the  option (A).

(A) Angles ∠B and ∠C are complementary, not congruent

Complementary angles are angles that when added together are equivalent to 90°

The possible two column table Noah used to attempt to prove that cos(θ) = sin(θ) obtained in a similar proof on the website can be presented as follows;

Statement [tex]{}[/tex]                   Reason

1 m∠B = θ [tex]{}[/tex]                   The acute angles in a right triangle are congruent

2 sin(θ) = AB/BC    [tex]{}[/tex]     Definition of sine

3 cos(m∠B) = AB/BC [tex]{}[/tex] Definition of cosine

4 cos(θ) = AB/BC [tex]{}[/tex]       Substitution

5 cos(θ) = sin(θ) [tex]{}[/tex]         Substitution

Part of the question is; What is the first mistake in Noah's statement used to prove that cos(θ) = sin(θ)

The first mistake is the statement and reason that angle m∠B = θ because all acute angles are congruent.

The acute angles in the right triangle are ∠B and ∠C

The sum of the acute angles in a right triangle is; ∠B + ∠C = 90°

Therefore the acute angles in a right triangle are always complementary, and not always congruent.

The correct option is therefore the option (A)

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Answer:

The correct number line that shows the solutions to x+8 > 15 is option B.

Step-by-step explanation:

The correct number line that shows the solutions to x+8 > 15 is option B.

On this number line, you can see that the values of x that make the inequality true are greater than 7. Therefore, the solution set for this inequality is x > 7.

The function whose graph matches this one y= 4 sin (π/7 x) - 2

As, The general form of a sine function is

y= A sin (kx) + C........(1)

From the given graph the maximum value of the function is 2 and minimum value of the function is -6.

So, Amplitude= (Max- Min)/2

A = (2- (-6))/2

A= 8/2

Amplitude= 4

Now, The function complete a cycle in 14 units, so period of the function is 14.

2π/k= 14

k = π/7

and, Midline= (Min + Max)/2 = (2-6)/2 = -2

So, the function is

y= A sin (kx) + C.

y= 4 sin (π/7 x) - 2

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Answer: Correct answer is B

Step-by-step explanation:

Remember that the coordinates (−1,π4) tell us the radius r=−1 and the angle θ=π4. So the point should be on the circle labeled 1 and form an angle of π4 with the negative x-axis. Point B is the correct point.

Answer:

[tex]a_{n}[/tex] = 5n + 20

Step-by-step explanation:

there is a common difference between consecutive terms in the sequence

30 - 25 = 35 - 30 = 5

this indicates the sequence is arithmetic with explicit formula

[tex]a_{n}[/tex] = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = 25 and d = 5 , then

[tex]a_{n}[/tex] = 25 + 5(n - 1) = 25 + 5n - 5 = 5n + 20

If professor Snozz earns 8% of "total-sales", then the amount that the professor make on selling of 300 copies is $708.

In order to find out how much Professor Snozz makes, we first calculate the "total-sales" revenue of the 300 copies of the book;

⇒ Total sales revenue = (number of copies sold) × (price per copy),

⇒ Total sales revenue = 300 × $29.50,

⇒ Total sales revenue = $8850;

Next, we calculate amount of royalty that Professor Snozz earns, which is 8% of the total sales revenue;

So, Royalty = 8% of "Total sales revenue";

⇒ Royalty = 0.08 × $8850,

⇒ Royalty = $708;

Therefore, Professor Snozz earns $708 as a royalty for selling 300 copies of his book.

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1. Daily cost of keeping the bulb lit for 5 hours is 5 cents.

2. Switching to an LED bulb could save $13.50 in a year.

Power consumed by the 100-watt bulb in 5 hours is:

= 100 watts x 5 hours

= 500 watt-hours

= 0.5 kilowatt-hours

The cost of electricity for 0.5 kilowatt-hours at a rate of 10 cents per kilowatt-hour is:

= 0.5 kWh x 10 cents/kWh

= 5 cents

b. The power consumed by the 26-watt LED bulb over 5 hours is:

= 26 watts x 5 hours

= 130 watt-hours

= 0.13 kilowatt-hours

The cost of electricity for 0.13 kilowatt-hours at a rate of 10 cents per kilowatt-hour is:

= 0.13 kWh x 10 cents/kWh

= 1.3 cents

Annual savings is:

= (Daily cost 100-watt bulb - Daily cost LED bulb) * 365 days

= (5 cents - 1.3 cents) x 365 days

= $13.50.

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The triangle which can be drawn as per the condition described is only option 2. an isosceles triangle with measure  20° and 80°.

Triangle which can be drawn as per the measurements are,

An acute triangle with sides measuring 7, 4, 2.

In an acute triangle, the square of the longest side is less than the sum of the squares of the other two sides.

According to the Pythagorean theorem.

7²< 4² + 2²

49 < 16 + 4

49 < 20

This is a contradiction, since 49 cannot be less than 20.

It is not possible to draw triangle.

An isosceles triangle with measures of angle 20° and 80°.

Sum of interior angles  of a triangle is 180°

Here, third angle = 180° - ( 20° + 80° )

⇒Third angle = 80°

Two angles are congruent ⇒ opposite sides to congruent angles are also congruent.

It forms a isosceles triangle.

An obtuse triangle with sides measuring 5, 10 and 15.

Side lengths 5, 10, and 15 do not form a triangle at all.

Since the sum of the two shorter sides is less than the longest side.

5 + 10 = 15

It is not possible to have an obtuse triangle with sides measuring 5, 10, and 15.

An scalene triangle with angle measuring 110° and 35°.

Sum of the interior angles is always 180°.

Measure of the third angle ,

180° - 110° - 35° = 35°

Three angles of the triangle measure 110°, 35°, and 35°.

It represents isosceles triangle.

Therefore, the possible triangle as per the given condition is only option 2. isosceles triangle with measure 20° and 80°.

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If a₁ = 9 and sequence aₙ = -3aₙ₋₁ , then the value of a₅ is approximately equal to 729.

To find the value of a₅, we need to use the recursive formula provided, which relates each term in the sequence to the previous one. The formula given is a bit unusual, as it defines each term in terms of the negative three times the previous term. However, we can use this information to work out the value of a₅.

Starting with a₁ = 9, we can use the recursive formula to find the next few terms of the sequence:

a₂ = -3a₁ = -3(9) = -27

a₃ = -3a₂ = -3(-27) = 81

a₄ = -3a₃ = -3(81) = -243

a₅ = -3a₄ = -3(-243) = 729

Therefore, the value of a₅ is 729. We can check that this is correct by verifying that it satisfies the given recursive formula:

a₄ = -3a₃ = -3(81) = -243

a₅ = -3a₄ = -3(-243) = 729

This confirms that our solution is correct.

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Answer:

To find the coordinates for all three possible locations of the fourth vertex, we need to consider the three different ways that a parallelogram can be formed on a 9 by 9 grid.

Method 1: The fourth vertex is directly below the first vertex.

In this case, the coordinates of the fourth vertex are (5, 9), as shown below:

Y 9 8 7 6 5 4 3 2 1 0

X 1 2 3 4 5 6 7 8 9

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . X

Method 2: The fourth vertex is directly to the right of the first vertex.

In this case, the coordinates of the fourth vertex are (1, 5), as shown below:

Y 9 8 7 6 5 4 3 2 1 0

X 1 2 3 4 5 6 7 8 9

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

X . . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

Method 3: The fourth vertex is diagonal to the first vertex.

In this case, the coordinates of the fourth vertex are (5, 5), as shown below:

Y 9 8 7 6 5 4 3 2 1 0

X 1 2 3 4 5 6 7 8 9

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . X . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

Therefore, the coordinates for all three possible locations of the fourth vertex are (5, 9), (1, 5), and (5, 5).

The product between the complex numbers gives:

(-2 + 8i)*(-2 + 6i) = -44 - 28i

Here we have the product of two complex numbers.

It is (-2 + 8i)*(-2 + 6i)

Expanding that we will get:

(-2 + 8i)*(-2 + 6i) = (-2)*(-2) + (-2)*(6i) + (-2)*(8i) + (8i)*(6i)            

Remember that i² = -1, then we will get:

(-2)*(-2) + (-2)*(6i) + (-2)*(8i) + (8i)*(6i)  = 4 - 12i - 16i - 48

                                                            = -44 - 28i

Then the expression simplified is:

(-2 + 8i)*(-2 + 6i) = -44 - 28i

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Answer:

figure A = square ( All sides are equal)

figure B = Rectangle (Two sides are equal)

Figure C = parallelogram (is a four-sided polygon (a quadrilateral) in which opposite sides are parallel and equal in length)

The proof for the above is given as  follows:

∠A ≅ ∠C -  Given

BD ⊥ ∠ABC - Given
AC ⊥ BD - Angle Bisector Theorem

According to the angle bisector theorem, a triangle's opposing side is split into two segments that are proportionate to its other two sides. A ray that splits a given angle into two equal angles is known as an angle bisector.

Thus, it is correct to state that AC ⊥ BD according to the angle bisector theorem.

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Answer:

[tex]100000( {.70}^{3} ) = 34300[/tex]

The number of hours when the two stocks would be the same is 1.68 hours.

The first step is to determine the price of stock A at noon.

Price of stock A at noon = price at 9am + (rate of increase per hour x time difference)

Time difference = 12 - 9am = 3 hours

= $13.92 + (0.11 x 3)

= $13.92 + 0.33

= $14.25

Value of stock A t hours after noon = $14.25 + (0.11 x t)

= $14.25 + 0.11t

The equation that can be used to determine the price of stock B at time t is:

Price of stock B at time t = beginning price - (rate of decline x time)

= $14.67 - (0.14 x t)

= $14.67 - 0.14t

When the two stocks are the same, the two equations would be equal to each other:

$14.25 + 0.11t = $14.67 - 0.14t

solve for t:

0.11t + 0.14t = $14.67 - $14.25

0.25t = 0.42

t = 0.42 / 0.25

t = 1.68 hours

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Journal entries are a record of financial transactions in chronological order, showing the accounts and amounts debited and credited for each transaction. Below is the journal entries of the transactions:

Constitutes the journal entries :-

Below are the debit and credit entries for each transaction:

Dec. 1:

Debit: Cash (55,000)

Credit: Common Stock (55,000)

Debit: Equipment (9,000)

Credit: Cash (9,000)

Debit: Prepaid Insurance (1,500)

Credit: Cash (1,500)

Dec. 9:

Debit: Land (16,000)

Credit: Cash (16,000)

Dec. 10:

Debit: Office Supplies (2,000)

Credit: Accounts Payable (2,000)

Dec. 19:

Debit: Cash (12,000)

Credit: Notes Payable (12,000)

Dec. 22:

Debit: Advertising Expense (1,700)

Credit: Cash (1,700)

Dec. 26:

Debit: Accounts Payable (300)

Credit: Cash (300)

Dec. 28:

Debit: Utilities Expense (180)

Credit: Accounts Payable (180)

Dec. 31:

Debit: Cash (16,600)

Debit: Accounts Receivable (2,600)

Credit: Service Revenue (17,600)

Debit: Salary Expense (3,800)

Debit: Rent Expense (1,300)

Credit: Cash (5,100)

Debit: Unearned Revenue (1,400)

Credit: Cash (1,400)

Debit: Cash Dividends (4,000)

Credit: Cash (4,000)

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Answer:6

Step-by-step explanation:

7w-6 + 8w+6 = 90

15w=90

w=90/15

w=6

The true statements about the samples:

Both groups have the same median (4).

Group A has a lower mean than Group B (4 vs 4.25).

Both groups have multiple modes.

The range of values in Group B is greater than in Group A.

For Group A, the average number is 4 with a range of numbers from 2 to 6. The middle value, also known as the median, is 4.

Using this information, we find that values 3, 4, and 5 occur twice each within the dataset.

For Group B, the mean, or average, number is found to be 4.25 among eight total entries ranging from a low of 1 to a high of 7.

Calculating for the middle value, which is defined as the median, it can be seen that the resulting output is again equivalent to 4. Of all data inputs, the two top-occurring amounts are 4 and 5, both appearing twice in the listing.

Here are the true statements about the samples:

Both groups have the same median (4).

Group A has a lower mean than Group B (4 vs 4.25).

Both groups have multiple modes.

The range of values in Group B is greater than in Group A.

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A company sampled two groups of students and asked them "How many books did you read this month?" The table shows the data they collected:

Group A: [3, 4, 5, 2, 5, 6, 3, 4]

Group B: [1, 6, 4, 5, 2, 5, 4, 7]