If g(x) = (7x¹ + 6)³ (4x³ + 1)5, find g'(x).
g'(x) =

The correct algebraic expression for the reduced price of the computer is p - 250, as stated in option B. It signifies subtracting $250 from the original price, 'p.' Option B

To determine the algebraic expression that represents the reduced price of a computer, let's consider the given information. It states that the original price of the computer was reduced by $250.

Let's represent the original price of the computer as 'p' in dollars. Since the price was reduced by $250, we need to subtract $250 from the original price.

The expression that represents the reduced price is obtained by subtracting $250 from 'p.' Therefore, the algebraic expression for the reduced price is p - 250, which corresponds to option B.

Option A, 250 + p, suggests adding $250 to the original price, which would result in a higher value, contrary to the information given.

Option C, 250 - p, represents subtracting the original price from $250, which is not correct as we are reducing the price, not subtracting it from a fixed value.

Option D, 250p, represents multiplying the original price by $250, which does not align with the given scenario of reducing the price by $250.

Option B

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Note: The complete question is:

The original price of a computer was reduced by $250.If p = the computer's original price in dollars, which algebraic expression represents the reduced price? A.250 + p B.p – 250 C.250 – p D.250p

If you have any specific questions or need assistance, feel free to ask, and I'll do my best to provide a helpful response within the scope of my training

As an AI language model my understanding of subjects and skills is based on the information and data available to me up until my last training update in September 2021. I can provide accurate and comprehensive responses within the limits of my training, but please keep in mind that I may not have knowledge of events or developments that have occurred after that cutoff date.

With a wide range of general knowledge, I can understand and generate responses on various topics such as science, history, literature, mathematics, and more. I can also assist with specific skills like writing, editing, brainstorming ideas, offering explanations, and providing recommendations.

However, it's important to note that while I strive to be helpful, I am still an AI and may not always provide perfect answers. I do not possess personal experiences or opinions, and I am not able to perform physical actions. My responses are generated based on patterns and examples from my training data.

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What Amy did wrong was not moving the pointer to the arc intersection with the horizontal side

An angle bisector is defined in geometry as a line that splits an angle into two equal angles.

The steps involved in constructing an angle bisector are;

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When you activate a prepaid device with equipment, you may have the opportunity to earn money through various means.

Firstly, as a retailer or reseller, you can make a profit by selling the prepaid device and associated equipment at a higher price than your purchase cost. This markup allows you to earn a margin on each sale.

Additionally, some service providers or retailers offer commission-based programs where you earn a commission or referral fee for each prepaid device activation. By promoting and selling these devices, you can earn a percentage of the total sale value or a fixed amount per activation.

Furthermore, you might have the chance to upsell customers on additional accessories or services during the activation process. By offering relevant accessories like cases, screen protectors, or headphones, you can increase the overall sale value and earn extra income.

It's worth noting that the specific earning potential can vary depending on factors such as the popularity of the device, the commission structure, and the competitiveness of the market. It's advisable to research and understand the terms and conditions of any commission or referral programs before engaging in such activities.

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The volume of the pyramid is 357.7 inches³.

The volume of the cone is 1230.9 yard³.

The volume of a pyramid can be represented as follows;

volume of the pyramid = 1 / 3 Bh

where

Therefore,

B = 10 × 8 = 80 inches²

Hence,

h² =  14² - 4²

h = √196 - 16

h = √180

h = √180 inches

volume of the pyramid = 1 / 3 × 80 × √180

volume of the pyramid = 357.7 inches³

Therefore, let's find the volume of the cone.

volume of the cone = 1 / 3 πr²h

h = √25² - 7²

h = √576

h = 24 yards

volume of the cone = 1 / 3 × 3.14 × 7² × 24

volume of the cone = 1230.9 yard³

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The given infinite sum 0.16 + 0.4 + 0.1 + 0.25 + ... is defined as it converges to a finite value. Option A is the correct answer.

To determine whether the given infinite sum is defined, let's examine its pattern.

If we observe the terms in the sum, we can see that each term is obtained by dividing the previous term by 4. Specifically, each term is one-fourth the value of the previous term.

Let's verify this pattern:

Term 1: 0.16

Term 2: Term 1 / 4 = 0.16 / 4 = 0.04

Term 3: Term 2 / 4 = 0.04 / 4 = 0.01

Term 4: Term 3 / 4 = 0.01 / 4 = 0.0025

It appears that each term is one-fourth the value of the previous term. If this pattern continues, we can write the nth term as:

Term n = (1/4)^(n-1) * 0.16

To determine whether the sum is defined, we need to check whether the terms approach a finite value or converge to a specific value.

As n approaches infinity, the term (1/4)^(n-1) * 0.16 will approach zero since (1/4)^(n-1) approaches zero exponentially. Therefore, the sum of the infinite terms in this sequence will converge to a finite value. Hence, Option A is the correct answer.

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1. a. The Total direct manufacturing cost is $212,350. b. The Total indirect manufacturing cost is -$128,650. 2. a.  the total manufacturing cost directly traceable to the Manufacturing Department is $212,350. b. the total manufacturing cost that is an indirect cost is $83,700. 3. a. the total direct selling expense that can be readily traced to individual sales representatives is $21,700. b.  the total indirect selling expense that cannot be readily traced to individual sales representatives is $38,750.

1. Assume the cost object is units of production:

a. The total direct manufacturing cost incurred to make 15,500 units can be calculated by multiplying the average cost per unit for each cost component by the number of units produced:

Total direct manufacturing cost = (Direct materials cost + Direct labor cost + Variable manufacturing overhead cost) × Number of units produced

Direct materials cost = $7.40/unit × 15,500 units = $114,700

Direct labor cost = $4.40/unit × 15,500 units = $68,200

Variable manufacturing overhead cost = $1.90/unit × 15,500 units = $29,450

Total direct manufacturing cost = ($114,700 + $68,200 + $29,450) = $212,350

b. The total indirect manufacturing cost incurred to make 15,500 units can be calculated by subtracting the total direct manufacturing cost from the average cost per unit for fixed manufacturing overhead:

Total indirect manufacturing cost = Fixed manufacturing overhead cost × Number of units produced

Fixed manufacturing overhead cost = $5.40/unit × 15,500 units = $83,700

Total indirect manufacturing cost = $83,700 - $212,350 = -$128,650

Note: The negative value indicates that the fixed manufacturing overhead cost is not fully utilized within the relevant range of production. It suggests that there may be unused capacity or fixed costs that are not being allocated to the production of 15,500 units.

2. Assume the cost object is the Manufacturing Department and that its total output is 15,500 units:

a. The total manufacturing cost directly traceable to the Manufacturing Department is the sum of the direct manufacturing costs:

Total manufacturing cost directly traceable to the Manufacturing Department = Total direct manufacturing cost

Using the values calculated in part 1a, the total manufacturing cost directly traceable to the Manufacturing Department is $212,350.

b. The total manufacturing cost that is an indirect cost and cannot be easily traced to the Manufacturing Department is the fixed manufacturing overhead cost:

Total manufacturing cost that is an indirect cost = Fixed manufacturing overhead cost

Using the value calculated in part 1b, the total manufacturing cost that is an indirect cost is $83,700.

3. Assume the cost object is the company's various sales representatives. Furthermore, assume that the company spent $44,950 of its total fixed selling expense on advertising, and the remainder of the total fixed selling expense comprised the fixed portion of the company's sales representatives' compensation:

a. When the company sells 15,500 units, the total direct selling expense that can be readily traced to individual sales representatives is the sales commissions:

Total direct selling expense = Sales commissions × Number of units sold

Sales commissions = $1.40/unit × 15,500 units = $21,700

Therefore, the total direct selling expense that can be readily traced to individual sales representatives is $21,700.

b. When the company sells 15,500 units, the total indirect selling expense that cannot be readily traced to individual sales representatives is the fixed portion of the company's sales representatives' compensation:

Total indirect selling expense = Total fixed selling expense - Total direct selling expense

Total fixed selling expense = $3.90/unit × 15,500 units = $60,450

Total indirect selling expense = $60,450 - $21,700 = $38,750

Therefore, the total indirect selling expense that cannot be readily traced to individual sales representatives is $38,750.

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The value of x in the secant intersection is 4.

If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

Therefore, let's find the value of x using the secant intersection theorem as follows;

4(4+x + 2) = 5(5 + x - 1)

4(6 + x) = 5(4 + x)

24 + 4x = 20 + 5x

24 - 20 = 5x - 4x

x = 4

Therefore,

x = 4

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We may apply the Pythagorean theorem to calculate the height of the tent, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the total of the squares on the other two sides. So, the height of the tent is 8.3077 feet.

In this case, the two sticks form the slanted sides of the tent, and the opening at the bottom forms the base of the triangle. We can consider the height of the tent as the missing side, which is perpendicular to the base.

Let's denote the height of the tent as 'h.' Using the Pythagorean theorem, we have:

(10 ft.)² + (h)² = (13 ft.)²

Simplifying the equation:

100 + h² = 169

Now, subtracting 100 from both sides:

h² = 169 - 100

h² = 69

Taking the square root of both sides:

h = sqrt(69)

Therefore, the height of the tent is approximately 8.3077 feet (rounded to four decimal places).

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The important variables are the two types of test questions which can be represented as :

Variables are used to represent unknown values which could be worked out in a mathematical expression or problem.

The variables or unknown in this case are the type of test questions. which are : m for multiple choice, s for short answer

Therefore, the correct option is C. m for multiple choice, s for short answer

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Answer:

The diagram illustrates that the two sides with lengths 4 and 3 can never meet to form a vertex, therefore the correct answer is C.

The correct pairings are:

a) Four less than the quotient of a number cubed and seven, increased by three: (n³/7) - 4 + 3

b) Five times the difference of a number squared and six: 5(n² - 6)

c) Nine more than the quotient of six and a number cubed, decreased by four: (6/n³) + 9 - 4

d) O twice the difference of nine and a number squared: 2(9 - n²)

The correct pairings of descriptions and expressions are as follows:

Four less than the quotient of a number cubed and seven, increased by three: (n³/7) - 4 + 3

This expression represents taking a number, cubing it, dividing the result by seven, subtracting four, and then adding three.

Five times the difference of a number squared and six: 5(n² - 6)

This expression represents taking a number, squaring it, subtracting six, and then multiplying the result by five.

Nine more than the quotient of six and a number cubed, decreased by four: (6/n³) + 9 - 4

This expression represents taking the cube of a number, dividing six by the cube, adding nine, and then subtracting four.

O twice the difference of nine and a number squared: 2(9 - n²)

This expression represents taking a number, squaring it, subtracting it from nine, and then multiplying the result by two.

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The area of a circle with a radius of 5 cm is given as follows:

78.5 cm².

The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:

A = πr²

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, and it's measure is given as follows:

r = 5 cm.

Hence the area of the circle is given as follows:

A = π x 5²

A = 78.5 cm².

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The similar triangles and their statements are

A. Side-Side-Side (SSS) Similarity

B. Side-Angle-Side (SAS) Similarity

C. Hypotenuse-leg (HL) similarity

A similarity statement is a statement that expresses the similarity between two or more geometric figures or objects. It describes the relationship between corresponding angles and corresponding sides of the figures.

The general form of a similarity statement for two figures, let's say figure A and figure B, is:

"Figure A is similar to Figure B"

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Answer:16

Step-by-step explanation:

25/100 × x = 4

x = 4 × 4

x = 16

The probability of rolling the specific outcome 1: 1/5 on a fair six-sided die is 1/6

To identify the probability of rolling a specific outcome on a fair six-sided die, we can use the concept of probability. The probability of an event is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes.

In this case, we want to find the probability of rolling a specific outcome, which is 1 out of 5. Since there is only one specific outcome we are interested in, and the die has a total of 6 possible outcomes (numbers 1 to 6), the probability can be calculated as:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 1 / 6

Therefore, the probability of rolling the specific outcome you mentioned (1 out of 5) on a fair six-sided die is 1/6.

In conclusion, when rolling a fair die, each of the six possible outcomes has an equal chance of occurring, resulting in a probability of 1/6 for any specific outcome.

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Answer: rotation of 90 counter clockwise about the origin

Step-by-step explanation:

Answer:

[tex]\textsf{(C)} \quad \dfrac{1}{4}[/tex]

Step-by-step explanation:

To find the probability of a point chosen at random being in the shaded area of the given diagram, we first need to calculate the areas of the larger circle and the shaded circle.

The formula for the area of a circle is A = πr², where r is the radius.

Given the radius of the larger circle is 8 units:

[tex]\begin{aligned}\sf Area\;of\;the\;larger\;circle&=\pi (8)^2\\&=64 \pi \end{aligned}[/tex]

Given the radius of the shaded circle is 4 units:

[tex]\begin{aligned}\sf Area\;of\;the\;shaded\;circle&=\pi (4)^2\\&=16 \pi \end{aligned}[/tex]

[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]

To find the probability that a point chosen at random is in the shaded area, divide the area of the shaded circle by the area of the larger circle:

[tex]\sf Probability= \dfrac{16 \pi}{64 \pi}=\dfrac{1}{4}[/tex]

Therefore, the probability of a point chosen at random being in the shaded area is 1/4.

Answer:

[tex]\frac{x}{y}[/tex] 1 over 4 (one-fourth)

Step-by-step explanation:

The size of angle marked n is ≈26.67 degrees.

Sparx 4:

Item A, bookwork code C20 requires us to determine the size of angle marked n in degrees.

We can solve the given question by using the angles sum rule that states that the sum of the angles of a triangle equals to 180 degrees.

The given figure represents an isosceles triangle since the two base angles are equal in length.

Also, the top line is parallel to the bottom line.

Using the angles sum rule for a triangle, we get:angle ABC + angle BCA + angle CAB = 180 degreesx + 2n + 50 = 180 degreesx = 180 - 2n - 50x = 130 - 2nWe know that angles that are opposite to equal sides of an isosceles triangle are equal.

Therefore, angle ABC = angle CAB = n

Thus, the above equation becomes:130 - 2n = n + 50.

Simplifying the equation, we get:3n = 80n = 80 / 3n ≈ 26.67 degrees.

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Answer:

The area of this triangle is (1/2)(9)(8) = 36.

Answer: A and B are not characteristics of surveys.

Step-by-step explanation: A survey is a type of research method that involves collecting data from a sample of individuals or groups, usually by asking them questions or observing their behavior. Surveys can be used to describe, compare, or explain various aspects of a population or phenomenon of interest.

Some of the common characteristics of surveys are:

Some of the types of research methods that involve one or more treatment groups and a control group, and that compare two or more treatments, are:

Hope this helps, and have a great day! =)

The solutions to the system of equations is (a) (1, 5)

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

The graph

This point of intersection of the lines of the graph represent the solution to the system graphed

From the graph, we have the intersection point to be

(x, y) = (1, 5)

Hence, the solutions to the system is (1, 5)

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1. Mr. John received more than 2 cords of wood based on the sizes of the stacked piles.

2. Based on the stacked piles, Mr. John received approximately 11,974 pieces of actual wood.

3. The cost per standard piece of wood is approximately $0.0417.

1. To determine if Mr. John received more or less than 2 cords of wood, we need to calculate the volume of each pile and compare it to the volume of a standard cord of wood.

Calculating the volume of each pile:

PILE #1:

Volume = 72 inches * 167 inches * 16 inches = 1,523,584 cubic inches

PILE #2:

Volume = 65 inches * 266 inches * 16 inches = 2,068,480 cubic inches

Calculating the volume of a standard cord of wood:

Volume of a standard cord = 4 feet * 4 feet * 8 feet = 128 cubic feet

Since 1 foot = 12 inches, the volume in cubic inches is 128 * 12 * 12 * 12 = 221,184 cubic inches.

Comparing the volumes:

Pile #1: 1,523,584 cubic inches

Pile #2: 2,068,480 cubic inches

Standard cord: 221,184 cubic inches

It is evident that both piles have significantly more volume than a standard cord of wood. Therefore, Mr. John received more than 2 cords of wood.

2. To determine the number of standard pieces of wood received, we need to calculate the number of pieces that can be obtained from the total volume of the piles.

Total volume of the piles = Volume of Pile #1 + Volume of Pile #2

Total volume = 1,523,584 cubic inches + 2,068,480 cubic inches = 3,592,064 cubic inches

Volume of a standard piece of wood = 5 inches * 5 inches * 12 inches = 300 cubic inches

Number of standard pieces of wood received = Total volume of the piles / Volume of a standard piece of wood

Number of pieces = 3,592,064 cubic inches / 300 cubic inches = 11,973.55 pieces (rounded to the nearest whole number)

Therefore, Mr. John received approximately 11,974 pieces of actual wood based on his stacked piles.

3. To calculate the cost per standard piece of wood, we need to divide the total cost of the two cords by the number of standard pieces received.

Total cost for both cords of wood = 2 cords * $250/cord = $500

Cost per standard piece of wood = Total cost / Number of standard pieces

Cost per piece = $500 / 11,974 = $0.0417 (rounded to four decimal places)

Therefore, the cost per standard piece of wood is approximately $0.0417.

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Answer:

∠ G = 73° , ∠ H = 98°

Step-by-step explanation:

EFGH is a cyclic quadrilateral, its 4 vertices lie on the circle.

the opposite angles sum to 180°

A

∠ E + ∠ G = 180° , that is

11x + 8 + 8x + 1 = 180

19x + 9 = 180 ( subtract 9 from both sides )

19x = 171 ( divide both sides by 19 )

x = 9

Then

∠ G = 8x + 1 = 8(9) + 1 = 72 + 1 = 73°

B

∠ H + ∠ F = 180° , that is

6y - 4 + 5y - 3 = 180

11y - 7 = 180 ( add 7 to both sides )

11y = 187 ( divide both sides by 11 )

y = 17

Then

∠ H = 6y - 4 = 6(17) - 4 = 102 - 4 = 98°

Answer:

A)  m∠G = 73°

B)  m∠H = 98°

Step-by-step explanation:

The diagram shows a cyclic quadrilateral.

A cyclic quadrilateral is a four-sided shape drawn inside a circle, where every vertex touches the circle's circumference.

As the opposite angles in a cyclic quadrilateral add up to 180°, then:

We can use these equations to find the values of x and y.

m∠E + m∠G = 180°

(11x + 8)° + (8x + 1)° = 180°

11x + 8 + 8x + 1 = 180

19x + 9 = 180

19x + 9 - 9 = 180 - 9

19x = 171

19x ÷ 19 = 171 ÷ 19

x = 9

m∠H + m∠F = 180°

(6y - 4)° + (5y - 3)° = 180°

6y - 4 + 5y - 3 = 180

11y - 7 = 180

11y - 7 + 7 = 180 + 7

11y = 187

11y ÷ 11 = 187 ÷ 11

y = 17

Now we have found the values of x and y, substitute them back into the angle expressions to find m∠G and m∠H.

m∠G = (8x + 1)°

m∠G = (8(9) + 1)°

m∠G = (72 + 1)°

m∠G = 73°

m∠H = (6y - 4)°

m∠H = (6(17) - 4)°

m∠H = (102 - 4)°

m∠H = 98°

Answer:

(x + 3)(5x + 2) , (2x - 1)(3x + 5)

Step-by-step explanation:

given

A = 5x² + 12x + 6

consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term

product = 5 × 6 = 30 and sum = 17

the factors are + 15 and + 2

use these factors to split the x- term

5x² + 15x + 2x + 6 ( factor the first/second and third/fourth terms )

= 5x(x + 3) + 2(x + 3) ← factor out (x + 3) from each term

= (x + 3)(5x + 2)

then

length = x + 3 , breadth = 5x + 2 or indeed the other way round

-------------------------------------------------------------------------------

given

A = 6x² + 7x - 5

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 6 × - 5 = - 30 and sum = + 7

the factors are - 3 and + 10

use these factors to split the x- term

6x² - 3x + 10x - 5 ( factor the first/second and third/fourth terms )

= 3x(2x - 1) + 5(2x - 1) ← factor out (2x - 1) from each term

= (2x - 1()3x + 5)

then

length = 2x - 1 , breadth = 3x + 5 or the other way round

The two equations to solve for angle α are sinα = u/t and sinα = r/s using the trigonometric ratio of sine

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

The bigger triangle with sides t, u, v and the smaller triangle with sides q, r , s are both right triangle so we can use the ratio of sine for their angle α to get the two equations as:

sin α = u/t {opposite/hypotenuse} for the bigger triangle.

sin α = r/s {opposite/hypotenuse} for the smaller triangle.

Therefore, the two equations to solve for angle α are sinα = u/t and sinα = r/s using the trigonometric ratio of sine

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The domain of the given table is { -3, 0, 3 } and the range is { -6, 0, 6 }. Option A.

The given table represents a set of ordered pairs (x, y). The x-values are -3, 0, and 3, and the corresponding y-values are -6, 0, and 6. To determine the domain and range, we need to identify the set of all possible x-values and y-values.

Domain: The domain represents the set of all possible x-values in the given table. In this case, the x-values are -3, 0, and 3. Therefore, the domain is { -3, 0, 3 }.

Range: The range represents the set of all possible y-values in the given table. In this case, the y-values are -6, 0, and 6. Therefore, the range is { -6, 0, 6 }.

Based on the above analysis, the correct answer is:

a. domain { -3, 0, 3 }, range: { -6, 0, 6 }.

This option correctly identifies the values in the given table as the domain and range, matching the values -3, 0, 3 for the domain and -6, 0, 6 for the range. Therefore, option a is the best answer. Option A is correct.

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The triangles ∆UTS and ∆UBA are similar, hence we can write the similarity statement as:"Triangle ∆UTS is similar to triangle ∆UBA."

To determine if triangles ∆UTS and ∆UBA are similar, we need to check if their corresponding angles are congruent and if their corresponding sides are proportional.

If ∆UTS is similar to ∆UBA, the following conditions must be true, then each angle in ∆UTS must have a corresponding congruent angle in ∆UBA. Also, the ratio of the lengths of corresponding sides in ∆UTS and ∆UBA must be equal.

AB/ST = 984/1271 = 0.7742

UB/UT = 768/994 = 0.7742

UA/US = 648/837 = 0.7742

AB/ST = UB/UT = UA/US

Therefore triangles ∆UTS and ∆UBA are similar, hence we can write the similarity statement as:"Triangle ∆UTS is similar to triangle ∆UBA."

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The probability that a die will land on 5 is 0.1.

The statement "If a probability is unlikely, then the probability is less than 1/2" is true in this context.

To determine the probabilities, we need to calculate the relative frequency of each outcome by dividing the frequency of that outcome by the total number of rolls (20 in this case).

The frequency table provided is as follows:

Value of Die | Frequency

1 | 5

2 | 3

3 | 4

4 | 5

5 | 2

6 | 1

To find the probability that a die will land on 5, we divide the frequency of 5 by the total number of rolls:

Probability of landing on 5 = Frequency of 5 / Total number of rolls

= 2 / 20

= 0.1

Therefore, the probability that a die will land on 5 is 0.1.

Similarly, to find the probability of landing on 1:

Probability of landing on 1 = Frequency of 1 / Total number of rolls

= 5 / 20

= 0.25

Thus, the probability that a die will land on 1 is 0.25.

Now, if a probability is unlikely, it means the probability is less than 1/2. In this case, we need to compare the probabilities to 0.5.

Since the probability of landing on 1 is 0.25, which is less than 0.5, we can conclude that the probability of landing on 1 is unlikely.

Therefore, the statement "If a probability is unlikely, then the probability is less than 1/2" is true in this context.

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