8 george thinks of an equivalent fraction for 23, such that the sum of its numerator and denominator is 45. harper thinks of an equivalent fraction for 511, such that the difference between its numerator and denominator is 30. can you find the sum of the denominators of the two fractions?

Answer:

C

Step-by-step explanation:

-2x + 10  Means that the line crosses the y axis at 10.  The slope is -2 that means that as the y changes by -2, the x changes by 1.  

The second equations means that we have a horizontal line with no slope that goes through -28 1/2

Fixed overheads are allocated to products on the number of litres of ice cream produced, irrespective of the size of the output. Liters Rands Expected Sales :500 ml ice cream = 60,000 litres

= 60,000 x R10

= R 600,0001 litre

ice cream = 80,000

litres = 80,000 x R 15 = R1,200,000

Total expected sales volume 140,000 litres R1,800,000 . From the given question, we are told that inventory is valued on the basis of equivalent units of inventory. Which means that two 500ml of ice cream is valued the same as one litre of ice cream. We are also told that variable overheads vary with direct labour hours. Fixed overheads are allocated to products on the number of litres of ice cream produced, irrespective of the size of the output.

Using this information we can prepare a sales budget for the company by estimating the sales volume in litres for each of the two sizes of ice cream containers and multiplying the sales volume by the respective sale price of each size. Since the number of litres is used to allocate fixed overheads, it is necessary to prepare the budget in litres as well. The total expected sales volume can be calculated by adding up the expected sales volume of the two sizes of ice cream products. The expected sales volume of 500 ml ice cream is 60,000 litres (500 ml x 0.12 million) and the expected sales volume of 1 litre ice cream is 80,000 litres (1 litre x 0.08 million). Adding up the two volumes, we get a total expected sales volume of 140,000 litres.

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The length of the gardens and the total area of Lisa's backyard is 26 ft. Therefore, option D is the correct answer.

The area of a trapezoid can be calculated if the length of its parallel sides and the distance (height) between them is given. The formula for the area of a trapezoid is expressed as, A = ½ (a+b)×h.

where (A) is the area of a trapezoid, 'a' and 'b' are the bases (parallel sides), and 'h' is the height (the perpendicular distance between a and b).

Given that, the vegetable garden and flower garden have an area of 216 ft

Here, the vegetable garden and flower garden is in the shape of trapezium with bases 10 ft and x ft and height is 12 ft

Here, area = 1/2 (10+x)×12

216=6(10+x)

(10+x)=36

x=26 ft

Therefore, option D is the correct answer.

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cp of 40 l of milk=6.50*40=260

sp of 56 l of mixture=56*7=392

392-260=132

gain%=132/260*100=50.76%

Step-by-step explanation:

2x + y + x+ 2y = 180

3x + 3y = 180

3y +20+2x+y=180

4y + 2x = 160

3x + 3y = 180

2x + 4y = 160

elimination

6x + 6y= 360

6x + 12y = 480

= 6y = 120

y= 20

substitute

3x + 3y = 180

3x + 3(20)= 180

3x + 60 = 180

3x = 120

x= 40

x+2y

40+2(20)=80

<4=<8= 80°

<7=180-<8=<180-80= 100°

angle 7 = 100°

angle 8 = 80°

A sample is a subgroup of the population that represents the population.

The three main types of samples are random, stratified, and quota samples. The following are the procedures to select a simple random sample of 150 students at your school:

Step 1: Create a list of the entire population of students at the school.

Step 2: Number each student on the list.

Step 3: Use a random number generator to select 150 random numbers from the list.

Step 4: Identify the students who correspond to the random numbers generated as part of the sample.

The following are the procedures to select a quota sample of 50 business and 50 engineering students:

Step 1: Identify the two groups, business and engineering students.

Step 2: Determine the proportion of each group in the population.

Step 3: Calculate the number of participants you will need from each group.

Step 4: Use convenience sampling to select the required number of participants for each group.

The following are the procedures to select a stratified sample of 100 high school students based on their grades:

Step 1: Create a list of all high school students.

Step 2: Stratify the students based on their grades.

Step 3: Determine the proportion of each grade in the population.

Step 4: Calculate the number of participants needed from each grade.

Step 5: Use a random sampling technique to select the required number of participants from each grade.

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The range of the functions f(x) = |x| 9 and g(x) = –6 then (f+g)(x) will be equal  to (f+g)(x)\(\geq\)3 for all the values of x.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

It is given that

\(f(x)=|x|+9\)

\(g(x)=-6\)

So now

\((f+g)(x)=|x|+9-6=|x|+5\)

So from the above equation, we can see that (f+g)(x) describes the range  (f+g)(x)\(\geq\)3

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Answers 76:

Step-by-step explanation:

Answer: 4x + 8 = 12

Step-by-step explanation: U combine 3x + 4x - 3x = 4x and just add 8 add 12 to the equation

Answer:

11-3x

Step-by-step explanation:

1) Multiply 5(1-x). To do this, you multiply 5 by both x and 1. You should get     5-5x.

1) Next, multiply 2(x+3). You should get 2x+6.

3) Finally, add like terms. Add 2x and -5x together and add 6 and 5 together. You should get -3x and 11.

The answer is 11-3x.

Answer:

$5.50

Step-by-step explanation:

Answer:

Step-by-step explanation:

A rational number can be written as a fraction of two integers.

√23 is irrational because we do not know what the square root of 23 is in terms of integers in a fraction.

104.42 is rational because it can be expressed as 10442/100 . We can express it as this because

104.42 * 1 = 104.42 * 100/100 = 10442/100, and multiplying something by 1 keeps it the same

√64 is rational because it is equal to 8, and 8/1 is equal to 8

49.396 with the 6 repeating is rational because we can express 49.39 as

49.39 * 1 = 49.39 * 100/100 = 4939/100, and we are then left with

49.396- 49.39 = 0.006 (with the 6 repeating). A repeating decimal can be expressed as x/9, with the x representing all values before the repetition begins multiplied by 10.

For example, 0.6 with the 6 repeating can be represented as 6/9. This is because 0.6 * 10 = 6, and we divide that by 9. Similarly, 0.006 with the 6 repeating can be represented by 0.06/9

We add the two fractions together to get

4939/100 + 0.06/9

multiply both fractions by the other's denominator to even them out and make the numerator of the second fraction an integer

(4939*9)/(100*9) + (0.06*100)/(9*100)

= 44451/900 + 6/900

= 44460/900

Assuming that the last number has only the digits given, that is rational because, similarly to 104.42, it can be multiplied by a power of 10 to result in (integer)/(integer), making it rational. If the dots represent infinite digits, then it is not rational because there are infinite digits that are not repeating, and there is no way to know the last digit, so it is impossible to write a fraction from it

Answer:The continuous compounding of interest in a bank leads to the formula A(t) = A0 * e^(rt) for the total amount in the account at time t, where r is the interest rate, A0 is the principal amount, and e is the base of the natural logarithm (approximately 2.71828).

Step-by-step explanation:

1. A0 represents the initial principal amount, which is the starting balance of the account.
2. r is the interest rate, expressed as a decimal (e.g., 0.05 for 5% interest rate).
3. t is the time, typically measured in years.
4. e is the base of the natural logarithm (approximately 2.71828).
5. The exponent rt represents the product of the interest rate (r) and the time (t).
6. A(t) represents the total amount in the account at time t, including both the principal and the interest earned.

By continuously compounding interest, the account balance grows at an exponential rate, and the formula A(t) = A0 * e^(rt) is used to calculate the account balance at any given time t.

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Answer:

The solution is: v = \(9\frac{1}{2}\)

Step-by-step explanation:

Given equation is:

\(\frac{4}{5}(v-7) = 2\)

The given equation is a linear equation in one variable. The solution requires isolating v on one side of the equation. Simple equality properties can be used to solve the equation.

So,

Multiplying both sides of equation with 5

\(5*\frac{4}{5}(v-7) =5* 2\\{4}(v-7) = 10\)

dividing both sides by 4

\(\frac{4(v-7)}{4} = \frac{10}{4}\\v-7 = \frac{5}{2}\\\)

Adding 7 on both sides

\(v-7+7 = \frac{5}{2}+7\\v = \frac{5+14}{2}\\v = \frac{19}{2}\\v = 9\frac{1}{2}\)

Hence,

The solution is: v = \(9\frac{1}{2}\)

Answer:

(6, 13) is not

(9, 16) is

Step-by-step explanation:

The preparation of the stockholders' equity statement for the year ended December 31, 2021, is as follows:

Court Casuals

Statement of stockholers' equity

December 31, 2021

Common Stock                        $116,000

Additional Paid-in Capital  $5,326,000

Retained Earnings              $3,677,000

Treasury Stock                         $-2,000

Total stockholders' equity  $9,117,000

The stockholders' equity statement includes the common stock, additional paid-in capital, retained earnings, and the subtraction of the treasury stock.

Court Casuals

Stockholers' equity on January 1, 2021

Common Stock $90,000

Additional Paid-in Capital $4,100,000

Retained Earnings $3,000,000

Net income for the year, 2021, = $900,000

May 18: Cash $1,300,000 Common Stock $26,000 Additional Paid-in Capital $1,274,000 (26,000 x $50 - $26,000)

May 31: Treasury Stock $4,500 Additional Paid-in Capital $175,500 (4,500 x $40 - $4,500) Cash $180,000

Jul 1: Cash Dividend $223,000 (90,000 + 26,000 - 4,500) x $2 Dividends Payable $223,000

July 31: Dividends Payable $223,000 Cash $223,000

August 18: Cash $130,000 Treasury Stock $2,500 Additional Paid-in Capital $127,500 (2,500 x $52 - $2,500)

Statement of Retained Earnings, December 31, 2021:

Beginning balance  $3,000,000

Net income                 $900,000

Dividends                     -223,000

Ending balance        $3,677,000

Beginning balance  $90,000

May 18: Cash              26,000

Ending balance       $116,000

Beginning balance  $4,100,000

May 18: Cash              1,274,000

May 31: Cash                -175,500

August 18: Cash            127,500

Ending balance      $5,326,000

May 31: Cash                 $4,500

August 18: Cash             -2,500

Ending balance            $2,000

Thus, we can summarize from the stockholders' equity that Court Casuals has outstanding shares of 114,000 (116,000 - 2,000) at $1 par, which is the difference between the ending balances of the common stock and the treasury stock accounts, after reflecting the equity transactions for the year.

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The joint pmf of X and Y is given by P(X = x, Y = y) = 1/15 for x,y = 1,2,...,5.

Since X and Y are independent, their joint pmf is simply the product of their marginal pmfs. The marginal pmf of X is given by P(X = x) = ∑y P(X = x, Y = y) = 1/15 ∑y 1 = 1/3, since there are three values of y for each x. Similarly, the marginal pmf of Y is P(Y = y) = 1/3. Therefore, the joint pmf of X and Y is P(X = x, Y = y) = P(X = x)P(Y = y) = (1/3)×(1/3) = 1/15 for x,y = 1,2,...,5.

Joint probability mass function (pmf) is a function that describes the probability distribution of two or more random variables. It assigns probabilities to all possible combinations of values that the random variables can take. For example, if X and Y are two random variables, the joint pmf P(X=x, Y=y) gives the probability of X=x and Y=y occurring together. The joint pmf satisfies the following properties:

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Answer:

\(\frac{x}{8}>9\)

Step-by-step explanation:

step one:

given

we can say that the total amount of cocoa made by Mrs.Fieldhouse is

x ounces

Step two:

Since the total batch which is x ounces was divided into 8 mugs

then the expression is x/8

The inequality for the situation is

\(\frac{x}{8}>9\)

Answer:

x ≥ 21

Hope it helps!

☁️My Answer☁️:

y = 90°

✧My Step-by-step explanation✧:

The angle x forms a straight line with the both the 50° angle and the 40° angle:

x + 50° + 40° = 180°

x = 90°

Which means…

y = x = 90°

Answer:

21

Step-by-step explanation:

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

AD        AH

-----  =  ---------

AB         AH +y

3        9

---- = ------

10         9+y

Using cross products:

3(9+y) = 9*10

27+3y = 90

3y = 90-27

3y =63

y = 63/3

y = 21

Answer:

y = 21

Step-by-step explanation:

According to the Side Splitter Theorem, if a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

Therefore, according to the Side Splitter Theorem:

\(\boxed{\sf AD : DB = AH : HC}\)

From inspection of the given triangle, the lengths of the line segments are:

To find the value of y, substitute the given line segment lengths into the proportion and solve for y:

\(\begin{aligned}\sf AD : DB &=\sf AH : HC\\\\3:7&=9:y\\\\\dfrac{3}{7}&=\dfrac{9}{y}\\\\3 \cdot y&=9 \cdot 7\\\\3y&=63\\\\\dfrac{3y}{3}&=\dfrac{63}{3}\\\\y&=21\end{aligned}\)

Therefore, the value of y is 21.

Answer: $521

Step-by-step explanation:

The volume of the sphere is given by the formula V = (4/3)*pi*R³, and in this case the volume is V = 3,052.08 yd³

The volume of a sphere of radius R is given by the formula below:

V = (4/3)*pi*R³

Where pi = 3.14

Here we can see that the radius is 9yd, then the volume of that sphere will be:

V = (4/3)*3.14*(9yd)³

V = 3,052.08 yd³

Sothe volume of the sphere is 3,052.08  cubic yards.

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Let x represent the amount of soup in each bowl. Since there were 4 bowls and 5 cups of soup leftover, the total amount of soup must be greater than or equal to 13 cups.

Mrs. McCallister made chicken noodle soup in the crockpot, and there were 4 bowls with soup. The recipe claimed that it would make at least 13 cups of soup, but there was 5 cups leftover. To figure out how much soup was in each bowl, we can set up an inequality. Let x represent the amount of soup in each bowl. Since there were 4 bowls and 5 cups of soup leftover, the total amount of soup must be greater than or equal to 13 cups. We can write this as an inequality: 4x + 5 ≥ 13. To determine how much soup was in each bowl, we can solve the inequality for x. Subtracting 5 from both sides, we have 4x ≥ 8. Dividing both sides by 4, we get x ≥ 2. This means that each bowl had at least 2 cups of soup.

In summary, we used an inequality to determine how much soup was in each bowl. The inequality modeled this situation by stating that the total amount of soup was greater than or equal to 13 cups. We then solved the inequality to find that each bowl had at least 2 cups of soup. This shows how inequalities can be used to solve real world problems.

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Answer:

x=10.4

Step-by-step explanation:

52+5x=10x

52=5x

10.4=x

The time Jodie have left to match the record of Mandy is 15.11 seconds

Jodie:

= 40.25 seconds

Time spent on the rope = 12.84 seconds

Total time spent = 40.25 seconds + 12.84 seconds

= 53.09 seconds

Total time she have left to match the record = Mandy's obstacle course - Total time spent

= 68.2 seconds - 53.09 seconds

= 15.11 seconds

Therefore, the time Jodie have left to match the record of Mandy is 15.11 seconds

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The largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 3y + 4z = 9 has dimensions x = 1.5, y = 1, and z = 2.25, with a maximum volume of 3.375 cubic units.

To find the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 3y + 4z = 9, we can use the method of Lagrange multipliers.

Let the sides of the rectangular box be represented by the variables x, y, and z. We want to maximize the volume V = xyz subject to the constraint x + 3y + 4z = 9.

The Lagrangian function is then given by L = xyz + λ(x + 3y + 4z - 9).

Taking the partial derivatives of L with respect to x, y, z, and λ, and setting them equal to zero, we get:

yz + λ = 0

xz + 3λ = 0

x*y + 4λ = 0

x + 3y + 4z - 9 = 0

Solving these equations simultaneously, we get:

x = 1.5, y = 1, z = 2.25, and λ = -0.5625

Therefore, the maximum volume of the rectangular box is V = 1.512.25 = 3.375 cubic units.

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The correct option C: r = √(√3)² + (√3)² = √6; θ  = arctan (1) = π/4.

The complex number z=x+iy is represented by the rectangular coordinates (√3,√3) and polar coordinates (6,π/4) respectively.

The polar coordinates r (a radial coordinate) and in Cartesian space (the angular coordinate, generally termed as  polar angle),

x = rcosθ  .....(1)

y = rsinθ,  .....(2)

where is indeed the counterclockwise angle first from x-axis and r is the radial distance to the origin. Considering x and y,

r² = x² + y²  ...eq 3

θ  = arc tan (y/x)

Using the polar coordinates explanation from above, we can deduce that;

r² = x² + y²  .

r² = √3² + √3²  .

r = √(√3)² + (√3)²

and

θ  = arc tan (√3/√3) = arctan (1) = π/4.

Thus, the complex number z=x+iy is represented by the rectangular coordinates (√3,√3) and polar coordinates (6,π/4) respectively.

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The compete question is attached.

Answer:

12

Step-by-step explanation:

Assuming that the 2  actually represents square, the equation is
\(f(x) = 12(x-2)^2 + 18\)

\((x-2)^2 = x^2 - 4x + 4\\\\12(x-2)^2 + 18 = 12( x^2 - 4x + 4) + 18 = 12x^2 -48x + 48 + 18 = 12x^2 -48x + 66\\\)

This equation is of the form
\(ax^2 + bx + c\)

\(a = 12, b = -48, c = 66\)

Note

Since the question is only asking for the a value which is the coefficient of x² it is clear that 12 is the coefficient without expanding (x-2)² but it is always better to proceed as above in case you are asked for b and c values also

Value of the function at x=a is \(12a^{2} -240a +1218\).

Given function f(x)=\(12(x-10)^{2} +18\)

We have to find the value of function at x=a.

For this we have to just put x=a in the function f(x)=\(12(x-10)^{2}+18\)

f(a)=12\((a-10)^{2} +18\)

we have to expand (x-10) to the power 2  to get the value of  function.

f(a)=\(12(a^{2} +10^{2} -20a)+18\)

=\(12a^{2}+1200-240a+18\\\)

=\(12a^{2} -240a+1218\)

Hence the value of function at x=a is \(12a^{2} -240a+1218\) means f(a)=\(12a^{2} -240a+1218\).

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Answer:

volume=3x³+15x²+12x

Step-by-step explanation:

v= l*w*h =(3x )(x+1) (x+4)

v=3x(x²+5x+4)

volume=3x³+15x²+12x