Christopher is the oldest of three sibling whose ages are consecutive odd integers. If the sum of their ages is 63, find Christopher’s age.

Answer:

x (x-5) 5( x-5)

(x×x)- (x× 5) + ( 5× x) - ( 5×5)

x squared - 5x + 5x -25

x squared -5

Answer:

To multiply out (x - 5) (x - 5), we can use the distributive property twice:

(x - 5) (x - 5) = x(x) - x(5) - 5(x) + 5(5)

= x^2 - 5x - 5x + 25

= x^2 - 10x + 25

Therefore, (x - 5) (x - 5) simplifies to x^2 - 10x + 25.

Step-by-step explanation:

Writing the expressions ⁸√93⁵ and ⁵√22⁷  in exponential form would result to

Information given in the problem

To write the given expression in radical form to equation in exponents in fraction form. This is done as follows

(base number) ^ (exponent of base number / number in radical side)

we complete it as below

the expression ⁸√93⁵ now becomes 93^(5/8)

the expression ⁵√22⁷ now becomes 22^(7/5)

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The system of inequalities has the following solution set as a result: -1, 0, 1, 2, 3.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the not equal sign (=) to indicate that two values are not equal. whenever several inequalities are use to compare the numbers, whether it is less than or greater than sign. This topic will cover the different inequality ,methods properties and symbols for solving linear inequalities in one variable and two variables that are used in algebra.

A finite set of equations for which common solutions are referred to in mathematics as a set of simultaneous equations, are  known as a system of equations or an equation system.

First of all  for first inequalities ,

we must first subtract 2 from both sides of the inequality 2-6 y <14.

-6 y < 12

now , we are dividing -6 both sides,

than the inequality symbol must be reversed:

than we get

y > -2

Hence, y > -2 is the solution set for the first inequality.

For second inequalities Now  we  first subtract 21 from both sides of the inequality

than we get,

-5 y > -20

The next step is to divide -5 by both sides.  

than, the inequality symbol must be reversed:

than we get

y < 4

The second inequality's solution set is therefore y 4.

We can contain all the integers between -2 and 4 (inclusive) to discover the integers in the solution set for both inequalities:

-2, -1, 0, 1, 2, 3, 4

In this set , the integers that fulfill both inequalities are

-1, 0, 1, 2, 3

The system of inequalities has the following solution set as a result: -1, 0, 1, 2, 3.

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This function y = |x| is shifted 6 units to the right and 6 units up from the original function f(x), and matches the dotted function .

Given that

y = |x|

To match the function y = |x|, we shif it 6 units to the right and 6 units up,  using the transformation:

f(x + 6) + 6

Let's see how this transformation works:

Shifting to the right by 6 units:

We replace x with x + 6, which moves the graph 6 units to the left. This transformation reflects on the inside of the function, so we write it as f(x + 6).

Shifting up by 6 units:

We add 6 to the entire function, which moves the graph 6 units up. This transformation reflects on the outside of the function, so we write it as f(x) + 6.

Putting these transformations together, we get:

f(x + 6) + 6

This function is shifted 6 units to the right and 6 units up from the original function f(x), and matches the dotted function y = |x|.

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By answering the presented question, we may conclude that  It is also necessary to examine the game's risk, as losing $1 is a possibility.

Probability theory is an area of mathematics that determines the likelihood that an event will occur or that a proposition is true. A probability is a number between 0 and 1, where 1 represents certainty and 0 represents how likely an event is to occur.

A probability is a numerical expression for the chance or likelihood that a given event will occur. Probabilities may either be stated as percentages ranging from 0% to 100% or as numbers ranging from 0 to 1. the proportion of occurrences among all equally likely alternatives that lead to a certain event relative to all conceivable outcomes.

To compute the expected value of this game, we must first compute the probability of each result and its associated payment.

The likelihood of picking a gold marble is 3/33, or 1/11. The reward for choosing a gold marble is $3.

The odds of picking a silver marble are 9/33, or 3/11. The reward for choosing a silver marble is $2.

The odds of picking a black marble are 21/33, or 7/11. The reward for choosing a black stone is -$1.

To determine the anticipated value, multiply each likelihood by the related reward and add the results:

Value expected = (1/11)($3) + (3/11)($2) + (7/11)(-$1)

$0.27 is the expected value.

This indicates that you can expect to win $0.27 on average for every game played. But, keep in mind that this is an average and you may not always win that much. It is also necessary to examine the game's risk, as losing $1 is a possibility.

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complete question - A bag contains 3 gold marbles, 9 silver marbles, and 21 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.

what is the expected value if you play this game ?

Answer:

Solve mentally:

a. 782 x 1000 =782,000

The rate of change of the graph as shown in the diagram is 0.75 pounds/months.

rate of change is the rate that describes how one quantity changes in relation to another quantity.

To calculate the rate of change of the graph as shown in the diagram, we use the formula below.

Formula:

Where:

Picking any two corresponding points in the graph,

Substitute these values into equation 1

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Answer: 114

Step-by-step explanation:

If x-3 is a factor of 5x³ - 3x² + 2x - k, then x = 3 is a root of the polynomial. This means that when x = 3, the polynomial is equal to zero.

Substituting x = 3 into the polynomial, we get:

5(3)³ - 3(3)² + 2(3) - k = 0

Simplifying this expression, we get:

135 - 27 + 6 - k = 0

Solving for k, we get:

k = 135 - 27 + 6 = 114

Therefore, the value of k is 114.

Answer:

give brainliest if correct

Step-by-step explanation:

Let's call the distance from the ball to the base of the goal "x". We can use the tangent function to set up an equation:

tan(27°) = opposite/adjacent

In this case, the opposite side is the height of the goal (9 feet) and the adjacent side is the distance we want to find (x). So we can rewrite the equation as:

tan(27°) = 9/x

To solve for x, we can cross-multiply and then divide by tan(27°):

tan(27°) * x = 9

x = 9 / tan(27°)

Using a calculator, we get:

x ≈ 17.20 feet

So the distance from the ball to the base of the goal is approximately 17.20 feet.

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We have been presented a compound inequality. We have to graph the inequality above on a number line.    

A compound inequality has been shown to us. On a number line, we are required to graph the above inequality.    

[tex]$x \leq 3 \text { or } x \geq 8[/tex]

The answer to the inequality is any value of x that is between 3 and 8 and less than or equal to 3.

At and, we'll have distinct dots x = 3 and x = 8.

The number line's first arrow would go from 3 to its left. (towards negative infinity). The opposite arrow will run from 8 to the number line's right side and towards positive infinity.

The complete question is?

Graph the compound inequality on the number line.

X ≤ 3 or x ≥ 8

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Answer:

z>-4

Step-by-step explanation:

You start with -2z-3<5 add 3 to both sides -2z<8 and divided by negative which flips your sign so you get z>-4 hope this helps :)

The volume of the solid of revolution is approximately 2.470 cubic unit.

To find the volume of the solid of revolution, we need to use the formula:

V = π∫[a,b] [tex]y^2[/tex] dx

where y is the distance between the function that is being rotated and the axis of revolution, which in this case is the y-axis.

To begin, we must determine the y-equation for the curve that defines the boundary of the region.

y = (1/2)x cosh x

Solving for x in terms of y, we get:

x = [tex]cosh^{-1}[/tex](2y/y)

We only need to find the volume for the region where y is not negative and then multiply the result by 2 because the curve is symmetric with respect to the y-axis.

The limits of integration for x are x = 1 and x = 2, which correspond to y-values of y = (1/2) cosh(1) and y = (1/2) cosh(2), respectively.

So, we can write the integral for the volume as:

V = 2π∫[[tex]0,(1/2)cosh(2)] [(cosh^{-1}(2y/y))^2] dy[/tex]

We can simplify this by using the identity [tex]cosh^{-1}(x) = ln(x + \sqrt{x^2 - 1}),[/tex] which gives:

V = 2π∫[[tex]0,(1/2)cosh(2)] [(ln(2y/y +\sqrt{((2y/y)^2 - 1)))^2}] dy[/tex]

This integral can be evaluated using integration by parts or numerical methods. Using numerical methods, we get:

V ≈ 2.470 cubic units (rounded to three decimal places)

Therefore, the volume of the solid of revolution is approximately 2.470 cubic unit.

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The expected value is ((18/37) x (2 x wager [we will receive the wager back and the winnings])) + ((19/37) x 0)

What is American roulette?

Guessing on which number on the wheel ball will come to rest is the objective of American Roulette. Every number contains the same chances as any other number of coming up on each spin (that is winning number on any spin has no effect on the outcome of next spin). The best chance of payout is provided by an outside bet. The possible outcomes of the game of roulette is covered by 'outside bets'. With the higher winning chances, the payout is not going to be incredibly generous(it's only 1:1 for bets like odd or even that covers almost like half the wheel).

Expected value is calculated by adding all the different possible outcomes multiplied by their probabilities.  

So, in this case (0.5 x $2) + (0.5 x $1).  

For specific example it would be determined by the number of options on a roulette wheel (generally 37).  

So winning on this bet in 18 outcomes (the even numbers) and losing on 19 outcomes (the odd numbers + 0).  

Putting it all together, the expected value is ((18/37) x (2 x wager [we will receive the wager back and the winnings])) + ((19/37) x 0).

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The probability that the cars selected consist of 2 midsized cars and 4 compact cars is approximately 0.2723 or 27.23%.

What is Probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. The probability of an event can also be expressed as a percentage between 0% and 100%.

We can use the formula for combinations:

nCk = n! / (k! * (n-k)!)

where n is the total number of objects, k is the number of objects being selected, and ! represents the factorial function.

In this case, there are 11 midsized cars and 12 compact cars, so n = 23. We want to select 6 cars consisting of 2 midsized cars and 4 compact cars, so k1 = 2 and k2 = 4.

The probability of selecting exactly 2 midsized cars and 4 compact cars is equal to the number of ways to select 2 midsized cars from 11 multiplied by the number of ways to select 4 compact cars from 12, divided by the total number of ways to select 6 cars from 23:

P(2M, 4C) = (11C2 * 12C4) / 23C6

where nCk represents the number of combinations of k objects from a set of n objects.

Evaluating this expression gives:

P(2M, 4C) = (55 * 495) / 100947

P(2M, 4C) ≈ 0.2723

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a. Jina's monthly payment is $[tex]1,944.87[/tex]  . b.Jina will repay a total amount of $[tex]23,338.44[/tex]. c. Over the course of the loan, Jina will pay interest totalling $[tex]1,338,44[/tex].

(a) applying the formula for the monthly payment on an amortized loan, we may calculate Jina's monthly payment.

[tex]P = (r \times A) / (1 - (1 + r)^(-n))[/tex]

where P denotes the monthly instalment, A denotes the loan balance, r denotes the monthly interest rate (calculated by dividing the annual interest rate by 12), and n is the total number of payments.

Plugging in the values we have:

[tex]A = $22,000[/tex]

[tex]r = 0.0785/12 = 0.006542[/tex]

[tex]n = 1 year \times 12 months/year = 12 months[/tex]

[tex]P = (0.006542 \times $22,000) / (1 - (1 + 0.006542)^(-12)) = $1,944.87[/tex]

So, Jina's monthly payment is $ [tex]1,944.87[/tex].

b. Jina will pay $ [tex]1,944.87[/tex] each in 12 equal monthly instalments. Thus, her entire loan repayment amount.

[tex]12 \times $1,944.87 = $23,338.44[/tex]

Therefore, Jina will repay a total amount of $  [tex]23,338.44.[/tex]

(c) The sum of the loan repayments minus the loan amount is the total amount of interest that Jina will pay during the course of the loan.

Total interest = Total amount to repay - Loan amount

Total interest = $[tex]23,338.44 - $22,000 = $1,338.44[/tex]

Therefore, a. Jina's monthly payment is $1,944.87. b.Jina will repay a total amount of $[tex]23,338.44[/tex]. c. Over the course of the loan, Jina will pay interest totaling $ [tex]1,338,44[/tex].

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Answer:250%

Step-by-step explanation:

Answer:

En este problema se trata de una función exponencial, donde la cantidad de microbios en el recipiente se duplica cada minuto.

Si x representa el número de minutos transcurridos y y la cantidad de microbios en el recipiente, entonces se puede expresar la función exponencial como:

y = a * (2)^x

Donde "a" es la cantidad inicial de microbios en el recipiente, en este caso a = 1.

Después de 30 minutos, la cantidad de microbios en el recipiente es:

2^30 = 1,073,741,824

Esto significa que si se coloca un solo microbio en el recipiente, se tardará 30 minutos en llenarlo.

Si se colocan 2 microbios en el recipiente, entonces la cantidad inicial de la función exponencial es a = 2, y se busca el valor de x tal que:

2 * (2)^x = 1,073,741,824

Dividiendo ambos lados por 2, se tiene:

(2)^x = 536,870,912

Tomando logaritmos base 2 en ambos lados, se tiene:

x = log2(536,870,912) = 29

Por lo tanto, si se colocan 2 microbios en el recipiente, se tardará 29 minutos en llenarlo.

Step-by-step explanation:

The line-of-sight distance from the television camera to the base of the stadium is  2,874.1 m.

The line-of-sight distance from the television camera to the base of the stadium is calculated by applying trigonometry ratio as shown below;

SOH CAH TOA

SOH = sin θ = opposite /hypothenuse side

TOA = tan θ = opposite side / adjacent side

CAH = cos θ = adjacent side / hypothenuse side

The altitude is the opposite side, while the hypotenuse side is the line of sight distance.

sin (8) = 400/h

h = 400 m/sin(8)

h = 2,874.1 m

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a) The number of tiles she will need is 736 tiles

b) The amount it would cost to tile the entire bathroom floor is £3312

From the question, we are to determine the number of tiles Mrs. Maryam will need to tile her entire bathroom floor

To determine the number of tiles that would be needed, we will determine the area of the bathroom floor

Area of the bathroom floor = (13 × 16) - (3 × 4) - (4 × 3)

Area of the bathroom floor = 208 - 12 - 12 m²

Area of the bathroom floor = 184m²

From the given information. the square tile she wants to buy is 50 cm long. That is, 0.5 m long

The area of one tile will be

Area of a tile = 0.5 × 0.5

Area of tile = 0.25 m²

Thus,

The number of tile she will need = 184m² / 0.25 m²

The number of tile she will need = 736 tiles

b) If each tile costs £4.50, we are to determine how much it would cost to tile her entire bathroom

The amount it would cost to tile the entire bathroom = 736 × £4.50

The amount it would cost to tile the entire bathroom  = £3312

Hence, the amount it would cost is £3312

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The value of angle QSR is determined as 50⁰.

The value of angle QSR can be obtained if we calculate the value of x.

The value of x is calculated by setting up the following equation as shown below;

(4x - 8) + 34 + (76 - x) = 180 (sum of angles in a straight line )

4x - 8 + 34 + 76 - x = 180

3x = 180 - 102

3x = 78

x = 78/3

x = 26

The value of angle QSR;

∠QSR = 76 - x

∠QSR = 76 - 26

∠QSR =  50⁰

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Answer:

⇒ X = (-2/7, 48/7)

Step-by-step explanation:

Use this formula to find the point X.

([mx₂ + nx₁] / [m+n], [my₂ + ny₁] / [m+n])

Where m:n is the ratio, and the points are x₁, y₁ and x₂, y₂.

The formula can be thought like this:

When the midpoint of a line is taken, we take the average of the x coordinates and the average of the y coordinates. This is in the ratio 1:1.

If we were to take the point on a line in a ratio [m:n], we take the weighted average.

X = ([3*2 + 4*-2] / [3 + 4], [3*4 + 4*9] / [3 + 4])

∴ X = (-2/7, 48/7)

Answer:

So I did the work, but it won't let me upload a picture of it, so when I solved it my answer that I had gotten foe this solution was x(-2/7,48/7).

I hope it was correct for you.

Answer:

Step-by-step explanation:

Therefore, 31cm is equivalent to approximately 12.2047 inches.

The  credit rating higher than 447 will put applicants in the top 2.5%.

We have Probability of X > x = 0.025

1 - p(z < x - 300 / 75)

z(0.975) = x - 300 / 75 = 1.96

x - 300 / 75 = 1.96

from here we have to cross multiply and solve for x

x = 300 + 147

x = 447

credit rating higher than 447 will put applicants in the top 2.5%.

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A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 300 and a standard deviation of 75. Applicants rated in the top 2.5% will have their loan processing fees waived. What credit rating do applicants need to be higher than to receive this extra perk? .

A credit rating higher than ____ will put applicants in the top 2.5%.

The statements that are always true about the angels are; 1. m∠5 + m∠6 =180° 2. m∠2 + m∠3 = m∠6 and 3. m∠2 + m∠3 + m∠5 = 180°

1. m∠5 + m∠6 =180°  means the sum of the measures of two angls, angle 5 (m∠5) and angle 6 (m∠6), is equal to 180 degrees. They are considered Linear pairs.

2.  m∠2 + m∠3 = m∠6  tells us that the sum of the measures of two interior angles, angl 2 (m∠2) and angle 3 (m∠3), amount to the measur of an exterior angle, angle 6 (m∠6), in a triangle.

3. The statement "m∠2 + m∠3 + m∠5 = 180°" means the sum measurment of three interior angls of a triangle, angle 2 (m∠2), angle 3 (m∠3), and angle 5 (m∠5), which is 180 degrees. Triangles sum total

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Answer:not enough info

Step-by-step explanation:

The above prompts have to do with Accounting Principles especially journal entries, income statements and Inventory Mangement. See the answers below.

1) The journal entries are given as follows:

Oct. 4: Purchased 180 bicycles at a cost of $145 each from the Nixon Bicycle Company, terms 2/10, n/30.

Inventory (180 x $145) 26,100

Accounts Payable 26,100

Oct. 5: Paid freight of $900 on the October 4 purchase.

Freight-In 900

Cash 900

Oct. 6: Sold 10 bicycles from the October 1 inventory to Team America for $250 each, terms 2/10, n/30.

Accounts Receivable 2,500

Sales Revenue 2,500

Cost of Goods Sold:

Inventory (10 x $150) 1,500

Cost of Goods Sold 1,500

Oct. 7: Received credit from the Nixon Bicycle Company for the return of 8 defective bicycles.

Accounts Payable 1,160

Inventory 1,160

Oct. 13: Issued a credit memo to Team America for the return of a wrong clear bicycle.

Sales Returns and Allowances 2,500

Accounts Receivable 2,500

Cost of Goods Sold:

Cost of Goods Sold 1,500

Inventory 1,500

Oct. 14: Paid Nixon Bicycle Company in full, less discount.

Accounts Payable 25,452

Inventory 648

Cash 24,804

Explanation:

On October 4, the company purchased 180 bicycles at a cost of $145 each for a total of $26,100. The journal entry is a debit to Inventory for $26,100 and a credit to Accounts Payable for $26,100.

On October 5, the company paid freight costs of $900 on the October 4 purchase. The journal entry is a debit to Freight-In for $900 and a credit to Cash for $900.

On October 6, the company sold 10 bicycles from the October 1 inventory to Team America for $250 each. The total sales revenue is $2,500. The cost of goods sold is calculated by multiplying the number of bicycles sold (10) by the cost per unit ($150), which equals $1,500. The journal entry for the sale is a debit to Accounts Receivable for $2,500 and a credit to Sales Revenue for $2,500. The cost of goods sold is recorded as a debit to Cost of Goods Sold for $1,500 and a credit to Inventory for $1,500.

On October 7, the company received a credit from Nixon Bicycle Company for 8 defective bicycles. The journal entry is a debit to Accounts Payable for $1,160 and a credit to Inventory for $1,160.

On October 13, the company issued a credit memo to Team America for the return of a wrong clear bicycle. The journal entry is a debit to Sales Returns and Allowances for $2,500 and a credit to Accounts Receivable for $2,500. The cost of goods sold is recorded as a debit to Cost of Goods Sold for $1,500 and a credit to Inventory for $1,500.

On October 14, the company paid Nixon Bicycle Company in full, less discount. The company received a 2% discount for paying within the discount period. The journal entry is a debit to Accounts Payable for $25,452, a debit to Inventory for $648, and a credit to Cash for $24,804.



2) The multiple step income statement for the year ended December 31, 2022 is given as follows:

A) McCoy Company

Income Statement

For the Year Ended December 31, 2022

Sales Revenue $645,000

Less: Sales Returns and Allowances 50,000

Sales Discounts 9,500

________

Net Sales 585,500

Cost of Goods Sold 396,000

________

Gross Profit $189,500

Operating Expenses:

Freight-Out 2,000

Advertising Expense 15,000

Interest Expense 19,000

Salaries and Wages Expense 84,000

Utilities Expense 23,000

Depreciation Expense 3,500

________

Total Operating Expenses 146,500

________

Income Before Taxes 43,000

Other Revenues and Gains:

Interest Revenue 25,000

________

Net Income $ 68,000

=======

B) Profit Margin = Net Income / Net Sales

= $68,000 / $585,500

= 0.1164 or 11.64%

Gross Profit Rate = Gross Profit / Net Sales

= $189,500 / $585,500

= 0.3239 or 32.39%

C) For the third prompt, see the attached.

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Answer:

rounded: 11.2, not: (11.180)

Step-by-step explanation:

using pythagorean theorem you can use a squared times B squared equals c squared which in this problem excecutes as 64+25=C and C equals 89. tghe square root of 89 is 9.43, which now enables you to use the theorem on abd which is 36+89=C, C being 11.180.

The expanded form of the given logarithm is:

[tex]1+ 3log_{2}({x}) - \frac{4}{3}log_{2}({y})[/tex]

From the question, we are to expand the given logarithm

From the given information,

The given logarithm is:

[tex]log_{2}\sqrt[3]{\frac{8x^{9}}{y^{4}} }[/tex]

The logarithm can be expanded as shown below:

[tex]log_{2}\sqrt[3]{\frac{8x^{9}}{y^{4}} }[/tex]

[tex]log_{2}(\frac{8x^{9}}{y^{4}})^{\frac{1}{3} }[/tex]

[tex]\frac{1}{3} log_{2}(\frac{8x^{9}}{y^{4}})[/tex]

[tex]\frac{1}{3} [log_{2}({8x^{9}}) - log_{2}({y^{4}})][/tex]

[tex]\frac{1}{3} [log_{2}({8}) + log_{2}({x^{9}}) - log_{2}({y^{4}})][/tex]

[tex]\frac{1}{3} [log_{2}({2^{3}}) + log_{2}({x^{9}}) - log_{2}({y^{4}})][/tex]

[tex]\frac{1}{3} [3log_{2}({2}) + 9log_{2}({x}) -4 log_{2}({y})][/tex]

[tex]\frac{1}{3} [3(1)+ 9log_{2}({x}) - 4log_{2}({y})][/tex]

[tex]\frac{1}{3} [3+ 9log_{2}({x}) - 4log_{2}({y})][/tex]

[tex]1+ 3log_{2}({x}) - \frac{4}{3}log_{2}({y})[/tex]

Hence,

The expanded form is:

[tex]1+ 3log_{2}({x}) - \frac{4}{3}log_{2}({y})[/tex]

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Answer: B: N is odd

Step-by-step explanation:

If 3N + 5 is a multiple of 10, then it can be written as:

3N + 5 = 10k, where k is an integer.

Subtracting 5 from both sides, we get:

3N = 10k - 5

Dividing both sides by 3, we get:

N = (10k - 5) / 3

For N to be an integer, 10k - 5 must be divisible by 3.

We know that any multiple of 10 that is divisible by 3 must have a units digit of 0, and the sum of its digits must be divisible by 3.

The units digit of 3N + 5 is 5, which is not 0, so N is not even. Therefore, option A is not correct.

The sum of the digits of 3N + 5 is 3 + 5 = 8, which is not divisible by 3. Therefore, N is not a factor of 30. Therefore, option C is not correct.

Similarly, since 3N + 5 is not divisible by 5, N cannot be a factor of 50. Therefore, option D is not correct.

Therefore, the only possible option is B: N is odd.

To see why, consider the following: if N is odd, then 3N is odd, and 3N + 5 is even. If 3N + 5 is even, then it must be divisible by 2, which means it is also divisible by 10 (since it is given that 3N + 5 is a multiple of 10). Therefore, N must be odd.