Find the total number of outcomes that are possible. Selecting a letter from the word TROPHY and a day from the month of May.

A. The relationship between ∠7 and ∠8 is that they are vertically opposites angles and they are equal.

B. Since 5y-29 and 3y+19 are vertically opposites angles, we can say equate the two angles (i.e. 5y-29 = 3y+19) and then solve for y.

C. y = 24, ∠7 =  89° and ∠8 = 89°

Angle geometry deals with the study of angles, their measurement, and their properties. An angle is formed when two lines or line segments intersect each other at a point.

A. The relationship between ∠7 and ∠8 is that they are vertically opposites angles. Since vertically opposites angles are equal, we can say  ∠7 = ∠8.

B. Since 5y-29 and 3y+19 are vertically opposites angles, we can say equate the two angles (i.e. 5y-29 = 3y+19) and then solve for y

C. 5y-29 = 3y+19

5y-3y= 19 + 29

2y = 48

y = 48/2

y = 24

Let's find either the value of  5y-29 or 3y+19:

Put y = 24 in 5y-29

5y-29 = 5(24) - 29 = 91°

∠7 + (5y-29) = 180°  (sum of angles on a straight line is 180°)

∠7 +  91° = 180°

∠7 = 180 - 91 = 89°

Since  ∠7 = ∠8

∠8 = 89°

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The sum of probabilities in a distribution always equals 1, as it ensures all possible outcomes have a certainty of 100%. It is a fundamental rule in probability, and deviations suggest issues with the distribution.

The sum of probabilities in a probability distribution always equals 1 because probabilities represent the likelihood of an event occurring, and it is certain that some event will occur. In other words, the total probability of all possible outcomes must add up to 100% or 1.

For example, if we flip a coin, the probability of getting heads is 0.5 and the probability of getting tails is also 0.5. The sum of these probabilities is 1, which means that one of these events is certain to happen when the coin is flipped.

If the sum of probabilities is not equal to 1, then it means that there is something wrong with the distribution, such as a missing outcome or an incorrect probability assignment. Therefore, it is a fundamental rule of probability that the sum of probabilities in a distribution always equals 1.

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Complete question: Why should the sum of the probabilities in a probability distribution always equal to 1?

The standard deviation of the sampling distribution of  30 seconds songs then the total number of songs are 36.

The mean and the standard deviation of the sampling distribution of x:

The mean and the standard deviation of the sampling distribution of x are defined according to the Central Limit Theorem, which states that:

The mean is the same as the population mean. The standard deviation is the division of the population standard deviation by the square root of the sample size. The central limit theorem states that as long as the sample size is large enough, the sampling distribution of the mean will always be normally distributed. The sampling distribution for the mean will be normal whether the population is normally distributed, Poisson, binomial, or any other distribution.

Now,

The parameters for this problem are given as follows:

Population mean of 225 seconds.

Population standard deviation of 60 seconds.

Sample size of 10 seconds.

Hence the standard deviation for the sampling distribution of x is given as follows:

s = 60/√(10) = 19 seconds.

if the sampling distribution of the songs is 30second tehn the tottal number of songs are 36

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Answer:  x=25.9

Step-by-step explanation:

Tan = opp / adj

Tan 67 ° = x / 11

11 Tan (67 °)= x

x = 25.914

  = 25.9 ( 3 significant figures)

Answer:

[tex]\large\boxed{\tt -10y + 10.2 }[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to simplify the given expression.}[/tex]

[tex]\textsf{Note that we can't simplify this expression down to 1 term.}[/tex]

[tex]\large\underline{\textsf{Why?}}[/tex]

[tex]\textsf{This is due to 2 numbers having the variable y, and 2 other numbers without y.}[/tex]

[tex]\textsf{Consider these terms Unlike Terms, as they have a difference in which we can't}}[/tex]

[tex]\textsf{combine them.}[/tex]

[tex]\textsf{Even though there are some Unlike Terms, there is a few Like Terms.}[/tex]

[tex]\textsf{Let's identify the Like Terms, and the Unlike Terms in our expression.}[/tex]

[tex]\large\underline{\textsf{Like Terms;}}[/tex]

[tex]\tt 4 \ and \ 6.2 \ are \ like \ terms. \ (Both \ don't \ have \ any \ variables)[/tex]

[tex]\tt -2y \ and \ -8y \ are \ like \ terms. \ (Both \ have \ the \ same \ variable)[/tex]

[tex]\large\underline{\textsf{Unlike Terms;}}[/tex]

[tex]\tt 4 \ and \ -2y \ are \ Unlike \ Terms.[/tex]

[tex]\tt 6.2 \ and \ -8y \ are \ Unlike \ Terms.[/tex]

[tex]\tt 4 \ and \ -8y \ are \ Unlike \ Terms.[/tex]

[tex]\tt 6.2 \ and \ -2y \ are \ Unlike \ Terms.[/tex]

[tex]\textsf{We know what the Unlike Terms, and Like Terms are for our expression.}[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\textsf{Solve by combining Like Terms in the expression.}[/tex]

[tex]\large\underline{\textsf{Combine Like Terms;}}[/tex]

[tex]\tt 4-2y + (-8y) + 6.2[/tex]

[tex]\textsf{When we add a negative term, we are actually subtracting with that term.}[/tex]

[tex]\tt 4-2y -8y + 6.2[/tex]

[tex]\underline{\textsf{Our final answer should be;}}[/tex]

[tex]\large\boxed{\tt -10y + 10.2 }[/tex]

Answer:

[tex] \sf \: -10y + 10.2[/tex]

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The expression is,

→ 4 - 2y + (-8y) + 6.2

Let's simplify the expression,

→ 4 - 2y + (-8y) + 6.2

→ 4 - 2y - 8y + 6.2

→ -2y - 8y + 6.2 + 4

→ (-2y - 8y) + (6.2 + 4)

→ (-10y) + (10.2)

→ -10y + 10.2

Hence, answer is -10y + 10.2.

The volume of the pyramid is 4480ft³

A pyramid is a three-dimensional shape. A pyramid has a polygonal base and flat triangular faces, which join at a common point called the apex.

The volume of a pyramid is expressed as:

V = 1/3 b × h

b = base area

h = height

Here, base are = 17.5 × 32

= 560ft²

Height = 24ft

V = 1/3 × 560 × 24

V = 560 × 8

V = 4480 ft³

Therefore the volume of the pyramid is 4480ft³

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Based on the line plot display, A, the most appropriate measure of center to represent the data in the graph is the median because there are no clear outliers present.

Median is an appropriate measure of center when there are outliers present in the data. Outliers are extreme values that are much larger or smaller than the rest of the data, and they can greatly affect the mean. In such cases, the median is a better measure of center because it is not affected by outliers.

Outliers can skew the mean, making it an unreliable measure of center in this case. The median, on the other hand, is less affected by outliers and provides a more representative measure of the central tendency of the data.

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Complete question:

The line plot displays the cost of used books in dollars.

Which measure of center is most appropriate to represent the data in the graph, and why?

O The median is the best measure of center because there are no outliers present.

The mean is the best measure of center because there are no outliers present.

O The median is the best measure of center because there are outliers present.

O The mean is the best measure of center because there are outliers present.

Answer:

x^2 - x - 6 = 0

Step-by-step explanation:

If the quadratic equation has solutions 3 and -2, then it can be factored as:

(x - 3)(x + 2) = 0

Expanding the left side of the equation, we get:

x^2 - x - 6 = 0

This is the quadratic equation that has a leading coefficient of 1 and solutions 3 and -2.

Answer:

After 16 years Mr. Jibril will be twice as old as his son.

Step-by-step explanation:

t - age Mr. Jibril

s - son age

t=4s (father is 4 times older than son)

t-4=7(s-4) (4 years ago they both have 4 year old less and father was 7 times older than son)

t=7s-28+4

t=7s-24

7s-24=4s

3s=24

s=8

t=32

x- years after Mr. Jibril will be twice as old as his son.

32+x=2(8+x)

32+x=16+2x

16=x

x=16

The given statement "for continuous random variables, the probability of any specific value of the random variable is one." is false because the random variable taking on any specific value is then given by the area under the PDF curve at that value, which is zero.

In fact, for continuous random variables, the probability of any specific value is zero. This may seem counterintuitive at first, but it is a fundamental property of continuous random variables.

The PDF is a function that describes the relative likelihood of the random variable taking on a particular value within its range. The probability of the random variable taking on a specific value is then given by the area under the PDF curve at that value.

Since the PDF is a continuous function, the probability of the random variable taking on any specific value is zero. This is because the area under a continuous curve at any single point is zero.

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The measure of the angle between the two planes is given as follows:

66.1º.

The Law of Cosines is a trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is also known as the Cosine Rule.

The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation holds true:

c^2 = a^2 + b^2 - 2ab cos(C)

The side opposite to the angle is of 241 km, hence the parameters are given as follows:

c = 241, a = 207, b = 233.

Then the angle measure is obtained as follows:

241² = 207² + 233² - 2 x 207 x 233cos(C)

96462cos(C) = 207² + 233² - 241²

96462cos(C) = 39057

cos(C) = 39057/96462

cos(C) = 0.4049

C = arccos(0.4049)

C = 66.1º.

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Answer:

8d[tex]\sqrt{e}[/tex]

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{ab}[/tex]  = [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex]

given

[tex]\sqrt{25d^2e}[/tex] - [tex]\sqrt{d^2e}[/tex] + 2[tex]\sqrt{4d^2e}[/tex]

evaluating each term separately

[tex]\sqrt{25d^2e}[/tex]

= [tex]\sqrt{25}[/tex] × [tex]\sqrt{d^2}[/tex] × [tex]\sqrt{e}[/tex]

= 5 × d × [tex]\sqrt{e}[/tex]

= 5d[tex]\sqrt{e}[/tex]

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

[tex]\sqrt{d^2e}[/tex]

= [tex]\sqrt{d^2}[/tex] × [tex]\sqrt{e}[/tex]

= d × [tex]\sqrt{e}[/tex]

= d[tex]\sqrt{e}[/tex]

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

[tex]\sqrt{4d^2e}[/tex]

= [tex]\sqrt{4}[/tex] × [tex]\sqrt{d^2}[/tex] × [tex]\sqrt{e}[/tex]

= 2 × d × [tex]\sqrt{e}[/tex]

= 2d[tex]\sqrt{e}[/tex]

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

then combining them gives

5d[tex]\sqrt{e}[/tex] - d[tex]\sqrt{e}[/tex] + 2(2d[tex]\sqrt{e}[/tex])

= 4d[tex]\sqrt{e}[/tex] + 4d[tex]\sqrt{e}[/tex]

= 8d[tex]\sqrt{e}[/tex]

The measure of ∠O is 56°. The solution has been obtained by using properties of circles.

What is a circle?

A circle is a round-shaped figure that has no sides or edges. A circle is a closed shape, a two-dimensional shape, and a curved shape in geometry.

We are given that m∠R = 28°.

Now, we take a point P on the circumference of the circle.

We know that in a circle, the angles that the same arc subtends on the circumference have equal measurements.

So, both the angles i.e. ∠P and ∠R are same as they are subtended by the same arc.

Therefore, we get

m∠P = m∠R = 28°

Moreover, an arc's angle at the circle's centre is twice as large as its angle at the circle's edge.

So, from this we get

⇒ m∠O = 2 * m∠P

⇒ m∠O = 2 * 28°

⇒ m∠O = 56°

Hence, the measure of ∠O is 56°.

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The complete question has been attached below

Therefore, the scale factor of triangle ABC to triangle UVW is  5 and option C is the correct choice.

Two triangles are shown to us in the photograph. We must determine the ABC to UVW scale factor.

To find the scale factor of our given triangles, we will divide one side of triangle UVW by its corresponding side of triangle ABC.

Original side  ×scale factor = new side

5 × scale factor =25

By multiplying both sides of the equation by 5, we obtain:

5/5×scale factor/5 =25/5

scale factor = 5

What exactly is scale factor?

A scale factor is a figure that, when multiplied by a certain amount, creates a smaller or bigger replica of the original figure. It is the ratio of a blueprint, map, model, or actual thing to the distance or object1. Every inch on a home layout, for instance, would correspond to 4 inches in real life if the scale factor was 1/41.

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Answer: ANSWER IS 5

Step-by-step explanation:

Answer:

18 sides

Step-by-step explanation:

We know the relation between exterior angle, interior angle. Given that each interior angle is 8 times the exterior. So, there are 18 sides for such a polygon given in question.

Answer:

x1 ≈ 0,84; x2 ≈ 4,16

Step-by-step explanation:

Find the discriminant and then both values of x according to the formulas (I added a photo of my solution)

The minimum cost of fencing the rectangular field with an area of 900 square meters is approximately $2,375.15.

Let's solve for one variable in terms of the other using the area equation:

l x w = 900

l = 900/w (by dividing both sides by w)

Now we can substitute this expression for "l" into the perimeter equation:

P = 2l + 2w

P = 2(900/w) + 2w

P = (1800/w) + 2w

To minimize P, we can take the derivative with respect to w and set it equal to zero:

dP/dw = -1800/w² + 2 = 0

Solving for w, we get:

w = √(1800/2) = 30√(2)

We can now use this value of w to find the corresponding value of l from the area equation:

l = 900/w = 900/(30√(2)) = 30√(2)

Therefore, the dimensions of the rectangular field that require the least amount of fencing while still having an area of 900 square meters are l = 30√(2) meters and w = 30√(2) meters.

The total length of fencing required is:

P = 2l + 2w

P = 2(30√(2)) + 2(30√(2))

P = 120√(2)

The minimum cost of the fence can be found by multiplying the total length of fencing by the cost per meter of fencing:

Cost = 14 x P = 14 x 120√(2) = 1680√(2) dollars = $2,375.15.

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Answer: 113.10 inches squared

Step-by-step explanation:

formula for area: A=(pi)r^2

the diameter is 2x the radius so the radius would be 12/2=6. plug 6 in for r and solve. The answer is 113.097 so when you round to the nearest hundredth it becomes 113.10

Answer:

The correct numerical expression using PEDMAS for "subtract the sum of 2 and 9 from the product of 4 and 3" is:

4 x 3 - (2 + 9)

Using the order of operations, first, we perform the addition inside the parentheses, then we multiply 4 and 3, and finally, we subtract the result of the sum from the product:

= 4 x 3 - 11

= 12 - 11

= 1

Therefore, the correct numerical expression is (4 x 3) - (2 + 9) = 1.

Step-by-step explanation:

The probability that Alice has the disease given that she tested positive is only about  0.00563

To solve this problem, we can use Bayes' theorem, which relates the conditional probabilities of two events. Let's define the following events

A: Alice has the disease.

B: Alice tests positive.

We want to find P(A|B), the probability that Alice has the disease given that she tested positive. Bayes' theorem tells us that

P(A|B) = P(B|A)× P(A) / P(B)

where

P(B|A) is the probability of testing positive given that Alice has the disease, which is 1 - the false negative rate = 0.85.

P(A) is the frequency of the disease in the population, which is 0.1% or 0.001.

P(B) is the overall probability of testing positive, which can be calculated using the law of total probability

P(B) = P(B|A) × P(A) + P(B|not A) × P(not A)

where

P(B|not A) is the probability of testing positive given that Alice does not have the disease, which is the false positive rate = 0.15.

P(not A) is the complement of P(A), i.e., the probability that Alice does not have the disease, which is 1 - P(A) = 0.999.

Therefore,

P(B) = 0.85 × 0.001 + 0.15 × 0.999 = 0.15084

Now we can substitute these values into Bayes' theorem

P(A|B) = 0.85 × 0.001 / 0.15084 = 0.00563

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The values of the variable x and y are x = 10 and y = 12.

In mathematics, the intersection of two or more lines refers to the point or points at which the lines meet or cross each other.

When two lines intersect, they form two pairs of opposite angles that add up to 180 degrees. If one pair of opposite angles is congruent, then their measures are equal.

Let's call the measure of the congruent angles a. Then we have:

a = 8x + 10 (the measure of one angle)

a = 15y/2 (the measure of the other angle)

Since these angles are congruent, their measures must be equal. So we can set the two expressions for a equal to each other:

8x + 10 = 15y/2

8x = 15y/2 - 10

 x = ( 15y/2 - 10) / 8  .................    equation 1

To solve for x and y, we need another equation. We know that the sum of the measures of the two angles in a linear pair is 180 degrees. So we can write:

a + a = 180

Substituting the expressions for a, we get:

8x + 10 + 15y/2 = 180

Substituting x =  ( 15y/2 - 10) / 8  into the expression we found for y, we get:

8( 15y/2 - 10) ÷ 8  + 10 + 15y/2 = 180

15y/2 - 10 +  10 + 15y/2 = 180

15y/2 + 15y/2  = 180

30y = 360

   y = 12

Substituting  y = 12 into the expression we found for x,

x = ( 15y/2 - 10) / 8

= ( 15 × 12 /2 - 10) / 8

= (15 × 6 - 10)/8

= 80/8

= 10.

Therefore, the values of x and y are x = 10 and y = 12.

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Answer:

1 and 19

Step-by-step explanation:

3(x-10)^2 = 3(x^2-20x+100) = 3x^2 - 60x + 300

If 3x^2 - 60x + 300 = 243, 3x^2 - 60x + 57 = 0

Divide by 3 to get x^2 - 20x + 19 = 0

use the quadratic equation (-b±√(b²-4ac))/(2a) to get

(20±√324)/2 = (20±18)/2 = 1 and 19

Answer: 20.64 dollars i think.

Step-by-step explanation: 20 percent of 24 is 4.8, so 24-4.8= 19.2

Then, 7 percent of 19.2 is 1.44. The answer is 20.64 dollars I think.

so if the inital amount in the body is 10mg, so half that will just be 5mg, so how long will that be?

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & 5~mg\\ P=\textit{initial amount}\dotfill &10~mg\\ r=rate\to 20\%\to \frac{20}{100}\dotfill &0.2\\ t=hours\dotfill &t\\ \end{cases}[/tex]

[tex]5 = 10(1 - 0.2)^{t} \implies \cfrac{5}{10}=0.8^t\implies \cfrac{1}{2}=0.8^t\implies \log\left( \cfrac{1}{2} \right)=\log(0.8^t) \\\\\\ \log\left( \cfrac{1}{2} \right)=t\log(0.8)\implies \cfrac{\log\left( \frac{1}{2} \right)}{\log(0.8)}=t\implies \stackrel{ \textit{about 3 hrs and 6 mins} }{3.1\approx t}[/tex]

In this setting, a probability of 0.33 means that out of all the people who fly on United Airlines, 33% of them have a frequent flyer account and accumulate miles for free trips.

The agent helping people confirm reservations and check baggage over the busy Thanksgiving day weekend is recording whether each passenger has a frequent flyer account, which means that for each individual passenger, there are two possible outcomes: either they have a frequent flyer account or they don't.

The probability of a passenger having a frequent flyer account is 0.33, which means that if the agent helps 100 passengers over the Thanksgiving weekend, we would expect approximately 33 of them to have a frequent flyer account, on average.

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The possible distances from art class to math class range from approximately 161.3 feet to 351.3 feet.

What is Pythagoras Theorem?

Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

If Braxton walks directly between his art class and math class, then the distance he covers is the shortest distance between the two classrooms, which is the length of the straight line connecting the two points.

We can use the Pythagorean theorem to find this distance:

d = √(95² + 112²) ≈ 144.3 feet

Therefore, the shortest possible distance between the two classrooms is approximately 144.3 feet.

To find the range of possible distances from art class to math class, we need to consider the distance Braxton covers if he stops at his locker.

We can use the triangle inequality to say that the distance between the two classrooms when Braxton stops at his locker must be greater than or equal to the difference between the distance from art class to the locker and the distance from locker to math class:

d ≥ |95 - 112| = 17 feet

So the distance between the two classrooms when Braxton stops at his locker must be at least 17 feet greater than the shortest distance between the two classrooms.

Therefore, the range of possible distances from art class to math class is:

144.3 + 17 ≤ d ≤ 144.3 + (95 + 112) = 351.3 feet

Hence, the possible distances from art class to math class range from approximately 161.3 feet to 351.3 feet.

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The old age dependency ratio as a decimal is 0.190.

The old age dependency ratio is a measure of the number of people who are considered "dependent" on those who are of working age.

Specifically, it is the ratio of the number of people aged 65 years and over to the number of people aged 15 to 64 years old.

Old Age Dependency Ratio = (Number of people over 65) / (Number of people aged 15-64)

Old Age Dependency Ratio = 40,809 / 214,965 = 0.1895

Therefore, Rounding this to the thousandths place the Old Age Dependency Ratio as a decimal is 0.190.

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The formula [tex]V = \pi r^2h[/tex] is used to find the height of a 1-gallon paint can with radius 3 inches, which is approximately 7.81 inches.

The formula for volume of a cylinder:

[tex]V = \pi r^2h[/tex]

where V,r and h are the volume, radius, and height respectively.

In this problem, we are given that the can has a volume of 231 cubic inches, which means:

[tex]231 = \pi r^2h[/tex]

We are also given that the radius of the can is 3 inches, so we can substitute this value into the equation:

[tex]231 = \pi (3^2)h[/tex]

Simplifying, we get:

231 = 9πh

Dividing both sides by 9π, we get:

h = 231 / (9π)

We can simplify this expression by using the approximation π ≈ 3.14:

h = 231 / (9 × 3.14)

h ≈ 7.81

Therefore, the approximate height of the paint can is 7.81 inches.

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If the pennants have a base of 2 meters, the area of one of the larger pennants is 4m².

It is determined by multiplying the length of the rectangle by its width. The formula for area of a rectangle is Area = Length × Width (A = L × W).

To calculate this, we can use the formula for area of a rectangle which is length multiplied by width.

In this case, the length and width of the pennant is both 2 meters, so we can calculate the area by multiplying 2m * 2m= 4m².

The sports team asked Katie to make 30 larger pennants, so the total area of all the pennants will be 120m² (4m² * 30).

This means that the total area of the 30 larger pennants is 120m².

The formula for area of a rectangle can be used to calculate the area of any shape that is rectangular in nature.

Therefore, it can be used to calculate the area of a pennant, or any other shape that is rectangular in nature.

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Let a be the first, b be second and c be the third whole number.

Since the sum of these three numbers is 100.

So, [tex]a+b+c=100[/tex] (equation 1)

Since, The first number is a multiple of 15

Therefore, [tex]a = 15n[/tex]

And, the second number is ten times the third number.

[tex]b = 10c[/tex]

Substituting the values of 'a' and 'b' in equation 1

So, [tex]15n+10c+c=100[/tex]

[tex]15n+11c=100[/tex]

[tex]11c=100-15n[/tex]

[tex]c=\dfrac{100-15n}{11}[/tex]

Therefore, [tex]100-15n[/tex] should be exactly divisible by 11.

So, by taking [tex]n= 1[/tex] and 2, [tex]100-15n[/tex] is not divisible by 11

Let [tex]n =3[/tex]

[tex]c=\dfrac{100-15\times3}{11}[/tex]

[tex]c= 5[/tex]

Now, second number (b) [tex]= 10c = 10\times5=50[/tex]

As, [tex]a+b+c=100[/tex]

[tex]a+50+5=100[/tex]

[tex]a+55=100[/tex]

[tex]a=45[/tex]

Therefore, the three whole numbers are 45, 50, 5.