What is the equation of the midline for the function f(x)? f(x)=12sin(x)+6 enter your answer in the box.

Answer:

Therefore, the total value of Mary's investment after two years is $700.

Step-by-step explanation:

To calculate the total value of Mary's investment after two years, we need to calculate the value of the investment after the first year, and then use that value to calculate the value after the second year.

In the first year, the value of the investment increases by 8%, so the value after the first year is:

Value after first year = $600 + 8% of $600

Value after first year = $600 + 0.08 * $600

Value after first year = $648

In the second year, the value of the investment increases by another 8%, so the value after the second year is:

Value after second year = Value after first year + 8% of Value after first year

Value after second year = $648 + 0.08 * $648

Value after second year = $699.84

Rounding to the nearest dollar, the total value of Mary's investment after two years is:

Total value after two years = $700

The volume of the largest right circular cone that can be inscribed in a sphere of radius 18 cm is approximately 11622.85 cubic centimeters.

To find the largest right circular cone that can be inscribed in a sphere of radius 18 cm, we need to find the cone with the largest possible volume that can fit inside the sphere.

Let's assume that the apex of the cone is at the center of the sphere. Since the cone is a right circular cone, the base of the cone will lie on the surface of the sphere, forming a circle with radius equal to the radius of the sphere, which is 18 cm.

Let's call the height of the cone "h" and the radius of the base of the cone "r". Then we can use the Pythagorean theorem to relate the height, radius, and slant height (which is equal to the radius of the sphere):

r^2 + h^2 = (18 cm)^2

The volume of a cone can be expressed as V = (1/3)πr^2h. We want to maximize this expression subject to the constraint above. We can use the constraint to eliminate one of the variables in the volume expression, then differentiate with respect to the remaining variable and set the derivative equal to zero to find the maximum.

From the constraint, we can solve for h^2:

h^2 = (18 cm)^2 - r^2

Substituting into the volume expression, we get:

V = (1/3)πr^2(18 cm - sqrt(r^2 + h^2))

Simplifying this expression, we get:

V = (1/3)πr^2(18 cm - sqrt((18 cm)^2 - r^2))

Differentiating with respect to r, we get:

dV/dr = (1/3)π(36 cm)r - (1/3)πr^3/sqrt((18 cm)^2 - r^2)

Setting this equal to zero and solving for r, we get:

r = (18 cm)/sqrt(2)

Substituting this value of r back into the expression for h, we get:

h = (18 cm)/sqrt(2)

Finally, substituting these values of r and h into the expression for the volume, we get:

V = (1/3)π((18 cm)/sqrt(2))^2((18 cm) - sqrt(((18 cm)/sqrt(2))^2 + ((18 cm)/sqrt(2))^2))

Simplifying this expression, we get:

V ≈ 11622.85 cubic centimeters

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Answer:

a. (x-5) meters

b. 390 m²

Step-by-step explanation:

A. We get the equation x²+x-30.

We need to find two factors of 30, which equals 1.
6 and -5 are factors of 30.
Now, we can see that (x-5) and (x+6) are the equations. (x+6) cannot be applied, so the answer is (x-5)

B. We can substitute x with 20, and when we plug it in, we get 390 meters.

Answer:

Step-by-step explanation:

a) To find the probability that Mateo will die in his 60th year, we use the value of the probability distribution given in the problem statement: P(x=60) = 0.01051.

To calculate the expected cost to Big Rock Insurance if Mateo dies in his 60th year, we multiply the death benefit of $50,000 by the probability of death:

Expected cost = P(x=60) * $50,000 = 0.01051 * $50,000 = $525.50.

So the expected cost to Big Rock Insurance if Mateo dies in his 60th year is $525.50.

b) To find the probabilities that Mateo will die in years 61, 62, 63, and 64, we use the values of the probability distribution given in the problem statement: P(x=61) = 0.01477, P(x=62) = 0.01744, P(x=63) = 0.02035, and P(x=64) = 0.02227.

To calculate the expected cost to Big Rock Insurance if Mateo dies in each of these years, we multiply the death benefit of $50,000 by the corresponding probability of death:

Expected cost if Mateo dies in his 61st year = P(x=61) * $50,000 = 0.01477 * $50,000 = $738.50.

Expected cost if Mateo dies in his 62nd year = P(x=62) * $50,000 = 0.01744 * $50,000 = $872.00.

Expected cost if Mateo dies in his 63rd year = P(x=63) * $50,000 = 0.02035 * $50,000 = $1017.50.

Expected cost if Mateo dies in his 64th year = P(x=64) * $50,000 = 0.02227 * $50,000 = $1113.50.

So the expected costs to Big Rock Insurance if Mateo dies in his 61st, 62nd, 63rd, and 64th years are $738.50, $872.00, $1017.50, and $1113.50, respectively.

c) To calculate the total expected cost to Big Rock Insurance over the years 60 through 64, we add up the expected costs for each year:

Total expected cost = Expected cost in year 60 + Expected cost in year 61 + Expected cost in year 62 + Expected cost in year 63 + Expected cost in year 64

Total expected cost = $525.50 + $738.50 + $872.00 + $1017.50 + $1113.50

Total expected cost = $4267.00

So the total expected cost to Big Rock Insurance over the years 60 through 64 is $4267.00.

d) If Big Rock Insurance wants to make a profit of $700 above the expected total cost payout for Mateo's death, it would need to charge a premium equal to the expected cost plus the desired profit:

Premium = Total expected cost + Desired profit

Premium = $4267.00 + $700.00

Premium = $4967.00

So Big Rock Insurance should charge a premium of $4967.00 for the policy if it wants to make a profit of $700 above the expected total cost payout for Mateo's death.

Answer:

-1 9/10, -1.7, -1.5, -1 1/10

Step-by-step explanation:

The numbers from least to greatest is   [tex]-1\frac{9}{10}[/tex], -1.7, -1.5,[tex]-1\frac{1}{10}[/tex]

A number system is defined as a system of writing to express numbers.

The given numbers are

-1.5, [tex]-1\frac{9}{10}[/tex], -1.7, [tex]-1\frac{1}{10}[/tex]

Now let us simplify each number or fraction

Convert mixed fractions to improper and find the decimal value.

[tex]-1\frac{9}{10}[/tex]=-81/10

[tex]-1\frac{9}{10}[/tex]=-8.1

[tex]-1\frac{1}{10}[/tex]=-9/10

[tex]-1\frac{1}{10}[/tex]=-0.9

So least to greatest is -8.1, -1.7, -1.5, -0.9

least to greatest is  [tex]-1\frac{9}{10}[/tex], -1.7, -1.5,[tex]-1\frac{1}{10}[/tex]

Hence, the numbers from least to greatest is   [tex]-1\frac{9}{10}[/tex], -1.7, -1.5,[tex]-1\frac{1}{10}[/tex]

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Answer:

k = 11.7

Step-by-step explanation:

Constant of Proportionality

When two quantities y and x are proportional to each other, they are related by the proportionality equation
y = kx
where k is known as the constant of proportionality

The y axis is Money earned in $

x axis is time worked in hours

The relationship is y = kx and we are asked to find k

The constant of proportionality for this graph is nothing but the slope of the graph.

Slope can be found by taking any two points on the graph, determining the difference in y values and dividing by the difference in corresponding x values;

Two points have been chosen for us:
(3, 35.1) and (7, 81.9)

Difference in y values = 81.9 - 35.1 = 46.8 (also known as rise)

Difference in x values = 7 - 3 = 4 (also known as run)

Slope = k = rise/run = 46.8/4 = 11.7

Therefore k = 11.7

Answer: k = 11.7

Step-by-step explanation: hope this helps0^0

Answer:

15.4 is the answer

Stepson

Therefore, the equation for the line tangent to the curve when x = 4 is y = (7/4) x + 7.

An equation is a mathematical statement that shows the equality between two expressions. Equations are used to solve problems and find solutions to mathematical or real-world problems. They typically involve variables, which are symbols that represent unknown values, and constants, which are known values that are used in the equation. Equations can take many forms, but they generally follow the pattern: expression = expression. Equations are an important tool in mathematics, science, and engineering, and they can be used to model and analyze many different types of systems and processes.

Here,

a. To find the equation for the secant line through the points where x has the given values, we need to find the slope of the line passing through the two points. The two points we need to consider are (4, 14) and (9, 21):

slope = (change in y) / (change in x)

= (21 - 14) / (9 - 4)

= 7 / 5

Now we can use the point-slope form of a line to find the equation of the secant line passing through these two points:

y - 14 = (7/5) (x - 4)

Simplifying this equation, we get:

y = (7/5) x + 6.6

Therefore, the equation for the secant line passing through the points where x has the given values is y = (7/5) x + 6.6.

b. To find the equation for the line tangent to the curve when x has the first value, we need to find the derivative of the function y = 7sqrt(x) with respect to x:

y' = (7/2) x*(-1/2)

Evaluating this derivative at x = 4, we get:

y'(4) = (7/2) (4*(-1/2)) = 7/4

This is the slope of the tangent line at x = 4. We can use the point-slope form of a line to find the equation of the tangent line at this point:

y - 14 = (7/4) (x - 4)

Simplifying this equation, we get:

y = (7/4) x + 7

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Since the boxes are sliding to the right at a constant velocity, the net force acting on each box is zero.

An equation is a mathematical statement that asserts the equality of two expressions. It typically consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The LHS and RHS contain mathematical expressions that can include variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and logarithms. Equations are used in many areas of mathematics and science to describe relationships between variables and to solve problems. They can be linear or nonlinear, simple or complex, and may involve one or more variables. The process of finding the values of variables that make an equation true is called solving the equation.

Here,

Therefore, the forces on each box must balance out. Let's consider the forces acting on each box:

Box A: Since it has a larger mass, it requires a larger force to slow down. Therefore, the force exerted by hand H on box A must be larger than the force exerted on box B. We can rank the forces on box A, box B, and hand H as follows:

Force exerted by hand H on box A (largest force)

Force exerted by hand H on box B

Force exerted by box A on hand H

Force exerted by box B on hand H

Force exerted by box A on box B (smallest force)

Box B: Since it has a smaller mass, it requires a smaller force to slow down. Therefore, the force exerted by hand H on box B must be smaller than the force exerted on box A.

Hand H: The forces exerted by box A and box B on hand H are equal and opposite (Newton's third law). Therefore, they cancel each other out and the net force on hand H is zero.

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Answer:

the original list price of the grinder was $147

Step-by-step explanation:

If the sale price is 20% off the original price, then the sale price is 100% - 20% = 80% of the original price. We can set up the equation:

Sale price = 0.8 * original price

We know the sale price is $117.60, so we can substitute and solve for the original price:

117.60 = 0.8 * original price

original price = 117.60 / 0.8

original price = 147

Therefore, the original list price of the grinder was $147.

The type of transformation that happened is a composition of a reflection across the y-axis followed by a translation upwards by 3 units.

The point (a, b) is the top of a rectangle, which means that the bottom of the rectangle must be at the point (a, c) for some c < b. Let's assume that the rectangle is centered at the origin, so its height is 2b and its width is 2c.

After the transformation, the point (a, b) maps to the point (-a, b+3). We can see that the x-coordinate of the point has been negated, and the y-coordinate has been increased by 3. This suggests that the transformation is a reflection across the y-axis followed by a translation upwards by 3 units.

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The probability that X falls inside this range according to the uniform distribution of a random variable is 0.38, or 38%.

The risk that an event will occur or maybe even a claim will now be true is measured by quantum mechanics, a mathematics field. The probability of an occurrence is a value between 0 and 1 and 1, where about range from 0 how likely the event is to occur and value of 1 indicates certainty. A probability is a numerical illustration of something like the possibility that a specific thing will take place. Probabilities can also be expressed using percentages ranging from 0% to 100% or from 0 to 1. the percentage of the number of outcomes to the proportion of occurrences in a full set of equally likely opportunities that lead to a particular occurrence.

given

As the boundaries are 0 and 2, a = 0 and b = 2

The likelihood that X falls between 0.68 and 1.44 is given by the formula P(0.68X1.44) = 1.44- 0.68 / 2-0

= 0.38

The probability that X falls inside this range according to the uniform distribution of a random variable is 0.38, or 38%.

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The quadratic formula can be used to resolve the equation x2 - 2x - 3 = 0.

x=(-b sqrt(b2 - 4ac)) / 2a

x = (2 ± sqrt(4 + 12)) / 2

If we simplify, we get:

x = (2 ± 2sqrt(4)) / 2

x = 1 ± sqrt (4)

As a result, x = 1 + 2 and x = 1 - 2 are the solutions.

The following are the answers, separated by commas:

3, -1

[tex]x^2 + 5x + 6 = 0[/tex]

[tex]x^2 + 5x + 6 = 0[/tex]

We can factor this equation into: to find its solution.

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

The following answers can therefore be determined using the zero product attribute: x + 2 = 0 or x + 3 = 0.

x = -2 or x = -3

The following are the solutions, each separated by a comma:

-2, -3

36. We can factor the equation to find the solution to x2 + 3x - 4 = 0.

(x + 4)(x - 1) = 0

We can calculate x + 4 = 0 or x - 1 = 0 using the zero product property.

We obtain the following results when we solve for x: x = -4 or x = 1.

Hence, the answers are x = -4 and x = 1.

Solution: -4, 1.

37. We can factor the equation to find the solution to x2 - 6x + 5 = 0.

(x - 5)(x - 1) = 0

We can calculate x - 5 = 0 or x - 1 = 0 using the zero product condition.

We obtain x = 5 or x = 1 when we solve for x.

Hence, the answers are x = 5 and x = 1.

Respondents: 5

38. We can apply the quadratic formula x = (-b (b2 - 4ac)) / 2 to solve 6x2 + 5x + 1 = 0. (2a)

We obtain the following equation by plugging in the variables a = 6, b = 5, and c = 1: x = (-5 (25 - 24)) / 12 x = (-5 1) / 12

We obtain x = -2/3 or x = -1/2 by simplifying.

The answers are therefore x = -2/3 and x = -1/2.

Solution: -2/3, -1/2

39. The equation 4x2 + 15x + 9 = 0 can be factored as follows:

(4x + 3)(x + 3) = 0

In response to the zero product property, we get either 4x + 3 = 0 or x + 3 = 0.

When we solve for x, we have x = -3/4 or -3.

Hence, x = -3/4 and x = -3 are the answers.

Response: -3/4, -3

[tex]40. x^2 - 36 = 0[/tex]

This problem can be solved by adding 36 to both sides to obtain:

x^2 = 36

The square root of both sides can then be calculated as follows:

x = ±6

As a result, the answers are x = 6 and x = -6.

The following are the answers, separated by commas:

6, -6

[tex]41. x^2 + 12x + 36 = 0[/tex]

We can factor this equation into: to find its solution.

(x + 6)(x + 6) = 0

The zero product attribute can then be used to identify the answers:

x + 6 = 0

x = -6

Hence, the answer is x = -6. There is just one solution because both components in the factored form are identical.

The answer is: -6.

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Answer:

Step-by-step explanation:

[tex]\mathrm{10+2x-3x=-\left(x+2\right)}[/tex]

*2x-3x=-x*

[tex]\mathrm{10-x=-\left(x+2\right)}[/tex]

Expand:-

[tex]\mathrm{10-x=-x-2}[/tex]

Cancel the x from both sides:-

[tex]\mathrm{10=-2}[/tex]

and since 10=-2 is false, there is no solution.

__________________

Hope this helps!

Answer:

The online price with 25% off is $17.25.

The original price is $21.56

To find the original price, you will multiply the discount price by 25%, or 0.25.

0.25 * 17.25 = 4.3125 or 4.31

Now you will ad that to the discount price to find the original price:

4.31 + 17.25 = 21.56

The original price was $21.56.

Step-by-step explanation:

Hope it helps! =D

Answer:

$21.56

Step-by-step explanation:

A percentage is a ratio, or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

To solve this, we can multiply the price by 1.25.

We multiply by 1.25 because in order to solve for the original price of an object that was 25% off, we have to add that 25% back. The reason we don't multiply by 0.25 is because if we were to do so, the price would be getting smaller, not larger.

Therefore, the original price is $21.56

Quadrilateral R'S'T'V' is smaller than Quadrilateral RSTV because a scale factor is less then 1.

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

Quadrilateral RSTV is dilated with the origin as the center of dilation using the rule (x, y) = (3/2x, 3/2y) to create quadrilateral R'S'T'V'.

Here, All the coordinates of vertex of Quadrilateral RSTV are,

R = (- 3, - 2)

S = (- 2, 3)

T = (2, 2)

V = (3, - 1)

Hence, By applying rule we get;

All the coordinates of vertex of Quadrilateral R'S'T'V' are,

R' = (- 3 × 3/2, - 2× 3/2) = (- 9/2. - 3)

S' = (- 2 × 3/2, 3 × 3/2) = (- 3, 9/2)

T' = (2 × 3/2, 2× 3/2) = (3, 3)

V' = (3 × 3/2, - 1 × 3/2) = ( 9/2. - 3/2)

Now, Distance between R and S;

RS = √ (- 3- (- 2))² + (- 2 - 3)²

     = √1 + 25

     = √26

And, Distance between R' and S';

R'S' = √ (- 3- (- 9/2))² + (- 3 - 9/2)²

     = √(3/2)² + (15/2)²

     = √9/4 + 225/4

    = √234/4

Hence, The scale factor is,

⇒ RS / R'S' = √26 / (√234/4)

                  = 2√26/ √234

                  = 2/3

                  = 0.67 < 1

Thus, Quadrilateral R'S'T'V' is smaller than Quadrilateral RSTV because a scale factor is less then 1.

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Answer:

102

Step-by-step explanation:

Angles in a quadrilateral is 360

120+85+53=258

360-258=102

Hope this helps!

His postal expenses total 6.5x + 2.5y $357.50 and 13x + 5y 715, respectively, according to two systems of inequality.

A relationship among two expressions or concepts that is not equal in mathematics is referred by the term inequality. Hence, inequalities results from imbalance. In mathematics, an equality establishes the connection between two quel numbers. Egality and inequality aren't the same thing. Use the not equal symbol most frequently when two quantities are not equal (). Values of any size can also be contrasted using a variety of inequalities. By changing the two sides until only components are left, many straightforward disparities can be solved. All the same, a host of mechanisms support inequality: Both sides' lowest values are split or added. Switch the left and the right.

given

It costs $2.50 to ship a card.

Buying a package will cost you $6.50.

Suppose x is the number of packages

Moreover, if y represents the number of cards

The situation is described by a system of inequalities that is

At least 16 more cards than packages make up the total number of cards.

⇒y ≥ 2x +16

Reiko wants to keep his postal expenses to a maximum of $357.50.

⇒6.5x +2.5y ≤ 357.5

⇒13x +5y ≤ 715

His postal expenses total 6.5x + 2.5y $357.50 and 13x + 5y 715, respectively, according to two systems of inequality.

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The net of a cylinder is a 2-dimensional representation of a 3-dimensional cylinder that has been "unwrapped" and laid flat. The net consists of two circles (representing the top and bottom of the cylinder) and a rectangle (representing the side of the cylinder).

The length of the base of the rectangle in the net of a cylinder represents the circumference of the cylinder, which is the distance around the circular base of the cylinder. The circumference of a circle is calculated using the formula C = 2πr, where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

In the net of a cylinder, the base of the rectangle is the same as the circumference of the circles because it is equal to the distance around the circular base of the cylinder. The width of the rectangle represents the height of the cylinder, which is the same as the distance between the top and bottom circles.

Answer:

Therefore, the length of the base of a rectangle in the net of a cylinder is the same as the circumference of the circles because it represents the distance around the circular base of the cylinder.

-120x^8y^7

To simplify the expression, you can use the product rule of exponents, which states that when you multiply two terms with the same base, you add the exponents.

Here, we have:

-12x^5y^2y(10x^3y^4)

= -12 * 10 * x^5 * x^3 * y^2 * y^5 (using the product rule to simplify y^2 * y^4 to y^6)

= -120x^8y^7 (using the product rule to simplify x^5 * x^3 to x^8)

Therefore, the simplified expression is -120x^8y^7.

The adjacent angles are ∠GFD and ∠JIF. The correct option is D.

The lines and angles are denied as when the two parallel lines are intersected by the transversal lines it forms different types of angles the angles are adjacent angles, supplementary angles, opposite angles, and alternate angles.

The adjacent angle is defined as the angle which is just side by side with another angle.

Here in the given image, the two adjacent angles are ∠GFD and ∠JIF. Because the angle ∠GFD is just in front of the angle ∠JIF.

Therefore, the correct option is D the adjacent angles will be ∠GFD and ∠JIF.

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Answer:

Where is the question??

The probability of throwing 3 shots is 100% and the sample space is set of all possible real number.

Probability is the measure of the likelihood that a given event will occur. In this case, the event is a basketball player making a shot from the free throw line.

Since the player has a 40% success rate, we can calculate the probability of him making x number of shots, where x is the number of shots that he throws.

Since the shots are independent of each other, the sample space for x is the set of all possible numbers of shots that he can make, from 0 to the total number of shots (3 in this case).

Therefore, the sample space for x is {0, 1, 2, 3}, which means that the player has a 0% probability of making 0 shots, a 40% probability of making 1 shot, an 80% probability of making 2 shots, and a 100% probability of making all 3 shots

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After Justin leaves his house he reaches a maximum distance of 20 blocks away from his house after 7 minutes of being out of his home.

To graph Justin's displacement we must use a Catersian plane. In this case we put the time on the X axis (time) and the distance on the Y axis (blocks). Once we set these parameters, we must put the information on the graph.

In the places where a time takes only the progressing of time without any displacement. Additionally, when you travel it is important to take into account the speed (blocks/minute) that Justin has to obtain a correct graph.

According to the above, after 7 minutes Justin is 20 blocks away from his house and this distance travels in 4 minutes to return home.

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Answer:

A right triangle is a type of triangle that has one angle measuring 90 degrees and two acute angles. It has a hypotenuse and two legs, and it is the only type of triangle that the Pythagorean theorem can be applied to. There are different types of right triangles, including isosceles right triangles, 45-45-90 triangles, and 30-60-90 triangles, each with its own unique properties.

Step-by-step explanation:

A right triangle is a type of triangle that has one angle which measures exactly 90 degrees, which we call the right angle. The other two angles are called acute angles and they are always less than 90 degrees.

A right triangle has a special property: the side opposite the right angle is called the hypotenuse. This is the longest side of the triangle and it is always opposite to the right angle. The other two sides are called legs.

One important thing to note is that the Pythagorean theorem only works for right triangles. This theorem tells us that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. This formula is often written as a^2 + b^2 = c^2, where a and b are the lengths of the legs and c is the length of the hypotenuse.

There are actually several different types of right triangles. For example, if the two legs have the same length, we call it an isosceles right triangle. If one of the acute angles measures exactly 45 degrees, we call it a 45-45-90 triangle, and if one of the acute angles measures exactly 30 degrees and the other measures 60 degrees, we call it a 30-60-90 triangle. These triangles have special properties that make them useful in many different areas of math and science.

In summary, a right triangle is a type of triangle that has one angle measuring 90 degrees and two acute angles. It has a hypotenuse and two legs, and it is the only type of triangle that the Pythagorean theorem can be applied to. There are different types of right triangles, including isosceles right triangles, 45-45-90 triangles, and 30-60-90 triangles, each with its own unique properties.

The correct diagnosis code to report a tibial closed fracture, a proximal end, of the left leg, the initial encounter is A.S82.191A.

Explanation:

Diagnosis codes are used to accurately report a patient's condition or injury. The code S82.191A specifically refers to a closed fracture of the proximal end of the tibia on the left leg, with this being the initial encounter for treatment.

The other options, S82.191B, S82.102A, and S82.102B do not accurately describe the condition or injury in question. S82.191B refers to a subsequent encounter for the same injury, while S82.102A and S82.102B refer to a closed fracture of the right leg's upper end of the tibia.

Therefore, the correct answer is A.S82.191A.

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The value of the equation a - 32 = 47 is a = 79.

The correct option is D.

A pair of algebraic equations with the equal symbol (=) in the center and the same value are referred to as an equation.

Given:

An equation,

a - 32 = 47.

To find the value of a:

We will use some mathematical operations.

Add 32 to both sides of the equation,

we get,

a - 32 + 32 = 47 + 32

a - 0 = 79

a = 79

Therefore, the value of a is 79.

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The requried, Daniel could expect to find 18 red skittles in the big bag.

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

Here,
Assuming that the ratio of red skittles to the total number of skittles in the bag is the same for both the small bag and the big bag, we can use proportions to solve the problem.

The proportion of red skittles to the total number of skittles in the small bag is,

= 9/45

Simplifying this fraction by dividing both the numerator and denominator by 9, we get 1/5. This means that one-fifth of the skittles in the small bag is red.

To find out how many red skittles Daniel could expect in the big bag, we need to multiply the total number of skittles in the big bag by one-fifth,

= 90 * 1/5 = 18

Therefore, Daniel could expect to find 18 red skittles in the big bag.

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The required value of X is 14