18. What are the zeroes of the function? (1 point)
y=(x-3)(x + 2)(x-2)
O-3, 2, -2
O-3, 2, 2
03, -2, 2
03, 2, 2

Answer:

I think that its the amount of water that decreases each day

Step-by-step explanation:

I'm taking the quiz now so we'll see if I'm right.

Answer:

It represents the amount of water left in the tank

Step-by-step explanation:

I had the exact same question, but asked for the slope, meaning they said the answer to the question. (EDG 2022)

This was my question- The graph shows the amount of water that remains in a barrel after it begins to leak. The variable x represents the number of days that have passed since the barrel was filled, and y represents the number of gallons of water that remain in the barrel.

A graph titled Water Supply with a number of days on the x-axis and gallons of water left on the y-axis. A line goes through points (6, 33) and (15, 15).

BRAINLIEST PLS

Answer:

5.49 x 10^14

Step-by-step explanation:

The calculator is showing the scientific notation but instead of EE, it changes to x 10 ^

B 4,2 because it is 6 units away from the point

The movies for the movie marathon can be chosen in 120  different ways .

In the question ,

it is given that

total number of movies = 10 movies

number of movies that need to be played in specific order = 7 movies .

we have to find how many different ways can the movies be selected for the movie marathon .

we can solve this with Combination ,

where n = 10  and r = 7

So C(n,r) =  C (10,7)

= 10! / (3! * 7! )

= (10*9*8*7!)/(3! * 7! )

= ( 10*9*8) / (3*2 )

= 10 * 3 * 4

= 120 ways .

Therefore , The movies for the movie marathon can be chosen in 120  different ways .

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The reciprocal of 6 and -12y -18x are:

\( \frac{1}{6} and \: \frac{1}{ - 12y - 18x} \)

1. In this scenario, the goalie saves 73% of the opponent's shots. Therefore, any digits from 00 to 72 represent shots that are saved, as they fall within the range of the goalie's saving ability.

2. To win the game, the Iceblades cannot let the other team score any goals. Therefore, the goalie needs to save all 5 shots taken by the other team for a group to be a success.

3. Group 1 is a success because the goalie saves all 5 shots taken by the other team. Since no goals are scored, the Iceblades maintain their one-goal lead and are on track to win the game.

4. In this simulation, the successes are the groups where the goalie saves all 5 shots. Based on the information given, Group 1 is the only success. Therefore, there is one success in the 10 groups.

5. Since there is only one success out of the 10 groups, the estimated probability of the Iceblades winning the game would be 1 out of 10, or 1/10. Expressed as a percentage, this is equal to 10%.

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Answer:

\(\boxed {\frac{dy}{dx}= 2x}\)

Step-by-step explanation:

Solving :

⇒ log y = log (x²)

⇒ log y = 2 log x

⇒ \(\mathsf {\frac{1}{y} \frac{dy}{dx} = \frac{1}{x} \times 2}\)

⇒ \(\mathsf {\frac{dy}{dx}= 2x}\)

Answer:

y’ = 2x

Step-by-step explanation:

Let y = f (x), take the natural logarithm of both sides ln (y) = ln (f (x))

ln (y) = ln (x²)

Differentiate the expression using the chain rule, keeping in mind that y is a function of x.

Differentiate the left hand side ln (y) using the chain rule.

y’/y = 2 In (x)

Differentiate the right hand side.

Differentiate 2 ln (x)

y’/y = d/dx = [ 2 In (x) ]

Since 2 is constant with respect to xx, the derivative of 2 ln (x) with respect to x is 2 d/dx [ln (x)]

y’/y = 2 d/dx [In (x)]

The derivative of ln (x) with respect to x is 1/x.

y’/y = 2 1/x

Combine 2 and 1/x

y’/y = 2/x

Isolate y' and substitute the original function for y in the right hand side.

y’ = \(\frac{2}{x}\) x²

Factor x out of x².

y’ = \(\frac{2}{x}\) (x * x)

Cancel the common factor.

y’ = \(\frac{2}{x}\) (x * x)                     (The x that is under 2 and the other x that I have underlined are the ones that cancel out)  

Rewrite the expression.

y’ = 2x

So therefore, the answer would be 2x.

The equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0 is 3x + 2y + z = 8.

We need a point b and a vector v along the line in order to characterize it. We might alternatively begin with the two points a and b and use the formula v = ab.
A point Q and a vector n perpendicular to the plane are required in order to describe a plane. Later on, we'll look at how to get n from various types of information, such as the positions of three points on a plane.

A plane is a flat, endlessly long, two-dimensional surface. A plane is a point with zero dimensions, a line with one dimension, and space with three dimensions in two dimensions. The picture below that is attached shows the answer.

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Question correction:

Find the equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0

The resultant equation after multiplying the equation 2x - 3y = 7 with 2 is  4x - 6y = 14

Algebraic expressions in mathematics are equations or expressions that have at least one variable and one constant. These algebraic expressions connect the numerous variables and constants through two fundamental mathematical processes, addition, and subtraction.

Here we have

2x - 3y = 7 is an equation multiplied by 2

=> 2 × ( 2x - 3y)  = 2 × 7

Multiply each term of the equation with 2

=>   2 × 2x - 2 × 3y = 2 × 7

=> 4x - 6y = 14

Therefore,

The resultant equation after multiplying the equation 2x - 3y = 7 with 2 is  4x - 6y = 14

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Answer:

The probability is 1/6

Step-by-step explanation:

Firstly, we need to get the total number of coins

that would be the sum of all the coins present

We have this as;

8 + 10 + 4 + 2 = 24 coins

The number of nickels is 4

So the probability of selecting a nickel is the number of nickels divided by the total number of coins

We have this as;

4/24 = 1/6

Answer:

figure 1

3 + 3 + 3 + 1 + 1 + 1= 12 units

area is 3x1 + 1x1 + 3x1 = 7 sq units

figure 2

perimeter do the same as figure 1 and youll get

32 units i assume

area do the same as figure

then bueno

The volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

The given vectors are:

A = [-4, 3, 2] cm, B = [2,1,3] cm and C= [1, 1, 4] cm

In order to calculate the volume of parallelepiped, we will use vector triple product equation:

Volume = A . (BXC)|, where BXC represents the cross product of vectors B and C.

Step-by-step solution:

We have, A = [-4, 3, 2] cm

B = [2,1,3] cm

C = [1, 1, 4] cm

Now, let's find BXC, using the cross product of vectors B and C.

BXC = | i    j     k|                    2      1     3                            1      1     4        | i    j     k |  = -i + 5j - 3k

Where, i, j, and k are the unit vectors along the x, y, and z-axes, respectively.

The volume of the parallelepiped is given by:

Volume = A . (BXC)|

Therefore, we have: Volume = A . (BXC)

\(Volume = [-4, 3, 2] . (-1, 5, -3)\\Volume = (-4 \times -1) + (3 \times 5) + (2 \times -3)\\Volume = 4 + 15 - 6\\Volume = 13\)

Therefore, the volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

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Answer:

To determine the number of outcomes for Nikia's random selection of a team card and a character card for a role-playing game, we can use a tree diagram, table, or list.

There are four possible teams: air, fire, land, and water. Once a team card is selected, there are three possible character cards: healer, spy, and thief. Therefore, the total number of outcomes is the product of the number of options for each selection, which is:

4 (number of team options) x 3 (number of character options) = 12

So there are 12 possible outcomes for Nikia's random selection of a team card and a character card. However, since Nikia has specified that her favorite team is air and her favorite character is spy, the number of outcomes that would satisfy her preferences is:

1 (air team) x 1 (spy character) = 1

Therefore, only one outcome would satisfy Nikia's preferences.

Therefore , the solution of the given problem of equation comes out to be  9x^3 - 8x^2.

A mathematical equation is a formula that uses the equal sign (=) to connect two statements and express equality. A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The equal sign is a crucial part of mathematical formulas, especially equations. Algebra is frequently utilized in equations. Algebra is used in mathematics when it is difficult to determine a precise quantity.

Here,

Polynomial function total

Polynomial functions are those that have a leading degree of three or higher. given the total;

(7x^3-4x^2)+(2x^3-4x^2)

Expand => (7x 3-4 times) + (2x 3-4 times)

= > 7x^3-4x^2 + 2x^3-4x^2

assemble similar terms

=> 7x^3 + 2x^3 - 4x^2 -4x^2

=> 9x^3 - 8x^2

Therefore , the solution of the given problem of equation comes out to be 9x^3 - 8x^2.

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a) To find the first three elements of the sequence defined by an = n^2 - 3n + 2, we simply substitute n = 0, 1, 2 into the expression for an and simplify: a0 = 2, a1 = 0, a2 = 0.

b) To show that the sequence satisfies the recurrence relation an = 2an-2 - an-2 + 2 for every n >= 2, we can use mathematical induction. Assume the relation holds for some arbitrary k >= 2. Then we can show that it also holds for k+1 by substituting k+1 into the expression and using the fact that an = (k+1)^2 - 3(k+1) + 2 = k^2 - k + 2 + 2k. After simplification, we arrive at the expression for ak+1 in terms of ak and ak-2, showing that the relation holds for k+1.

a) To find the first three elements of the sequence, we simply substitute n = 0, 1, 2 into the expression for an and simplify:

a0 = (0)^2 - 3(0) + 2 = 2

a1 = (1)^2 - 3(1) + 2 = 0

a2 = (2)^2 - 3(2) + 2 = 0

Therefore, the first three elements of the sequence are 2, 0, 0.

b) To show that the sequence satisfies the recurrence relation an = 2an-2 - an-2 + 2 for every n >= 2, we need to show that the expression for an can be written in terms of the previous two terms of the sequence, a(n-2) and a(n-1), using the given recurrence relation.

We can write:

an = n^2 - 3n + 2

  = (n-2)^2 - 3(n-2) + 2 + 2(n-2)

  = (n-2)^2 - 3(n-2) + 2n

Next, we can substitute n-2 for n in the expression for a(n-2) to get:

a(n-2) = (n-2)^2 - 3(n-2) + 2

Finally, we can substitute n-1 for n in the expression for a(n-1) to get:

a(n-1) = (n-1)^2 - 3(n-1) + 2

Now, we can use these expressions to write an in terms of a(n-2) and a(n-1) as follows:

an = (n-2)^2 - 3(n-2) + 2n

  = a(n-2) + 2(n-1) - (n-1)^2 + 3(n-1)

  = 2a(n-2) - a(n-1) + 2

Therefore, we have shown that the sequence satisfies the recurrence relation an = 2an-2 - an-2 + 2 for every n >= 2.

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Fo.05=will be greater than 19.15

Fo.01=will be greater than 3.10

Fo.025=will be greater than 12.48

Fo.10=will be greater than 3.24

To find the F-values using an F-distribution table, we need to specify the significance level (α) and the degrees of freedom for the numerator (v₁) and denominator (v₂). Here are the F-values for the given scenarios:

a. Fo.05 where v₁ = 7 and v₂ = 2:

For a significance level of α = 0.05, and degrees of freedom v₁ = 7 and v₂ = 2, the F-value will be greater than 19.15.

b. F0.01 where v₁ = 18 and v₂ = 16:

For a significance level of α = 0.01, and degrees of freedom v₁ = 18 and v₂ = 16, the F-value will be greater than 3.10.

c. Fo.025 where v₁ = 27 and v₂ = 3:

For a significance level of α = 0.025, and degrees of freedom v₁ = 27 and v₂ = 3, the F-value will be greater than 12.48.

d. Fo.10 where v₁ = 20 and v₂ = 5:

For a significance level of α = 0.10, and degrees of freedom v₁ = 20 and v₂ = 5, the F-value will be greater than 3.24.

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Answer:

\(\dfrac{\sqrt[12]{55296} }{2}\)

Step-by-step explanation:

Given expression:

\(\dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}\)

\(\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:\)

\(\implies \dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}=\dfrac{6^{\frac{1}{4}}}{2^{\frac{1}{3}}}\)

Multiply the numerator and denominator by \(2^{\frac{2}{3}}\) :

\(\implies \dfrac{6^{\frac{1}{4}}}{2^{\frac{1}{3}}} \times \dfrac{2^{\frac{2}{3}}}{2^{\frac{2}{3}}}\)

\(\textsf{Apply exponent rule to the denominator} \quad a^b \cdot a^c=a^{b+c}:\)

\(\implies \dfrac{6^{\frac{1}{4}}}{2^{\frac{1}{3}}} \times \dfrac{2^{\frac{2}{3}}}{2^{\frac{2}{3}}}=\dfrac{6^{\frac{1}{4}} \cdot 2^{\frac{2}{3}}}{2^{\frac{1}{3}+\frac{2}{3}}}=\dfrac{6^{\frac{1}{4}} \cdot 2^{\frac{2}{3}}}{2}\)

Rewrite 1/4 as 3/12 and 2/3 as 8/12 :

\(\implies \dfrac{6^{\frac{1}{4}} \cdot 2^{\frac{2}{3}}}{2}=\dfrac{6^{\frac{3}{12}} \cdot 2^{\frac{8}{12}}}{2}\)

\(\textsf{Apply exponent rule} \quad a^c \cdot b^c=(a \cdot b)^c:\)

\(\implies \dfrac{6^{\frac{3}{12}} \cdot 2^{\frac{8}{12}}}{2}=\dfrac{(6^3 \cdot 2^{8})^\frac{1}{12}}{2}\)

Simplify the operation in the parentheses:

\(\implies \dfrac{(6^3 \cdot 2^{8})^\frac{1}{12}}{2}=\dfrac{(216\cdot 256)^\frac{1}{12}}{2}=\dfrac{(55296)^\frac{1}{12}}{2}\)

\(\textsf{Finally, apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:\)

\(\implies \dfrac{(55296)^\frac{1}{12}}{2}=\dfrac{\sqrt[12]{55296} }{2}\)

\(\\ \rm\Rrightarrow \dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}\)

\(\\ \rm\Rrightarrow \dfrac{6^{\dfrac{1}{4}}}{2^{\dfrac{1}{3}}}\)

\(\\ \rm\Rrightarrow \dfrac{2^{\dfrac{1}{4}}3^{\dfrac{1}{4}}}{2^{\dfrac{1}{3}}}\)

\(\\ \rm\Rrightarrow 2^{\dfrac{1}{4}-\dfrac{1}{3}}3^{\dfrac{1}{4}}\)

\(\\ \rm\Rrightarrow 2^{\dfrac{-1}{12}}3^{\dfrac{1}{4}}\)

\(\\ \rm\Rrightarrow \dfrac{3^{\dfrac{1}{4}}}{2^{\dfrac{1}{12}}}\)

\(\\ \rm\Rrightarrow \dfrac{3^{\dfrac{3}{12}}}{2^{\dfrac{1}{12}}}\)

\(\\ \rm\Rrightarrow \left(\dfrac{3^3}{2}\right)^{\dfrac{1}{12}}\)

\(\\ \rm\Rrightarrow \sqrt[12]{\dfrac{3^3}{2}}\)

\(\\ \rm\Rrightarrow \sqrt[12]{\dfrac{3^3\times 2^82^3}{22^82^3}}\)

\(\\ \rm\Rrightarrow \sqrt[12]{\dfrac{27(256)(8)}{2^12}}\)

\(\\ \rm\Rrightarrow \dfrac{\sqrt[12]{6912(8)}}{2}\)

\(\\ \rm\Rrightarrow \dfrac{\sqrt[12]{55296}}{2}\)

The 95th percentile of the variance of a random sample of size 15 from a normal population with a variance of 3 is approximately 23.685.

The sampling distribution of the variance follows a chi-square distribution, with degrees of freedom equal to n-1, where n is the sample size.
When the population variance is known, we can use the chi-square distribution to find the probability of getting a certain sample variance. In this case, the population variance is given as 3.
Therefore, the sampling distribution of the variance will be a chi-square distribution with 14 degrees of freedom:

(n-1 = 15-1 = 14).

To find the 95th percentile of the chi-square distribution with 14 degrees of freedom, we can use a chi-square table or a calculator. Using a chi-square table or calculator, we find that the 95th percentile of the chi-square distribution with 14 degrees of freedom is approximately 23.685.

This means that there is a 95% chance that the sample variance will be less than or equal to 23.685.

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The 95th percentile of the variance of a random sample of size 15 from a normal population with a variance of 3 is approximately 23.685.

The sampling distribution of the variance follows a chi-square distribution, with degrees of freedom equal to n-1, where n is the sample size.

When the population variance is known, we can use the chi-square distribution to find the probability of getting a certain sample variance. In this case, the population variance is given as 3.

Therefore, the sampling distribution of the variance will be a chi-square distribution with 14 degrees of freedom:

(n-1 = 15-1 = 14).

To find the 95th percentile of the chi-square distribution with 14 degrees of freedom, we can use a chi-square table or a calculator. Using a chi-square table or calculator, we find that the 95th percentile of the chi-square distribution with 14 degrees of freedom is approximately 23.685.

This means that there is a 95% chance that the sample variance will be less than or equal to 23.685.

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The sampling technique being used in this scenario is known as "Systematic Sampling."

Systematic sampling involves selecting every kth element from a population after starting at a random initial element. In this case, the researchers are randomly generating 30 seat numbers, which serves as the starting point. They then survey the passengers who are sitting in those specific seats, selecting every 10th passenger (assuming there are 300 passengers on the flight).

By systematically selecting passengers based on their seat numbers, the researchers ensure that the sample is representative of the entire population of passengers on the flight.

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Answer:

8 divided by 864 = 108

6 divided by 3810 = 635

9 divided by 5319 = 591

Step-by-step explanation:

Hope this helped have an amazing day!

The total gain at the end of the second year for both accounts combined is $509.09.

We have,

Amount saved = $8500

40% of 8500 is saved in saving account = 0.4 x 8500 = $3400

Remainder amount in stock plan = 8500 - 3400 = 5100

Working for savings plan

A = P(1 + r/n\()^{nt\)

A = 3400(1 + 0.042/1)²

A = $3691.60

So, we gain = 3691.6 - 3400 = $291.6

Working for stock plan:  

The stock plan decreases 3% in the first year

= 5100 x 0.97

= $4947

and increases 7.5% in the second year.

= 4947 x 1.75

= $5318.03

So, we gain = 5318.03 - 5100 = $218.03

Thus, the total gain is

= 291.06 + 218.03

= $509.09

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The coefficient of variation for a)0.394 b)0.850 c)0.523 if standard deviation values are a $ 2,710 $ 1,070 b 2,140 1,820 c 2,160 1,130

The coefficient of variation as compared to  standard deviation is a factual proportion of the scattering of data of interest around the mean. The measurement is usually used to analyze the information scattering between particular series of information.

Dissimilar to the standard deviation that must continuously be viewed as with regards to the mean of the information, the coefficient of variation tells a somewhat straightforward and fast instrument to look at changed information series.

We know very well that coefficient of variation is defined as the ratio of standard deviation to the expected value, or in other words

Coefficient of variation=standard deviation/expected value

a)Standard deviation value=$1,070 and expected value is $2,710

Therefore, coefficient of variation=(1070/2710)=0.394

b)Standard deviation value=$1,820 and expected value is $2,140

Therefore, coefficient of variation=(1820/2140)=0.850

c)Standard deviation value=$1130 and expected value is $2,160

Therefore, coefficient of variation=(1130/2160)=0.523

Hence, coefficient of variation value is a)0.394 b)0.850 c)0.523

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The correct answer is b. Expected value. The mean of a discrete random variable generalizes the concept of expected value. The expected value of a discrete random variable is the weighted average of all possible outcomes, where the weights are the probabilities associated with each outcome.

It represents the long-term average value that we would expect to observe if we repeated the random experiment multiple times.

In the context of a discrete random variable, the mean (or expected value) is calculated by multiplying each possible value of the variable by its corresponding probability and summing them up. It provides a measure of central tendency and represents the average value we would expect to obtain from the random variable over a large number of trials.

The population mean (mean of a variable) refers to the average value of a variable in the entire population, not specifically related to a random variable. The sample mean is the average value of a variable calculated from a sample of observations. The distribution of a discrete random variable refers to the pattern of probabilities associated with each possible outcome of the variable.

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The length of IJ in ΔHIJ is approximately 2.8 feet when rounded to the nearest tenth of a foot.

To find the length of IJ in ΔHIJ, we can use trigonometric ratios. In this case, we can use the tangent function since we know the measure of angle I and the length of side HI.

Using the tangent function, we can set up the equation: tan(I) = IJ/HI. Rearranging the equation, we have IJ = HI * tan(I).

In this scenario, I = 26° and HI = 5.7 feet. Substituting these values into the equation, we can calculate the length of IJ.

Calculate the tangent of angle I: tan(26°) ≈ 0.4877.

Multiply the tangent value by the length of HI: 5.7 feet * 0.4877 ≈ 2.7777 feet.

Therefore, the length of IJ in ΔHIJ is approximately 2.8 feet.

Using the given information, we can apply trigonometry to find the length of side IJ. In a right triangle, the tangent function relates the angle I to the ratio of the lengths of the opposite side (IJ) and the adjacent side (HI).

First, we find the tangent of angle I by using the given measure: tan(26°). This gives us the ratio of IJ to HI.

Next, we substitute the known values: HI = 5.7 feet. By multiplying HI with the tangent of angle I, we get the length of IJ.

In this case, tan(26°) ≈ 0.4877. Multiplying this by HI = 5.7 feet, we find that IJ ≈ 2.7777 feet.

Therefore, the length of IJ in ΔHIJ is approximately 2.8 feet when rounded to the nearest tenth of a foot.

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Alice decides to buy only one bottle per week, instead of two. That means that she is saving half of her last expenses. There are 52 weeks in one year, so the savings can be calculated as:

Savings = (# of weeks) * (average cost of a bottle of wine)

We know that a bottle of wine costs $15 on average, so:

Savings = 52*15

Savings = $780

Answer:

The product of the first and last digits is 40.

Step-by-step explanation:

Multiple of 4 rule:

The last two digits must form a number that is divisible by 4.

Multiple of 11 rule:

We find the alternate sum of the digits, and it must be divisible by 11.

A SECRET CODE has 5 digits. The middle 3 digits are 926

So the code is

x926y

Divisible by 4:

This means that the 6y must be divisible by 4, which means that the possible values of y are 0, 4, 8.

Value of x when y = 0:

x9260

x - 9 + 2 - 6 + 0 = x - 13

It will be divisible by 11 when x - 13 = 22, that is, x = 9. However, the digit 9 is already used, which means that y = 0 is not a possible option.

Value of x when y = 4:

x9264

x - 9 + 2 - 6 + 4 = x - 9

It will be divisible by 11 when x - 9 = 0, that is, x = 9, which is not possible, as we saw above. Or

x - 9 = 11

x = 2

The digit 2 is also possible, so y cannot be 4.

Value of x when y = 8:

x9268

x - 9 + 2 - 6 + 8 = x - 5

x - 5 = 0 -> x = 5

So, the number is:

59268

What is the product of the first and last digits?

5*8 = 40

The product of the first and last digits is 40.

Answer:

\( \sf \: 104.4\)

Step-by-step explanation:

(7.36)(10)(9)−(6.2)(10)(9)

=(73.6)(9)−(6.2)(10)(9)

=662.4−(6.2)(10)(9)

=662.4−(62)(9)

=662.4−558

=104.4