Use the formula to find the surface area of the figure. Show your work.

The correct expansion of (x + 4y)³ using the binomial theorem is (c) [tex]\left[\begin{array}{c}3&0\end{array}\right][/tex] (4y)³(x)⁰ + [tex]\left[\begin{array}{c}3&1\end{array}\right][/tex] (4y)²(x)¹ + [tex]\left[\begin{array}{c}3&2\end{array}\right][/tex] (4y)¹(x)² + [tex]\left[\begin{array}{c}3&3\end{array}\right][/tex] (4y)⁰(x)³

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

(x + 4y)³

The binomial theorem of expansion states that

Given that an expression is (a + b)ⁿ, the current term is

ⁿCₓ * (a)ˣ * (b)ⁿ ⁻ ˣ

Using the above as a guide, we have the following:

(x + 4y)³ = ³C₀ (x)⁰(4y)³ +³C₁ (x)¹(4y)² + ³C₂ (x)²(4y)¹ + ³C₃ (x)³(4y)⁰

Rewrite as

(x + 4y)³ = [tex]\left[\begin{array}{c}3&0\end{array}\right][/tex] (4y)³(x)⁰ + [tex]\left[\begin{array}{c}3&1\end{array}\right][/tex] (4y)²(x)¹ + [tex]\left[\begin{array}{c}3&2\end{array}\right][/tex] (4y)¹(x)² + [tex]\left[\begin{array}{c}3&3\end{array}\right][/tex] (4y)⁰(x)³

This means that the correct expansion is (c) [tex]\left[\begin{array}{c}3&0\end{array}\right][/tex] (4y)³(x)⁰ + [tex]\left[\begin{array}{c}3&1\end{array}\right][/tex] (4y)²(x)¹ + [tex]\left[\begin{array}{c}3&2\end{array}\right][/tex] (4y)¹(x)² + [tex]\left[\begin{array}{c}3&3\end{array}\right][/tex] (4y)⁰(x)³

Read more about binomial expansion at

https://brainly.com/question/13602562

#SPJ1

Answer:

infinite

Step-by-step explanation:

because if you were to graph it or something 1 could go to 10 like 1 could fit into ten without exeeding the limit going to low or to high

Characteristics that are harmful to a species tend to decrease in frequency from generation to generation because these characteristics usually have a low survival value for the species.

Option 2.

Characteristics that are harmful to a species are numerous and some of them affect species in many ways.

Some of the harmful characteristics to species include the following;

Poor genetic diversity - species that are not diverse will not survive long the nearest future as tend to go into extinct.

Poor habitat ; species with limited habitation will not survive long.

Poor reproductive rate - this factor does not favour species wide spread and fast growth

Predators - this factor kill and reduce the number of available species

Learn more about harmful characteristics here: https://brainly.com/question/9445762

#SPJ1

A real distance of 27 meters will be represented by a distance of 54 centimeters on the plane.

We know that the scale factor of the plane is:

6cm to 3m

Then each meter on the plane will be represented by:

1m = (6cm/3) = 2cm

So each meter in the real world is represented by 2 centimeters on the plane.

Then a real distance of 27 meters will be reprsented by:

27m = 27*(2cm) = 54cm

That distance is represented by 54 centimeters.

Learn more about scale factors at:

https://brainly.com/question/25722260

#SPJ1

The statement "In the study of logic, p q is to be understood in the exclusive sense, whereby if 'p' and 'q' are both true, the compound claim pvq is, as a whole claim, true" is true.

This principle is known as the exclusive disjunction, which means that the truth value of p v q is only true if either p or q is true, but not both.

In other words, if both p and q are true, then the statement p v q is still considered true because only one of them needs to be true for the whole statement to be true. This concept is essential in the study of logic as it helps to clarify the relationship between different statements and propositions.

Furthermore, this principle is often used in mathematics, computer science, and other fields that rely heavily on logical reasoning. It enables us to make accurate predictions and draw valid conclusions from a set of given premises or statements.

In conclusion, the exclusive disjunction is a crucial concept in the study of logic that helps us understand the truth value of compound claims. Therefore, the statement "In the study of logic, p q is to be understood in the exclusive sense, whereby if 'p' and 'q' are both true, the compound claim pvq is, as a whole claim, true" is true.

In the study of logic, the statement "p ∨ q is to be understood in the exclusive sense, whereby if 'p' and 'q' are both true, the compound claim p ∨ q is, as a whole claim, true" is actually false. This is because the given description refers to the "inclusive" sense of the disjunction (OR) operator, rather than the exclusive sense.

In logic, there are two types of disjunctions: inclusive and exclusive. The inclusive disjunction, represented by p ∨ q, is true when at least one of p or q is true. This means that if both p and q are true, the compound claim p ∨ q is also true, which matches the given description in the question.

On the other hand, the exclusive disjunction, represented by p ⊕ q or p XOR q, is true only when either p or q is true, but not when both are true. If p and q are both true, then the compound claim p ⊕ q is false.

So, the statement in the question actually describes the inclusive disjunction, not the exclusive disjunction, and is therefore false.

Learn more about disjunction at: brainly.com/question/30509648

#SPJ11

Answer:

The angle between building 1 and building 3 at building 2 is not a right angle, and hence, the buildings do not form a right triangle.

Step-by-step explanation:

Examining the stem and leaf plot, the number of drivers that travelled below 70 miles per hour is

A. 8

A stem and leaf plot is a type of data display used in statistics to organize and rank data while retaining individual data points.

It is a visual representation of a frequency distribution of numerical data where each value is split into a stem (usually the leftmost digits) and a leaf usually the rightmost digit).

Using the information we can write out the speed of drivers that drove below 70 miles per hour

54, 56, 59, 62, 62, 63, 64, and 68

This gives 8

Learn more about stem and leaf plot at

https://brainly.com/question/31634385

#SPJ1

Answer:

c

Step-by-step explanation:

Looking at Jen's slope, we can see that the slope is steeper, but has a higher starting point, meaning that while she can hold more gas, she burns through her gas quicker.

On the other hand, DJ's car starts at a lower point on the graph, meaning their car holds less gas, But has a less steep slope, meaning their car has better mileage.

This means the answer is c: Jen's car holds more gasoline, but DJ's car gets better gas mileage

Given that QT is the perpendicular bisector of PR.The bisector of any line segment divides it into two equal parts, each of which has the same measure.To begin, let's define a few terms.

Angle bisector - An angle bisector is a line or segment that divides an angle into two equal parts.The given figure is shown below: We are given QT is the perpendicular bisector of PR. That means QT is perpendicular to PR and it bisects it. That is, it divides it into two equal halves.Suppose, PR = 2xFrom the given information, we know that the perpendicular bisector QT divides PR into two equal halves.

So,PQ = QR

Now, In right triangle

TPQ,QT² = TP² + PQ²QT² = TP² + QR² (since PQ = QR)QT² = TP² + (2x)² (since PQ = QR = 2x)QT² = TP² + 4x²

Also, In right triangle

TRQ,QT² = TR² + QR²QT² = TR² + (2x)²QT² = TR² + 4x²

We now have two equations:

QT² = TP² + 4x² QT² = TR² + 4x²

The above two equations can be equated:

TP² + 4x² = TR² + 4x²TP² = TR²

Thus, we can say that

TP = TRLet TP = TR = a

By Pythagoras theorem in right angled triangle

TPQ,TP² + PQ² = TQ²a² + (2x)² = QT²a² + 4x² = QT²

The answer is 4x² + a² = QT².

To know more about line segment visit :

https://brainly.com/question/30072605

#SPJ11

The simulation that can best be used to compute the probability would be one that randomly generates a large number of outcomes and records the number of games it takes for Janet to win in each simulation.

A simulation that randomly generates a large number of outcomes and records the number of games it takes for Janet to win in each simulation can be used to compute the probability of it taking at least six games for her to win.

By running the simulation many times and calculating the proportion of simulations in which Janet wins after six or more games, an estimate of the probability can be obtained.

More on probability simulation can be found here: https://brainly.com/question/11740786

#SPJ1

In the question it ask for a slope of -6 so the answer is D.

The water tariff for Mogale City in August 2022 is R18 per kl, so her water bill excluding VAT will be R144.

Mrs Mabaspacked is a registered resident and she used 14 kt of water for the month of August 2022. The first 6 kl of water is free for registered residents, so she will only be charged for the remaining 8 kl. The water tariff for Mogale City in August 2022 is R18 per kl, so her water bill excluding VAT will be 8 kl x R18/kl = R144.

Water used: 14 kl

Free water: 6 kl

Water used after deduction of free water: 14 kl - 6 kl = 8 kl

Water tariff: R18 per kl

Water bill excluding VAT: 8 kl x R18/kl = R144

Learn more about tariff on

https://brainly.com/question/1172085

#SPJ1

Answer:

1/16

Step-by-step explanation:

The probability of selecting an Independent on the first draw is 5/16, since there are 5 Independents out of 16 total members.

Assuming that the first person selected is an Independent, there are now 4 Independents left out of 15 total members for the second draw. So the probability of selecting a second Independent given that the first person selected was an Independent is 4/15.

Therefore, the probability of selecting two Independents in succession is:

(5/16) * (4/15) = 1/16

So the probability of selecting two Independents is 1/16 or approximately 0.0625.

Answer: y = -4x + 2

Step-by-step explanation:

The distance between the center of the circle and the given point is 13 units.

The distance between the center of the circle (0, 0) and the given point (-5, 12) should be equal to the radius of the circle.

Using the distance formula,

d= √(-5-0)² + (12-0)²

d = √25 + 144

d = √169

d = 13 unit

Therefore, the distance between the center of the circle and the given point is 13 units.

Any point on the circle will have a distance of 13 units from the center.

Learn more about Distance Formula here:

https://brainly.com/question/25841655

#SPJ1

If Gary's car gets about 20 miles per gallon.

a.  Gary can drive about 198 miles on 9.9 gallons of gas.

b.  the cost of 9.9 gallons of gas at $2.90 per gallon would be  $28.71.

a. Number of miles

Miles = Gallons * Miles per gallon

Miles = 9.9 gallons * 20 miles/gallon

Miles = 198 miles

Therefore Gary can drive about 198 miles on 9.9 gallons of gas.

b. Cost of the gas

Cost = Price per gallon * Gallons

Cost = $2.90/gallon * 9.9 gallons

Cost = $28.71

Therefore the cost of 9.9 gallons of gas at $2.90 per gallon is $28.71.

Learn more about miles here:https://brainly.com/question/29806974

#SPJ9

Answer: Which Option do You Drag and Drop into the Box?

Step-by-step explanation:

Let's call the number of rotations of the larger gear "L" and the number of rotations of the smaller gear "S". We know that when the larger gear completes 1 rotation, the smaller gear completes 1 3/4 rotations.

We can set up a proportion to solve for S:

S/1 3/4 = L/1/4

Simplifying the right side of the equation, we get:

S/1 3/4 = 4L

Multiplying both sides by 7/4 to get rid of the fraction on the left side, we get:

S = 28/4 L

Simplifying, we get:

S = 7L

This means that the smaller gear completes 7 rotations every time the larger gear completes 1 rotation.

Therefore, the correct value to drag and drop into the box is 7.

{Hope This Helps! :)}

The measure of Angle WBK, the angles are supplementary,

complementary, adjacent, vertical, or part of a triangle.

The measure of Angle WBK (represented by b).
1. Identify the relationships between the angles: the angles are supplementary, complementary, adjacent, vertical, or part of a triangle or other polygon.
2. Write an equation using the angle relationships:  if two angles are supplementary, the sum of their measures is 180 degrees. If Angle WBK is supplementary to Angle WBL, we would write the equation b + m(WBL) = 180, where m(WBL) represents the measure of Angle WBL.
3. Solve the equation: the values into the equation and solve for b, the measure of Angle WBK.

To know more about Angle .

https://brainly.com/question/30759856

#SPJ11

When we subtract a velocity vector from another velocity vector, the result is B. another velocity.

When we subtract a velocity vector from another velocity vector, we are essentially finding the difference between the two velocities. This difference is also a velocity vector, but in a different direction and with a different magnitude. Therefore, the answer is another velocity, option B.

It is important to note that acceleration is a change in velocity, not the result of subtracting one velocity from another. Scalar refers to a quantity with only magnitude, whereas velocity is a vector quantity with both magnitude and direction. Displacement refers to the change in position of an object and is not directly related to subtracting velocity vectors.

To know more about velocity visit:

https://brainly.com/question/14534415

#SPJ11

The gradient of the trail you hiked up is approximately 754.6 ft/mi. This means that for every mile you hiked horizontally, the elevation increased by about 754.6 feet.

The gradient of the trail is essentially the steepness of the trail, or the rate at which the elevation changes per unit of horizontal distance. To find the gradient in ft/mi, we need to calculate the total change in elevation and divide it by the total horizontal distance.
The total change in elevation is the difference between the elevation at the summit and the elevation at the trail head, which is:
6,849 ft - 645 ft = 6,204 ft

The total horizontal distance of the trail is 8.2 mi. To convert the total change in elevation to ft/mi, we divide it by the total horizontal distance
6,204 ft / 8.2 mi = 754.63 ft/mi
Rounding this to the tenths place gives us:
Gradient = 754.6 ft/mi

To know more about gradient visit:-

https://brainly.com/question/30249498

#SPJ11

Answer:

Step-by-step explanation:

Let's first expand the left side of the given equation:

(2x+5)a + (x+3)b = 2x+4

2xa + 5a + xb + 3b = 2x + 4

Now, let's group the terms with x and the terms without x:

(2a + b)x + (5a + 3b) = 2x + 4

We can see that the coefficients of x are equal on both sides, so we can equate the coefficients of x and the constant terms separately:

2a + b = 2 (1)

5a + 3b = 4 (2)

Solving these two equations, we get:

a = 2/7

b = 8/7

Now, we can substitute these values of a and b into the expression (a-b)^2 and simplify:

(a-b)^2 = (2/7 - 8/7)^2

= (-6/7)^2

= 36/49

Therefore, the value of (a-b)^2 is 36/49.

Answer:

x=23

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

have a great day and thx for your inquiry :)

Answer:

Step-by-step explanation:

To solve the equation |5-4r| = 17, we need to consider two cases:Case 1: 5 - 4r is positiveIf 5 - 4r is positive, then we have:5 - 4r = 17Subtracting 5 from both sides, we get:-4r = 12Dividing both sides by -4, we get:r = -3So if 5 - 4r is positive, then the solution to the equation is r = -3.Case 2: 5 - 4r is negativeIf 5 - 4r is negative, then we have:-(5 - 4r) = 17Simplifying the left side by distributing the negative sign, we get:-5 + 4r = 17Adding 5 to both sides, we get:4r = 22Dividing both sides by 4, we get:r = 5.5So if 5 - 4r is negative, then the solution to the equation is r = 5.5.Therefore, the solution set of the equation |5-4r| = 17 is {-3, 5.5}.To show this solution set on a number line, we can draw a number line and mark the points -3 and 5.5 with open circles, since these values are not included in the solution set. Then, we shade the part of the number line between -3 and 5.5, since any value of r in this interval satisfies the equation. The resulting number line looks like this:

So the solution set of the equation is the interval (-3, 5.5).

Answer:

w

Step-by-step explanation:

So the base of the ladder is moving away from the wall at a rate of 3/4 feet per minute when the top of the ladder is 4 feet from the ground.

We can use the Pythagorean Theorem to relate the ladder's length to the distance it is from the wall. Let's call the distance from the wall "x", and the length of the ladder "y". Then:

x^2 + y^2 = 5^2

We can take the derivative with respect to time of both sides of this equation, using implicit differentiation:

2x(dx/dt) + 2y(dy/dt) = 0

Now we can plug in the values we know and solve for the rate at which the base of the ladder is moving away from the wall (which is the same as the rate at which x is increasing):

x = sqrt(5^2 - 4^2) = 3

y = 4

dx/dt = 1 (given)

dy/dt = ?

Plugging in these values, we get:

2(3)(1) + 2(4)(dy/dt) = 0

Simplifying:

6 + 8(dy/dt) = 0

Solving for dy/dt:

dy/dt = -6/8 = -3/4

To know more about feet,

https://brainly.com/question/31812541

#SPJ11

Answer:

[tex]y=4[/tex]

Step-by-step explanation:

The approximate volume of the sphere is 606.25 cm³, which is closest to option D. 606 cm³.

To find the approximate volume of a sphere, we'll use the formula:
Volume = (4/3) × π × r³
Given that the sphere has a diameter of 10.5 cm, we can find its radius by dividing the diameter by 2:
Radius (r) = Diameter / 2 = 10.5 cm / 2 = 5.25 cm
Now, we can plug the radius into the volume formula:
Volume = (4/3) × π × (5.25 cm)³
Volume ≈ (4/3) × 3.14 × (144.703125 cm³)
Volume ≈ 4.1867 × 144.703125 cm³
Volume ≈ 606.25 cm³
The approximate volume of the sphere is 606.25 cm³, which is closest to option D. 606 cm³.

For more questions on  volume

https://brainly.com/question/28298028

#SPJ11

Answer: A and D

Step-by-step explanation: Its obvious.

Answer:

Square

Parallelogram

Step-by-step explanation:

Inner diagonals are all right angles and both diagonals are congruent.

Also, a square must be a parallelogram.

Answer:

972

Step-by-step explanation: