ABCD is a parallelogram. P is a point on AB such that LPAD = 110° and PC = BC. Calculate (a) LABC, LDCP
please do it with explanation.​

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

Answer:

The answer is C

Step-by-step explanation:

The zeros of g(x) = x³ + 6x² - 9x-54 are -6, 3, 6. Therefore, the correct answer is C.

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

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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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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The equation that represents the relationship between p and a is a = p - 6.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 0)/(7 - 6)

Slope (m) = 1/1

Slope (m) = 1.

At data point (6, 0) and a slope of 1, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 0 = 1(x - 6)  

y = x - 6 ≡ a = p - 6

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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:

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.

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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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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The symmetric property of congruence is Option C) If AB ≅ CD, then CD ≅ AB.

The symmetric property of congruence states that if one segment is congruent to another segment, then the second segment is also congruent to the first.

Therefore, the correct answer is C) If AB ≅ CD , then CD ≅ AB.

This statement shows that if segment AB is congruent to segment CD, then segment CD is also congruent to segment AB, which satisfies the definition of the symmetric property of congruence.

Answer choices A) and D) do not represent the symmetric property of congruence, as they simply state that a segment is congruent to itself or to another segment without reversing the order of the comparison.

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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:

The tip of the minute hand on a clock travels 15π inches in 45 minutes if the distance from the center to the tip is 10 inches.

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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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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The 99% confidence interval for the population proportion p is (0.776, 0.824).

To find the 99% confidence interval for a proportion, we can use the formula:

CI = p^ ± z*(SE)

where p^ is the sample proportion, SE is the standard error, and z is the critical value from the standard normal distribution corresponding to the level of confidence.

For a 99% confidence interval, the critical value z is 2.576.

Substituting the given values into the formula, we have:

CI = 0.80 ± 2.576*(0.03/√200)

Simplifying this expression, we have:

CI = 0.80 ± 0.024

This means that we are 99% confident that the true population proportion falls between 0.776 and 0.824. We can interpret this interval as a range of plausible values for the population proportion, based on the sample data.

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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 scale factor used is 1/4.

We have,

Length of sides of triangle D 24, 32, and 40.

Length of sides of triangle D' 6, 8, and 10.

So, scale factor

= length of corresponding side in D' / length of corresponding side in D

= 6/24

= 1/4

Thus, the scale factor used is 1/4.

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a) The angles outside the side PQ measure 65° and 25°

The angles outside the side QR measure 85° and 95°

The angles outside the side PR measure 55° and 35°

b) The arc PR, PQ and PR measure 120°

a)

Let us assume that the inscribed square be ABCD and equilateral triangle is PQR.

Let side PR of triangle intersects the quadrilateral at points M and N.

So, we get a triangle DMN outside the equilateral triangle.

Here, ∠DMN = 55°, ∠D = 90°

So, ∠MND = 180 - (90 + 55)

                 = 35°

Similarly,  side PQ of triangle PQR intersects the quadrilateral at points X and Y.

So, we get a triangle AXY outside the equilateral triangle.

From triangle PXM we get the measure of angle PXM which is 65 degrees.

As angle PXM and angle AXY are opposite angles, the measure of angle AXY = 65°

∠A = 90°

So, ∠AYX = 180° - (∠A + ∠AXY )

                 = 180° - (90° + 65°)

                 = 25°

Let the side QR of triangle PQR intersects the quadrilateral at points L and K.

so we get new quadrilateral LKBC

In this quadrilateral ∠B = 90°, ∠C = 90°

From triangle QYL, we get the measure of angle QLY = 95°

So, the measure of ∠KLB = 95° .......(∠QLY and ∠KLB opposite angles)

So, the remaining angle LKC of quadrilateral LKBC would be,

∠LKC = 360° - (∠B + ∠C + ∠KLB)

∠LKC = 360° - (90 °+ 90° + 95°)

∠LKC = 85°

b)

We know that he angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

so, the measure of arc PR = 120°

the measure of arc PQ = 120°

the measure of arc RQ = 120°

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Answer: 132 cubic cm

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

We can see here that the statements that are true are:

B. The symbol should be used because (8, 13, 22, 36) is a set and none of the elements in - 13 is a set.

C. The ∉ symbol should be used because ∉ is not an element of the set.

F. The ∈ symbol should be used because ∉ is not an element of the set.

A set in mathematics is a collection of unique objects, referred to as elements or members, that are paired off according to some shared quality.

Numbers, letters, words, forms, persons, and other mathematical things can all be included in a set.

We can see here that -13 ∉  (8, 13, 22, 36).

These statements are true because -13 is not actually an element of (8, 13, 22, 36). Thus, in the given set of data, -13 is not seen in the given set.

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(i)  [tex]\lim_{x \to \frac{\pi^-}{2}}[/tex] h(x) = 3

(ii) [tex]\lim_{x \to \frac{\pi^+}{2}}[/tex] h(x) = -1

(iii) h(0) = 1/7

The value of λ must be 7, for h(x) to be continuous at x = 0.

The given function is,

h(x) = 1/7, when x = 0

      = 1 - 2 cos 2x, when x < π/2

      = 1 + 2 cos 2x, when x > π/2

      = x cos x/sin λx, when x < 0

Now,

(i) [tex]\lim_{x \to \frac{\pi^-}{2}}[/tex] h(x) = [tex]\lim_{x \to \frac{\pi^-}{2}}[/tex] (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3

(ii) [tex]\lim_{x \to \frac{\pi^+}{2}}[/tex] h(x) = [tex]\lim_{x \to \frac{\pi^+}{2}}[/tex] (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1

(iii) h(0) = 1/7

Since the function is continuous at x = 0, so

[tex]\lim_{x \to 0}[/tex] h(x) = h(0)

[tex]\lim_{x \to 0}[/tex] x cos x/sin λx = 1/7

[tex]\lim_{x \to 0}[/tex] cos x.[tex]\lim_{x \to 0}[/tex] 1/λ(sinλx/λx) = 1/7

1/λ = 1/7

λ = 7

Hence the value of λ must be 7.

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If Cole brought 21 cans and his sister brought 7 cans less, then the total number of cans brought by them is 35 cans.

The number of cans which Cole brought = 21 cans of food.

His sister brought in 7 fewer cans than he did, which means she brought in:

⇒ 21 - 7 = 14 cans of food,

Let the total number of food-cans be = "f",

So, the equation to find the number of cans is written as :

⇒ x = 21 + 14,

On adding the number of cans,

We get,

⇒x =  21 + 14 = 35,

Therefore, together they brought in 35 cans of food.

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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:

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)

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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Based on the graph, there is no association because the distribution of preferred transportation differs among the age groups. The Option C is correct.

The significant factors is accessibility and convenience because younger individuals may be more likely to use public transportation such as buses or trains because it is more affordable and convenient than owning a car.

But the older individuals may prefer to use personal cars because it provides more flexibility and control over their transportation needs. Another factor that influences is the cost of ownership, maintenance, and fuel.

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Answer:

The artist used 1680 colored squares of glass.

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.