Which triangle could be drawn as it is described?

Answers

Answer 1

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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Related Questions

6
Professor Snozz wrote a new book, Pi to
Ten Million Places. He earns 8% of total
sales dollars as a royalty. If 300 copies
of his book are sold at $29.50 each, how
much does Professor Snozz make?

Answers

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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Which of the following represents the symmetric property of congruence?
A) If AB = CD, then AB ≅ EF

C) If AB ≅ CD , then CD≅ AB

D) AB ≅ AB

Answers

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 =-3a n-1 then find the value of a5

Answers

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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Mr. James is teaching his students about the volume of rectangular prisms. He has various rectangular prisms with a height of 6 inches. The table shows the relationship between the base of the prism and its volume. Which equation can be used to find B, the area of the base with a volume of V?

Answers

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

B = V/6.

What is a proportional relationship?

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.

Missing Information

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

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Write an explicit formula for an, the nth term of the sequence 25,30,35,....

Answers

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

1. Your utility company charges 10 cents per kilowatt hour of electricity. Complete parts (a) and (b) below.

a) What is the daily cost of keeping a 100-watt light bulb lit for 5 hours each day?

Answer:

b) How much will you save in a year if you replace the bulb with an LED that provides the same amount of light using only 26 watts of power? Round your answer to the nearest cent.

Answer:

Answers

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.

What is costs of running a 100-watt light bulb?

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.

Answers

Answer:

The artist used 1680 colored squares of glass.

Which number line shows the solutions to x+8 > 15? O A. B. O C. O D. -8-6-4-2 -8 -6 -4 -2 -8 -6 -4 2 4 6 8 4 -8 -6 -4 -2 0 2 4 8

Answers

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.

For what value of A is the function, (x), continuous at x=0?

Answers

(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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you roll a die numbered from 1 to 6. What is the probability that the sum is not 6?

Answers

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

If you are throwing 1 die then the probability is 5/6 or 83.3% but if you are rolling 2 die then the probability is 25/36 or 69.4%

what is debit and credit of this transactions? On December 1, NNC began an electro repair shop,Samson Quality Automotive. The following transactions occurred during December Dec. 1 Samson contributed birr 55,000 cash to the business in exchange for shares of common stock. 1 Purchased birr 9,000 of equipment paying cash. 1 Paid birr 1,500 for a five-month 9 Paid birr 16,000 cash to purchase land to be used in operations. insurance policy starting on December 1. 10 Purchased office supplies on account, birr 2,000. 19 Borrowed birr 12,000 from the bank for business use. Samson signed a notes payable to the bank in the name of the corporation. The note is due in five years. 22 Paid birr 1,700 for advertising expenses. 26 Paid birr 300 on account. 28 The business received a bill for utilities to be paid in January, birr 180. 31 Revenues earned during the month included birr 14,000 cash and birr 2,600 on account. 31 Paid employees' salaries birr 3,800 and building rent birr 1,300. Record as a compound entry. 31 The business received birr 1,400 for auto screening services to be performed next month.

Answers

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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Fill the blank with either E or to make the statement true.
- 13 {8, 13, 22, 36}
***
fill in the answer box to complete your choice

Answers

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.

What is a 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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Give the coordinates for all three possible
locations of the fourth vertex.
Y
9
8
7
6
5
4
3
2
1
0
X
1 2 3 4 5 6 7 8 9

Answers

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).

could i have the different proofs for this thank you

Answers

The proof for the above is given as follows:

∠A ≅ ∠C - Given

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

What does the Angle Bisector Theorem say?

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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Complete the equation that represents the relationship between p and a.

Answers

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

How to determine an equation of this line?

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:

x and y represent the data points.m represent the slope.

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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calculate the area of a circle whose circumference is 44cm

Answers

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.

simplify(-2+8i)(-2+6i)

Answers

The product between the complex numbers gives:

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

How to simplify the expression?

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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Find a function of the form
or whose graph matches this one:

Answers

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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Suppose that the demand of a certain item is x=-0.7p+10.
Evaluate the elasticity at 6.

Answers

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

What is the item's demand if elasticity is at 6?

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

Answers

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°

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°

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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Cole and his sister took part in a canned food drive. Cole brought in 21 cans of food. His sister brought in 7 fewer cans than he did. Together, how many cans did they bring in?

Answers

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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Identify parallelograms, rectangles and squares

Answers

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 price stock A at 9 am was $13.92. since then the price has been increasing at the rate of $0.11 each hour. At noon the price of Stock B was 14.67. It begins to decrease at the rate of $0.14 each hour. if the two rates continue , in how many hours will the prices of the two stocks be the same

Answers

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

In how many hours would the two stocks be the same?

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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An office building worth $1 million when completed in 2010 is being depreciated linearly over 25 years. What was the book value of the building in 2013? What will it be in 2019? (Assume the scrap value is $0

Answers

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.

5. How far does the tip of a minute hand on a clock travel in 45 minutes if the
distance from the center to the tip is 10 in? Leave your answer in terms of .
work:
distance traveled =
15
in.

Answers

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.

Which of the points below correctly plots the point (−1,π/4)?

A polar graph
Select the correct answer below:

A
B
C
D

Answers

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.

The correct answer is b!

I need help 20 pointttsss!!

Answers

Answer: 132 cubic cm

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

A car is driving on a road with a velocity of 20 − 10t miles per hour,
where t is the time in hours since the car started driving. What is the total distance
travelled by the car between times t = 0 and t = 3? Show work.
a. 5mi
b. 10mi
c. 15mi
d. 20mi
e. 25mi

Answers

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

c. 15 mi.

How to obtain the total distance?

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.

More can be learned about velocity and distance at https://brainly.com/question/4931057

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Using a scientific calculator or graphing calculator find the inverse tangent of the ratio. Round to the nearest degree.
StartFraction 3 Over 1 EndFraction
a.
71°
b.
19°
c.
72°
d.
18°

Answers

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°.

Based on the graph, is there an association between age and preferred mode of transportation?
O There is an association because the distribution of preferred transportation differs among the age groups.
O There is an association because the distribution of preferred transportation is the same among the age groups.
O There is no association because the distribution of preferred transportation differs among the age groups.
There is no association because the distribution of preferred transportation is the same among the age groups.

Answers

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

What influences difference in preferred transportation among all age group?

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.