The straight line depreciation equation for a luxury car is y = −3,400x + 85,000.
a. What is the original price of the car?
b. How much value does the car lose per year?
c. How many years will it take for the car to totally depreciate?

The equation is y = ax² + bx + c,  standard form of the parabola is y = ax² + bx + c.

The equation for a parabola in standard form is given by:

y = ax² + bx + c

where a, b, and c are constants and x and y are variables.

To convert from vertex form to standard form, you can follow these steps:

Expand the squared term in the vertex form to get the x² term in standard form. For example, if the vertex form is:

y = a(x - h)² + k

then expand (x - h)² to get x² - 2hx + h², giving:

y = a(x² - 2hx + h²) + k

Distribute the 'a' term to get the coefficient of x². This gives:

y = ax² - 2ahx + ah² + k

Combine the constant terms to get the constant coefficient. This gives:

y = ax² - 2ahx + (ah² + k)

Therefore, the standard form of the parabola is y = ax² + bx + c, where:

a = the coefficient of x², which is a

b = the coefficient of x, which is -2ah

c = the constant term, which is (ah² + k)

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The probability that exactly one of the two games will be won by Sally. against Martin [tex]= 0.42[/tex] or 42%.

Use the concept of probability defined as:

Probability is the ratio of:

The number of favorable outcomes to the total number of outcomes for the occurrence of an event.

Given that,

Sally plays two games against Martin.

Sally had a chance to win, tie, or drop each game.

The probability that Martin will lose against Sally is [tex]0.3[/tex].

The probability that Martin will lose against Sally in a tie is [tex]0.1[/tex].

We need to calculate the probability that Sally will win exactly one of the two games against Martin.

To calculate the probability that Sally will win exactly one of the two games against Martin:

Use a combination of probabilities.

Since there are 2 games,

So in this case:

There are 2 possible outcomes:

1. When Sally plays, she either loses the first game and wins the second one, or she wins the first game and loses the second one.
The probability of Sally winning the first game and losing the second game can be calculated,

By multiplying the probability of winning (0.3) with the probability of losing,(1 - 0.3 = 0.7).

Similarly,

2. By doubling the likelihood of losing, which is, the chance of Sally losing the first game and winning the second game,

[tex]1 - 0.3 = 0.7[/tex] with the probability of winning (0.3).

To determine the likelihood that Sally will triumph in precisely one of the two games: Add up this probability as follows:

(0.3 x 0.7) + (0.7 x 0.3)  = 0.42

Hence,

The probability that exactly one of the two games will be won by Sally against Martin = 0.42 or 42%.

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Answer:

y= -x^2

vertex:  (0, 0)

a= -1

domain:  (-∞, ∞)

range:  (-∞, 0]

axis of symmetry:  y-axis (x = 0)

increasing on:  (-∞, 0)

decreasing on:  (0, ∞)

y= (x-2)^2-3

vertex: (2, -3)

a = 1

vertical shift:  shift of 3 units downwards from the origin

horizontal shift:  2 units to the right

width: 1

reflected? nope

y= (x-1)^2-2  

vertex:  (1, -2)

a= 1

domain: all real numbers

range:   y ≥ -2

axis of symmetry:  x = 1

increasing on:   (-∞, 1]

decreasing on:   [1, ∞)

y = (x+1)^2+2

vertex:  (-1, 2)

a = 0

vertical shift:  2 units upwards from the origin

horizontal shift:  1 unit to the left

width:  infinite

reflected? no

Improper fraction: 8 21 4 6 7 15 - This fraction is an improper fraction because the numerator (the top number in the fraction) is larger than the denominator (the bottom number in the fraction).

A numerator is the top number in a fraction. It is used to identify the number of parts of a whole that are being considered. For example, in the fraction 3/4, the numerator is 3, which is the number of parts being considered out of the total 4 parts.

Like fractions: 5' 5' 8' 2 - This fraction is a like fraction because the numerators and denominators are the same.
Proper fraction: 2 5 1 9 11 3 12 11 2 - This fraction is a proper fraction because the numerator is smaller than the denominator.
Unlike fraction: 4'4" 7'25'8'513'21' - This fraction is an unlike fraction because the numerators and denominators are different.

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The expression that represents the perimeter of the rectangle is 22.6g - 15.8h.

The formula for the perimeter of a rectangle is:

Perimeter = 2(Length + Width)

We are given expressions for the width and length of the rectangle, so we can substitute these expressions into the formula to get an expression for the perimeter:

Width = 9.8g - 4.5h

Length = 1.5g - 3.4h

Perimeter = 2(Length + Width)

Perimeter = 2((1.5g - 3.4h) + (9.8g - 4.5h))

Now, we can simplify the expression by distributing the 2 to both terms inside the parentheses:

Perimeter = 2(1.5g - 3.4h) + 2(9.8g - 4.5h)

Perimeter = 3g - 6.8h + 19.6g - 9h

Finally, we can combine like terms to get the final expression for the perimeter:

Perimeter = 22.6g - 15.8h

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By answering the presented question, we may conclude that 6 * 36 function square inches equals 216 square inches.

Mathematicians examine numbers and their variations, equations and associated structures, forms and their locations, and prospective positions for these things. The term "function" refers to the relationship between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs in which each input leads to a single, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible functions are on functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions.  

Part A: To breakdown the provided geometry into triangles, draw three lines from the hexagon's centre to its three opposing vertices, as illustrated below.

Part B: Because the hexagon is equilateral, each of the six triangles is also equilateral. To find the area of each triangle, we may apply the formula for the area of an equilateral triangle.

[tex](\sqrt(3)/4) * a2 = Area[/tex]

 A

        /\

       /  \

  G   /____\   B

      \    /

       \  /

        \/

        F

[tex](\sqrt(3)/4) * 122 = 36\sqrt(3)[/tex] square inches

Part C: Since the hexagon is split into six congruent triangles, its total area is six times that of one triangle. As a result, the table's surface area is:

6 * 36 square inches equals 216 square inches.

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Answer:

45 ÷ 5 = 9

9 × 9 = 81

it will take them 81 hours

AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

What is congruent ?

Congruent refers to having the same shape and size. In mathematics, two objects are said to be congruent if they are identical in shape and size, and can be superimposed onto one another. The symbol used to represent congruence is ≅. Congruence applies to various geometric objects, such as triangles, rectangles, circles, and more. When two objects are congruent, they have all corresponding angles equal and all corresponding sides equal in length.

Step 1: Statement: [tex]$\angle DBE = \angle EBC$[/tex]

Reason: Given that overline BE bisects [tex]$\angle DBC$[/tex]

Step 2: Statement: [tex]$\angle DBC + \angle EBC = 180^\circ$[/tex]

Reason: Angle sum property of a straight line.

Step 3: Statement: [tex]$\angle ABC + \angle EBC = 180^\circ$[/tex]

Reason: Angles on a straight line sum to [tex]180^\circ$, and $\overline{BE} || \overline{AC}$[/tex] implies that [tex]\angle ABC$ and $\angle EBC$[/tex] are co-interior angles.

Step 4: Statement: [tex]$\angle ABC = \angle DBC$[/tex]

Reason: From step 2 and step 3, [tex]$\angle ABC + \angle EBC = \angle DBC + \angle EBC = 180^\circ$[/tex]. Thus, [tex]$\angle ABC = \angle DBC$[/tex].

Step 5: Statement: [tex]$\triangle ABE \cong \triangle CBE$[/tex]

Reason: By the angle-angle-side congruence criterion, since [tex]$\angle DBE = \angle EBC$[/tex] (from step 1) and [tex]$\angle ABC = \angle DBC$[/tex] (from step 4), and [tex]$\overline{BE}$[/tex] is common to both triangles.

Step 6: Statement: [tex]$AB = BC$[/tex]

Reason: By step 5, [tex]$\triangle ABE \cong \triangle CBE$[/tex], so corresponding sides are congruent, including [tex]$\overline{AB} \cong \overline{BC}$[/tex].

Therefore, AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

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Answer:

Field A

Step-by-step explanation:

This is just a blind eye guess, but when something is consistant, it tends to get more similar answers, field b has a large variety and amount of answers, whereas field a tends to be concetrated around one number, which makes there less possibilities and makes it more constant.

Hope I helped!

Let W = width of rectangle

Let W + 2 = length of rectangle = L

Perimeter = 2L + 2W

         56 = 2L + 2W

     since L = W + 2, we can substitute and solve

         56 = 2(W + 2) + 2W

         56 = 2W + 4 + 2W

         56 = 4W + 4

         52 = 4W

          W = 13

      the length 2 more than 13, which is 15

Area = L • W

       = 15 • 13

      = 195

It Is possible for you and your friend to share the iced tea equally. Each of you gets two cups each.

Equivalent fraction can help solve the problem. 4/2 = 2/1

Number of cups of iced tea = 4

Number of people sharing iced tea = 2(you and your friend)

Number of cups each person gets = Number of cups of iced tea / Number of people sharing iced tea

= 4/2

= 2 cups of iced tea per person.

The fraction is 4/2 which is equivalent to 2/1

Ultimately, each person can get two cups of iced tea each.

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Yes, this is true. The R-squared value indicates how much of the variability of the data can be explained by the model. A higher R-squared value indicates that more of the variability of the data can be explained by the model, thus making the predictions more accurate.

To understand the concept better, let's consider an example. Suppose you have a model that predicts the price of a house based on its location, size, and other factors. Model A has an R-squared value of 0.7, while Model B has an R-squared value of 0.9. This means that Model B can explain more of the variability of the data than Model A, making it the more accurate predictor of the house price.

Additionally, the higher R-squared value of the model can also be an indication of the model's ability to generalize. If the model has a high R-squared value, it is likely that it can be applied to new data and still provide an accurate prediction. On the other hand, if the model has a low R-squared value, it may be difficult to apply it to new data and obtain accurate predictions.

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The possible amounts of money Luke can spend renting his apartment in Hillwood in order for Luke to have some money left over each month is x ≤ 5645.

An inequality is a mathematical statement that describes a relationship between two values, usually variables.

Luke's monthly income is $7645 and his other monthly expenses are $2000. Therefore, he can spend at most the difference between these two amounts on rent and still have money left over.

Let's use x to represent the cost of the rent in Hillwood.

So the inequality is:

x ≤ 7645 - 2000

Simplifying,

x ≤ 5645

Therefore, the possible amounts of money Luke can spend renting his apartment in Hillwood in order for Luke to have some money left over each month is x ≤ 5645.

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The center of the prices is 135 and the variability is 19, ranging from 130 to 154.

To calculate the center and variability of these prices, begin by finding the mean of the set of numbers. To do this, add each of the numbers together and divide by the total number of prices in the set. In this case, the numbers are 125, 135, 130, 140, 135, 154. Adding them together yields 759. Dividing this by 6 since there are 6 numbers in the set, yields a mean of 126.5. This is the center of the prices.

To calculate variability, subtract the lowest number from the highest number. In this set, the lowest number is 130 and the highest number is 154. Subtracting 130 from 154 yields a variability of 24. This is the variability of the prices.

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Answer:

y'=3x²

Step-by-step explanation:

[tex]y=ax^{n} \\y'=an*x^{n-1} \\y=x^{3} \\a=1,n=3\\y'=1*3x^{3-1} \\y'=3x^{2}[/tex]

Answer: 9%

Step-by-step explanation:

After answering the presented question, we can conclude that q (if q is equation greater than n/2) q - n n - q q (if q is less than n/2)

In mathematics, an equation is a statement that states the equality of two expressions. An equation consists of two sides separated by an algebraic equation (=). The argument[tex]"2x + 3 = 9,"[/tex] for example, states that the sentence[tex]"2x + 3[/tex]" equals the value "9." The goal of solving equations is to find the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, linear or nonlinear, and contain one or more parts. In the equation[tex]"x^2 + 2x - 3 = 0,"[/tex] the variable x is raised to the second power. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.

We can simply compare two phrases at a time to arrange them from least to greatest:

If q is bigger than n/2, then q is the largest expression since q > n - q. If q is less than or equal to n/2, the largest expression is n - q, because n - q > q. Depending on the value of q, the greatest expression is either n - q or q.

When we add everything up, we get:

If q is more than n/2, the order is q, q - n, n - q.

If q = n/2, the sequence is q - n, n - q, q.

As a result, the ultimate order is:

q (if q is greater than n/2) q - n n - q q (if q is less than n/2)

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If 15 boxes of the Cremora received during December 2022, should be enough to last a year for the family of four, the total number of kilograms is 23.36 kg.

The total number in kilograms can be computed by using the multiplication operation.

In this situation, the yearly average usage per individual in the family is computed and the result multiplied by the number of the family members.

The number of family members = 4

The average usage of the Cremora = 16 g per day

The average usage of the Cremora per person per 365 days = 5.84 kg (0.016 x 365)

Thus, the total number of kilograms from the 15 boxes of Cremora is 23.36 kg (5.84 kg x 4).

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Answer:

Step-by-step explanation:

5

Answer:Option b. y = 0.

Step-by-step explanation:

We can be 95% confident that the true proportion of US young adults who can recall a story a parent told them about when the parent was young lies within this interval.

(a) Using StatKey, we can generate a bootstrap distribution for the proportion of US young adults who can recall a story a parent told them about when the parent was young. We start by inputting the data into StatKey and selecting "Bootstrap One Proportion" under "One Categorical Variable." We set the number of bootstrap samples to 10,000 and click "Simulate" to generate the bootstrap distribution.

The resulting bootstrap distribution has a mean of 0.9387 and a standard error of 0.0156.

To find the 95% confidence interval for the proportion, we can use the formula:

proportion ± z × SE

where z is the z-score for a 95% confidence level, which is approximately 1.96.

Plugging in the values, we get:

0.9387 ± 1.96 × 0.0156

which gives us a 95% confidence interval of (0.9084, 0.9689).

(b) Given the confidence interval from part (a), we cannot be confident that the claim that "more than 90% of teenagers and young adults can retell family stories when asked" is correct. The lower bound of the confidence interval is 0.9084, which is below 90%. While the point estimate of 0.9387 is above 90%, there is still a reasonable chance that the true proportion is below 90%.

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The equation for the given downward parabola is:

 y = -x²+1

What is a parabola?

Any point on a parabola is located at an equal distance from both a fixed point and a fixed straight line. It is a U-shaped plane curve. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively. The topic of conic sections includes a parabola, and all of its principles are discussed here. A parabola's general equation is either y = a(x-h)² + k or x = a(y-k)²+ h, where (h,k) signifies the vertex.

The given graph is a downward parabola.

The parabola equations are second-degree equations.

So we can eliminate options 1 and 2.

Now we can substitute the coordinate values and check for the correct equation.

One of the points on the parabola is (2,-3).

Taking equation y = -x²+1

y = -2²+1 = -4+1 = -3

Let us check for one more point.

Taking the point (-1,0).

y = -(-1)²+1 = -1+1 = 0

Therefore the equation for the given downward parabola is:

 y = -x²+1

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In ∠CAT and ∠TAD is a linear pair.

m ∠CAT = 42° and

m ∠TAD = 135°

Angle:

In Euclidean geometry, an angle is a figure formed by two radii, called sides of the angle, which share a common extremity, called vertex of the angle. The angle formed by two rays is located in the plane containing the rays. Corners are also formed by the intersection of two planes. This is called dihedral angles. Two intersecting curves can also define an angle, which is the angle of the light that hits the corresponding curve at the point of intersection.

Angle is also used to refer to an angle or rotation measurement. This measurement is usually defined as the ratio of an arc's length to its radius and can be drawn. In the case of geometric angles, an arc is centered on a vertex and bounded by an edge. In the case of a rotation, the arc is centered on the center of the rotation and bounded by any other point and its image through the rotation.

According to the angle:

We are given that angle CAT and angle TAD are a linear pair.

m ∠CAT = 42°

and, m ∠TAD = 2x -6

We have to find the measure of angle TAD.

   m ∠CAT + m ∠TAD = 180°

⇒ 42° +m ∠TAD = 180°   (linear pair sum =180 degrees)

⇒ m ∠TAD = 180° - 42°

⇒ m ∠TAD = 135°

Complete Question:

∠CAT and ∠TAD are a linear pair, if M∠CAT = 2x-5 and M∠TAD = 5x+10, what is the measure of ∠CAT and ∠TAD? Draw a picture labelling the given information and show your work

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(a) Let in the beginning Eric had 3x red pens and Kai had x blue pens

2/5 * 3x = 6x/5
Eric gave 6x/5 red pens to Kai.

Now Eric has 3x - 6x/5 = 9x/5 red pens.

Kai gave x/2 blue pens to Eric

Now Eric has a 9x/5 + x/2 = (18x + 5x)/10 = 23x/10

Now Kai has x - x/2 = x/2 blue pens.

Now Kai has total x/2 + 6x/5 = 17x/10 pens.

required fraction = (x/2)/(17x/10) = x/2 * 10/17x = 5/17

5/17 is the answer.

(b) After another round of transfer Eric has total 23x/10 - 15 pens and Kai has total 17x/10 + 15 pens.

23x/10 - 15 = 17x/10 + 15

(23x - 150)/10 = (17x + 150)/10

23x - 150 = 17x + 150

6x = 300

3x = 150

Eric had 150 pens in the beginning.

The answers to the questions are as follows;

a). 308.

b). 1.309

c). 30.9%

d). Not continuous.

As evident from the task content; the given expression is; Q(t)=308(1.309)^t.

On this note, by comparison with the standard form of an exponential function; f (x) = a (b)^t.

a = 308 and b = 1.309.

a). Hence, the quantity at time t = 0 is;

Q(0) = 308(1.309)⁰

Q (0) = 308.

b). Since the growth/decay factor, b is greater than 1; the quantity is increasing over time.

c). The percentage growth rate is; (1.309 - 1) × 100% = 30.9%.

d). The growth rate in this case is not continuous as the growth does not happen at every instance.

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The roots of the given quadratic equation as required to be determined are; Choice D; x = (2 ± i√26) / 3.

As evident from the task content; the roots of the quadratic equation; 3x² + 10 = 4x are to be determined.

Given; 3x² + 10 = 4x

Therefore; 3x² - 4x + 10 = 0 where a = 3, b = -4 and c = 10.

Therefore, using the quadratic formula;

x = ( -b ± √(b² - 4ac) ) / (2a)

We have that;

x = (-(-4) ± √4² - (4×3×10) ) / 2(3)

x = (4 ± 2√-26) / 6

x = (2 ± i√26) / 3

Ultimately, the roots of the given quadratic equations are given as; Choice D; x = (2 ± i√26) / 3.

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Answer:

a. Z=1.98

Assuming a one-tailed test, we need to find the area to the right of the Z-score in the standard normal distribution table. The p-value can be calculated as:

p-value = 1 - P(Z ≤ 1.98)

Using a standard normal distribution table, we can find that the area to the left of 1.98 is 0.9761. Therefore,

p-value = 1 - 0.9761 = 0.0239

b. Z=2.49

Assuming a one-tailed test, we need to find the area to the right of the Z-score in the standard normal distribution table. The p-value can be calculated as:

p-value = 1 - P(Z ≤ 2.49)

Using a standard normal distribution table, we can find that the area to the left of 2.49 is 0.9934. Therefore,

p-value = 1 - 0.9934 = 0.0066

c. z=-1.02

Assuming a one-tailed test, we need to find the area to the left of the Z-score in the standard normal distribution table. The p-value can be calculated as:

p-value = P(Z ≤ -1.02)

Using a standard normal distribution table, we can find that the area to the left of -1.02 is 0.1562. Therefore,

p-value = 0.1562

Inverse Statement- If tοday is nοt Sunday, then it is nοt a hοliday. Cοntrapοsitive Statement- If it is nοt a hοliday, then tοday is nοt Sunday.

A cοnditiοnal statement is a type οf lοgical statement that asserts a relatiοnship between twο prοpοsitiοns. It is an "if-then" statement that states that if οne thing is true, then anοther thing is true as well. The hypοthesis is the prοpοsitiοn that is assumed tο be true, while the cοnclusiοn is the prοpοsitiοn that is inferred frοm the hypοthesis.

Other types οf statements include:

Cοnverse: When the hypοthesis and cοnclusiοn οf a cοnditiοnal statement are swapped.

Inverse: When the hypοthesis and cοnclusiοn οf a cοnditiοnal statement are negated.

Cοntrapοsitive: When the hypοthesis and cοnclusiοn οf a cοnditiοnal statement are swapped and negated.

Here,

Cοnditiοnal statement: If tοday is Sunday, then it is hοliday.

Cοnverse: If tοday is a hοliday, then it is Sunday.

Inverse: If tοday is nοt Sunday, then it is nοt a hοliday.

Cοntrapοsitive: If it is nοt a hοliday tοday, then it is nοt Sunday.

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The probability of rolling anything but a 1 is 1, which means that rolling a 1 is impossible with this die.

what is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain.

We are given that the die has the following properties:

Probability of rolling 6, 3, or 2 on any roll is 1/2.

Probability of rolling 2, 5, or 4 on any roll is 1/2.

Probability of rolling 2 on any roll is 3/8.

Let's use these properties to answer the given questions:

(a) To find the probability of rolling either a 6, a 3, or a 1, we need to first find the probability of rolling a 1. We know that the probability of rolling either a 6, a 3, or a 2 is 1/2, so the probability of not rolling any of these numbers on a given roll is also 1/2. Similarly, the probability of not rolling either a 2, a 5, or a 4 is also 1/2.

Therefore, the probability of rolling a 1 is:

P(rolling a 1) = 1 - P(not rolling any of 6, 3, 2) - P(not rolling any of 2, 5, 4)

= 1 - (1/2) - (1/2)

= 0

Since the probability of rolling a 1 is 0, the probability of rolling either a 6, a 3, or a 1 is the same as the probability of rolling either a 6 or a 3, which is 1/2. Therefore:

P(rolling either a 6, a 3, or a 1) = 1/2

(b) To find the probability of rolling anything but a 1, we can subtract the probability of rolling a 1 from 1. Since we already know that the probability of rolling a 1 is 0, the probability of rolling anything but a 1 is:

P(rolling anything but a 1) = 1 - P(rolling a 1)

= 1 - 0

= 1

Therefore, the probability of rolling anything but a 1 is 1, which means that rolling a 1 is impossible with this die.

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Step-by-step explanation:

Answer:

  A.  is a rational number.

Step-by-step explanation:

You want to know whether a product of rational numbers is rational.

You know that the product of fractions is ...

  [tex]\dfrac{a}{b}\times\dfrac{c}{d}=\dfrac{ac}{bd}[/tex]

where a, b, c, d are integers.

A rational number can always be expressed as the ratio of two integers. The product of any two integers is an integer, so the product of any two rational numbers is rational.