Suppose you have two six-sided dice where each side is equally likely to land face up when rolled.

What is the probability that you will roll doubles?
(Give your answer as a number between 0 and 1. Round to 2 decimal places.)

What is the probability that you will roll a sum of twelve?
(Give your answer as a number between 0 and 1. Round to 2 decimal places.)

Answer:

[tex]\textsf{1.}\quad \sf \overline{AZ} = 28 \; meters[/tex]

[tex]\textsf{2.}\quad \sf \overline{AM} = 28 \; meters[/tex]

[tex]\textsf{3.}\quad b = \sf 4[/tex]

[tex]\textsf{4.}\quad \sf Perimeter = 112\; meters[/tex]

[tex]\textsf{5.}\quad \sf \overline{MX} = 22\; meters[/tex]

[tex]\textsf{6.}\quad \sf \overline{AX} = 10\sqrt{3}\; meters[/tex]

[tex]\textsf{7.}\quad \sf \overline{EX} = 10\sqrt{3}\; meters[/tex]

[tex]\textsf{8.}\quad \sf \overline{AE} = 20\sqrt{3}\; meters[/tex]

Step-by-step explanation:

All sides of a rhombus are the same length. Therefore, for rhombus MAZE:

[tex]\sf \overline{AZ} = \overline{AM} = \overline{ZE} = \overline{EM}[/tex]

Given:

As the sides of a rhombus are the same length, we can equate the expressions for sides AZ and AM, and solve for b:

[tex]\begin{aligned}\overline{\sf AZ}&=\overline{\sf AM}\\8b-4&=5b+8\\8b-4-5b&=5b+8-5b\\3b-4&=8\\3b-4+4&=8+4\\3b&=12\\3b \div 3&=12 \div 3\\b&=4\end{aligned}[/tex]

Therefore, the value of b is 4.

To find the length of AZ and AM, substitute the found value of b into one of the expressions:

[tex]\begin{aligned}\overline{\sf AZ}&=8b-4\\&=8(4)-4\\&=32-4\\&=28\end{aligned}[/tex]

Therefore, as AZ = AM, then AZ = 28 and AM = 28.

[tex]\hrulefill[/tex]

As the sides of a rhombus are equal in length, each side length is 28 meters (as found previously).

The perimeter of rhombus MAZE is the sum of its side lengths. Therefore:

[tex]\begin{aligned}\sf Perimeter\;MAZE&=\sf \overline{AZ} +\overline{AM} +\overline{ZE}+ \overline{EM}\\&=28+28+28+28\\&=112\; \sf meters\end{aligned}[/tex]

Therefore, the perimeter of rhombus MAZE is 112 meters.

[tex]\hrulefill[/tex]

The point of intersection of the diagonals of rhombus MAZE is point X.

As the diagonals of a rhombus are perpendicular bisectors of each other, then:

[tex]\sf \overline{AX}=\overline{EX}\quad and \quad \overline{AX}+\overline{EX}=\overline{AE}[/tex]

[tex]\sf\overline{MX}=\overline{ZX}\quad and \quad\overline{MX}+\overline{ZX}=\overline{MZ}[/tex]

Given MZ = 44 meters, and MX is half of MZ, then:

[tex]\sf \overline{MX}=\overline{ZX}=22\;meters[/tex]

As the diagonals bisect each other at 90°, m∠MXA= 90°. Therefore, ΔMXA is a right triangle with hypotenuse AM = 28 and leg MX = 22.

As we know the lengths hypotenuse AM and leg MX, we can use Pythagoras Theorem to calculate the length of the other leg, AX:

[tex]\begin{aligned}\sf \overline{AX}^2+\overline{MX}^2&=\sf \overline{AM}^2\\\sf \overline{AX}^2+22^2&=\sf 28^2\\\sf \overline{AX}^2&=\sf 28^2-22^2\\\sf \overline{AX}&=\sqrt{\sf 28^2-22^2}\\\sf \overline{AX}&=\sf 10\sqrt{3}\; meters\end{aligned}[/tex]

As the diagonals bisect each other, AX = EX. Therefore:

[tex]\sf \overline{EX}=\sf 10\sqrt{3}\; meters[/tex]

The length of diagonal AE is the sum of segments AX and EX. Therefore:

[tex]\begin{aligned}\sf \overline{AE}&=\sf \overline{AX}+\overline{EX}\\&=\sf 10\sqrt{3}+10\sqrt{3}\\&=\sf 20\sqrt{3}\; meters\end{aligned}[/tex]

[tex]\hrulefill[/tex]

Note: The attached diagram is drawn to scale.

Answer:

question where is the question?

We may be confident that this is the correct scale factor because both equation equations yield the same value of k. As a result, the dilatation has a scale factor of 5/8 and is centered at the origin.

An equation is a statement in mathematics that states the equality of two expressions. An equation has two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9". The purpose of equation solving is to determine which variable(s) must be changed in order for the equation to be true. Simple or complex equations, regular or nonlinear equations, and equations with one or more elements are all possible. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are employed in a variety of mathematical disciplines, including algebra, calculus, and geometry.

Let (x,y) be a point on the plane and k be the dilation scale factor centred at the origin. The image of (x,y) under dilation is thus given by (kx, ky).

The dilation is given as (4,6) to (5/2,15/4). That is to say:

[tex]k(4) = 5/2 \sk(6) = 15/4\\k = 5/8 \sk = 5/8[/tex]

We may be confident that this is the correct scale factor because both equations yield the same value of k. As a result, the dilatation has a scale factor of 5/8 and is centered at the origin.

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The parameter for determining the diameter of an object depends on the specific object being measured. Here are some examples of parameters that can be used to determine diameter  the answer is  5276.7 cm3. Thus, option D is correct.

The formula for the volume of a sphere is  [tex]V = (4/3)πr^3[/tex] , where r is the radius of the sphere.

Since we are given the diameter of the sphere, we can find the radius by dividing the diameter by 2:

[tex]r = 21.6 cm / 2 = 10.8 cm[/tex]

Substituting this value into the formula, we get:

[tex]V = (4/3)\pi(10.8)^3[/tex]

[tex]= 4.18879 \times (10.8)^3[/tex]

[tex]= 5276.794 cm^3[/tex]

Rounding to the nearest tenth, we get:

[tex]V \approx 5276.8 cm^3[/tex]

Therefore, the answer is D) 5276.7 cm3.

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The given question is incomplete. the complete question is given below.

The diameter of a sphere is 21.6 cm. What is the sphere's volume? Round to the nearest tenth, if necessary. A) 693.2 cm3 B) 1453.8 cm3 C) 1868.5 cm3 D) 5276.7 cm3

Answer:

We can use the half-angle formula for sine to find the exact value of sin(a/2) in terms of sin(a):

sin(a/2) = ±√[(1 - cos(a))/2]

where the ± sign depends on the quadrant of a/2.

To use this formula, we first need to find cos(a). We can do this using the identity:

sin^2(a) + cos^2(a) = 1

Substituting sin(a) = 7/9, we get:

(7/9)^2 + cos^2(a) = 1

Simplifying and solving for cos(a), we get:

cos(a) = ±4/9

Since a is in quadrant I, we take the positive value of cos(a):

cos(a) = 4/9

Now we can use the half-angle formula for sine to find sin(a/2):

sin(a/2) = ±√[(1 - cos(a))/2]

Substituting cos(a) = 4/9, we get:

sin(a/2) = ±√[(1 - 4/9)/2]

Simplifying, we get:

sin(a/2) = ±√(5/18)

Since a is in quadrant I, a/2 is also in quadrant I, so we take the positive value of sin(a/2):

sin(a/2) = √(5/18)

Therefore, the exact value of sin(a/2) is √(5/18)

Rewriting 4 x 3/6 as the product of a unit fraction and a whole number is: 12 * 1/6

The parameters are given as:

Number - 4

Fraction - 3/6

The following steps can be used to determine the product as the product of a whole number and a unit fraction:

Step 1 - Remember the whole number are those numbers that involve all positive integers and zero.

Step 2 - Also remember that the unit fraction is nothing but a fraction whose numerator is 1.

Step 3 - Write the given expression.

4 * 3/6

Step 4 - Convert the given fraction into a unit fraction by multiplying 4 by 3 in the above expression.

4 * 3 * 1/6

Step 5 - Simplify the above expression.

12 * 1/6

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Answer:

1250/500

=2.5

Multiplied by interest rate (30)

2.5 times 30

= $75.00

Step-by-step explanation:

Hope I helped.

Roderick earns an interest of $30 per year for every $500 deposited in his savings account. This means that the interest rate per $500 deposit is:Interest rate per $500 = $30/$500 = 0.06 or 6%To calculate the interest earned on Roderick's savings account, we first need to determine how many $500 deposits he has. We can do this by dividing his total savings by $500:Number of $500 deposits = $1,250/$500 = 2.5

The successor of -34 is -33 using the formula "n+1".

A phrase that follows or is right after a specific number, term, or value is known as a successor.

The successor of n is "n+1" if n is a number (and n belongs to any whole number).

The terms just after, immediately after, and next number/next value are also used to describe a successor.

As is common knowledge, integers are collections of numbers that range from negative infinity to positive infinity.

The integers are.........., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,.................. The preceding and following numbers will also be negative integers if the provided number is a negative integer.

So, the successor of -34:

= -34 + n

= -34 + 1

= - 33

Therefore, the successor of -34 is -33 using the formula "n+1".

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The volume of the solid is (64/3)√3 cubic units, which is answer choice B.

A circle is a geometric shape in a two-dimensional plane, consisting of all the points that are at a fixed distance, called the radius, from a given point, called the center. The distance around the circle is called the circumference. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14159. The formula for the area of a circle is A = πr^2, where r is the radius of the circle. Circles have many real-world applications, such as in the design of wheels, gears, and other rotating objects. They are also important in mathematics and science, as they provide a simple and elegant way to study and understand the properties of curves and curved surfaces.

We can approach this problem by considering a vertical slice of the solid taken perpendicular to the y-axis. This slice will be an equilateral triangle with a side length that depends on the y-coordinate.

At y = 0, the circle x² + y² = 16 intersects the x-axis at x = ±4. This means that the equilateral triangle at y = 0 has side length 2√3 times the distance from the origin to the x-axis, which is 4√3. Therefore, the area of this triangle is:

A(0) = (√3/4) (4√3)² = 12√3

At a general y-coordinate y > 0, the equilateral triangle will have side length equal to the distance between the points where the circle intersects the line y = k, where k is the y-coordinate. This distance can be found using the Pythagorean theorem:

d = √(16 - k²) - √k² = √(16 - 2k²)

The area of the equilateral triangle at y is then:

A(y) = (√3/4) d² = (√3/4) (16 - 2k²)

To find the volume of the solid, we can integrate the cross-sectional areas with respect to y from 0 to 4, using the formula for the area of an equilateral triangle:

V = ∫(0 to 4) A(y) dy = ∫(0 to 4) (√3/4) (16 - 2k²) dy

= (√3/4) (16y - (2/3) y³)|0 to 4

= (√3/4) [(64 - (2/3)(64)) - (0 - 0)]

= (64/3)√3

Therefore, the volume of the solid is (64/3)√3 cubic units, which is answer choice B.

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Answer:

To add mixed numbers, we need to add the whole numbers separately and fractions separately.

Starting with the whole numbers, we have:

9 1/2 − 3 7/8 + 4 4/5 − 1 1/2

= (9 + 4) − (3 + 1) + (4/5 − 1/2) + (1/8 − 7/8) (grouping the terms)

= 10 − 4 + (8/10 − 5/10) + (−6/8) (converting fractions to have a common denominator)

= 6 + 3/10 − 3/4 (simplifying fractions and adding whole numbers)

= 5 7/20 (expressing the result as a mixed number in simplest form)

Therefore, the value of the expression is 5 7/20.

The radius r for the circle C is equal to 39 using the Pythagoras rule for the right triangle ABC

Since the line AB is tangent to the circle at point B, then the triangle ABC is a right triangle and the Pythagoras rule can be applied as follows:

(50 + r)² = r² + 80²

r² = (50 + r)² - 80²

r² = (50 + r - 80)(50 + r + 80) {difference of two square}

r² = (r - 30)(r + 130)

r² = r² + 130r - 30r - 3900 {expansion of brackets}

r² - r² + 130r - 30r = 3900 {collect like terms}

100r = 3900

r = 3900/100 {divide through by 100}

r = 39

Therefore, the radius r for the circle C is equal to 39 using the Pythagoras rule for the right triangle ABC.

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The fraction that is equivalent to 5/7 is 15/21

It is important to note that fractions are simply described as part of a whole number or element.

Also, equivalent expressions are defined as expressions that have the same solution but differ in the mode of arrangement of the values.

From the information given, we have;

The numerator be x

The denominator is 9 less than twice the numerator

This is represented as;

x/2x - 9 = 5/7

Cross multiply the values, we have;

7(x) = 5(2x - 9)

expand the bracket

7x = 10x - 45

collect the like terms, we have;

7x - 10x = -45

-3x = -45

Make 'x' the subject

x = 15

Then, the fraction = 15/21

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Answer:

D. A triangle with sides measuring 5 inches, 7 inches, and 9 inches. This is because the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In option A, the side lengths satisfy this condition since 50 + 35 > 25. In option B, the side lengths do not satisfy this condition since 5 + 10 < 15. In option C, the side lengths satisfy this condition since 8 + 12 > 85. In option D, the side lengths do not satisfy this condition since 5 + 7 < 9, 7 + 9 > 5, and 5 + 9 > 7.

Okay, just think of dilations as scaling the object bigger or smaller. You are just multiplying all points on the shape by a common scalar.

The only other thing is a negative dilation reflects the shape over the origin (which is quite intuitive cause you negate all the coordinates).

Now for question 1 your just trying to find the scale factor given an original point and a dilated point. Since all points are multiplied by the same factor,

(-3,6)x = (-4,8)

x=4/3

For the second question, just check points to see if all follow the same dilation scale factor. For our purposes it suffices to just check the each vertex.

(1,1) -> (2,2) so the scale factor must be 2

(1,4) -> (2,8) good

(5,1) -> (10,2) good

(5,4) -> (10,8) good

So, this transformation describes a dilation. The scale factor is 2.

Step-by-step explanation:

the width is 23.5ft and the length is 47ft

An equation to represent relationship of the weights shown on the scale include the following: 22 + x = 34.

Based on the information provided about the weights on this balanced scale, we can logically deduce the following parameters;

Each small square = 1 unit.

Each larger square = 10 units.

The variable x represent the weight of the triangle.

Since there are four small squares and three large squares each labeled ten on one side of this balanced scale, we have:

Total weight = 4(1) + 3(10)

Total weight = 34 units.

Similarly, there are two small squares, two large squares, and a triangle labeled x on the other side of this balanced scale, we have:

Total weight = 2(1) + 2(10) + x

Total weight = 22 + x

By equating the two equations, we have:

22 + x = 34

x = 34 - 22

x = 12

In conclusion, there are 34 units on each side of this balanced scale.

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The maximum height reached after the 13th bοunce is 6.14 cm.

The height οf bοunce is the height tο which an οbject rebοunds after cοIIiding with a surface, such as a baII bοuncing οn the grοund οr a diver bοuncing οff a diving bοard. The height οf the bοunce depends οn severaI factοrs, incIuding the initiaI height οf the οbject, the surface it cοIIides with, the eIasticity οf the οbject and the surface, and the angIe οf incidence.

Tο sοIve this prοbIem, we need tο use the fοrmuIa fοr the height οf each bοunce:

[tex]h = (3/4)^{{n}} \times H[/tex]

where h is the height οf the nth bοunce, H is the initiaI height (in this case, 187.00 cm), and n is the number οf bοunces.

We want tο find the maximum height reached after the 13th bοunce, which means we need tο find the height οf the 13th bοunce and then muItipIy it by 3/4 tο get the maximum height.

Using the fοrmuIa abοve, we can find the height οf the 13th bοunce:

[tex]h = (3/4)^{{13}} \times 187.00[/tex]

h ≈ 8.18 cm

Nοw we can find the maximum height:

maximum height = (3/4) × h

maximum height = (3/4) ×8.18

maximum height ≈ 6.14 cm

Therefοre, the maximum height reached after the 13th bοunce is apprοximateIy 6.14 cm.

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Answer:

here is your answer  attached

Step-by-step explanation:

Answer:

63m+18

Step-by-step explanation:

9*7m is 63m and 9*2 is 18

Combine them and you get 63m+18!

Therefore, the difference between the most common and least common amounts on the line plot is 8.

"Least common" refers to the item or value that appears the fewest number of times in a given set or group. For example, if you have a set of numbers {2, 4, 2, 5, 3, 4, 1}, the least common number in the set is 1 because it appears only once, while the most common number is 2 and 4 because they both appear twice. In a line plot, the least common amount is the one that appears the fewest number of times on the p.

Given by the question.

To find the difference between the most common and least common amounts on a line plot, follow these steps:

Look at the line plot and identify the most common amount. This is the amount that appears the most frequently on the plot.

Look at the line plot and identify the least common amount. This is the amount that appears the least frequently on the plot.

Subtract the least common amount from the most common amount. The result will be the difference between the most common and least common amounts on the line plot.

For example, if the most common amount on the line plot is 10 and the least common amount is 2, then the difference would be:

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Given:-

To find:-

Answer:-

In the given right angled triangle, we may use the trigonometric ratios. We can see that the measure of the longest side is "x" which is hypotenuse and it needs to be find out. The perpendicular in this case is "2" .

We may use the ratio of sine here as , we know that in any right angled triangle,

[tex]\implies\sin\theta =\dfrac{p}{h} \\[/tex]

And here , p = 2 and h = x , so on substituting the respective values, we have;

[tex]\implies \sin\theta = \dfrac{2}{x} \\[/tex]

Again here angle is 60° . So , we have;

[tex]\implies \sin60^o =\dfrac{2}{x} \\[/tex]

The measure of sin45° is √3/2 , so on substituting this we have;

[tex]\implies \dfrac{\sqrt3}{2}=\dfrac{2}{x} \\[/tex]

[tex]\implies x =\dfrac{2\cdot 2}{\sqrt3}\\[/tex]

Value of √3 is approximately 1.732 . So we have;

[tex]\implies x =\dfrac{4}{1.732} \\[/tex]

[tex]\implies \underline{\underline{\red{\quad x = 2.31\quad }}}\\[/tex]

Hence the value of x is 2.31 .

Answer:

The length of side x to the nearest tenth is 2.3.

Step-by-step explanation:

From inspection of the given right triangle, we can see that the interior angles are 30°, 60° and 90°. Therefore, this triangle is a 30-60-90 triangle.

A 30-60-90 triangle is a special right triangle where the measures of its sides are in the ratio  1 : √3 : 2.  Therefore, the formula for the ratio of the sides is b: b√3 : 2b where:

We have been given the side opposite the 60° angle, so:

[tex]\implies b\sqrt{3}=2[/tex]

Solve for b by dividing both sides of the equation by √3:

[tex]\implies b=\dfrac{2}{\sqrt{3}}[/tex]

The side labelled "x" is the hypotenuse, so:

[tex]\implies x=2b[/tex]

Substitute the found value of b into the equation for x:

[tex]\implies x=2 \cdot \dfrac{2}{\sqrt{3}}[/tex]

[tex]\implies x=\dfrac{4}{\sqrt{3}}[/tex]

[tex]\implies x=2.30940107...[/tex]

[tex]\implies x=2.3\; \sf (nearest\;tenth)[/tex]

Therefore, the length of side x to the nearest tenth is 2.3.

Answer:

To solve for x, we can start by cross-multiplying the equation to eliminate the denominators:

(a+bx)(c+d) = (c+dx)(a+b)

Expanding the terms on both sides:

ac + adx + bc + bdx^2 = ac + abx + cdx + bd

Simplifying and rearranging the terms:

adx + bdx^2 - abx - cdx = bd - ac

dx(ad - ab - c) = bd - ac

Now, since we know that cb=ad, we can substitute ad=cb into the equation:

dx(cb - ab - c) = bd - ac

dx(cb - ab - c) = b(cd - ac)

x = b(cd - ac)/(d(cb - ab - c))

Therefore, the solution for x is:

x = b(cd - ac)/(d(cb - ab - c))

As a result, Ava's luggage will weigh 123622200 grams more than the permitted maximum.

Weight is the force of gravity that pulls objects toward the core of the Earth. The resulting force that pulls a substance toward Earth is known as gravity. In contrast to gravity force, which occurs among any two masses, this only occurs between Earth as well as a mass.

First, we need to convert all the weights to grams, since the weight limit is given in kilograms and the weights of clothes, electrical accessories, and toiletries are given in grams.

Maximum weight limit = 2020 kg = 2020000 g

Weight of empty suitcase = 33 kg = 33000 g

Weight of clothes = 55 kg = 55000 g

Weight of electrical accessories = 44 kg = 44000 g

Weight of 55 hardback books = 55 x 720720 g = 39639600 g

Weight of toiletries = 46004600 g

Total weight of suitcase and contents = 33000 + 55000 + 44000 + 39639600 + 46004600 = 125642200 g

Amount over maximum weight limit = total weight - maximum weight limit = 125642200 - 2020000 = 123622200 g

Therefore, Ava's suitcase will be over the maximum weight limit by 123622200 grams.

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The value of x in the rectangle is 36.

A rectangle is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.

All angles measure 90∘ in a rectangle. The sum of angles in a rectangle is 360 degrees.

Therefore, let's find the value of x in the angles.

Hence,

∠2 = x + 30

∠5 = 2x - 48

Therefore,

∠2 + ∠5 = 90°

x + 30 + 2x - 48 = 90

3x - 18 = 90

3x = 90 + 18

3x = 108

divide both sides by 3

x = 108 / 3

x = 36

Therefore,

x = 36

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Answer:

Let's start by finding the volume of water in the trough as a function of its depth.

At a depth of h cm, the cross-sectional area of the water is an isosceles trapezoid with bases of length b1 = 40 + (h/5) cm and b2 = 90 + (h/2) cm, and height 50 cm. The average width of the trapezoid is (b1 + b2)/2 = 65 + (3h/10) cm. Therefore, the volume of water in the trough at this depth is:

V(h) = 10 m x [(65 + (3h/10)) / 100 cm] x h cm

Simplifying this expression, we get:

V(h) = (13/2000) h^2 m^3

Now, we can use the chain rule to find the rate of change of V with respect to time t, given that dV/dt = 0.1 m^3/min:

dV/dt = (dV/dh) x (dh/dt) = (26/2000) h (dh/dt)

At the moment when the water is 10 cm deep, we have:

h = 10 cm

dV/dt = 0.1 m^3/min

Plugging in these values, we get:

0.1 m^3/min = (26/2000) x 10 cm x (dh/dt)

Solving for dh/dt, we get:

dh/dt = 0.1 m^3/min / (26/2000) / 10 cm

dh/dt ≈ 0.192 m/min

Therefore, the water level is rising at a rate of approximately 0.192 m/min when the water is 10 cm deep.

Step-by-step explanation:

2.2 percentage answer you silly

Answer:

D) 115.2π cm².

Step-by-step explanation:

The surface area of a cylinder can be calculated using the formula:

Surface Area = 2πr² + 2πrh

where r is the radius and h is the height of the cylinder.

In this case, r = 4 cm and h = 10.4 cm. Substituting these values in the formula, we get:

Surface Area = 2π(4)² + 2π(4)(10.4)

Surface Area = 2π(16) + 2π(41.6)

Surface Area = 32π + 83.2π

Surface Area = 115.2π

Therefore, the exact surface area of the candle is 115.2π cm².

The answer is (D) 115.2π cm².

Answer: The answer is D, 115.2π cm²

Step-by-step explanation: When we use the formula of 2πrh+2πr2=2·π·4·10.4+2·π·42 to get the surface area, which equals 361.91

We can divide this by pi to get 115.2π cm²

Hope this helped!

Answer: 0.24z

Step-by-step explanation: If you make 24% a decimal you will get 0.24. Then you make your equation 0.24z or 0.24 x z .