9
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Bonnie withdrew $1,200 from her savings account. She spent of the money on travel arrangements. She spent of the remaining amount at the
hardware store. Finally, she treated her friend to lunch with some of the remaining money. After lunch, Bonnie had $300.50 left. How much money did
Bonnie spend on lunch?
Bonnie spent $
on lunch.
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a) The 95% confidence interval is (1.638, 3.236).

b) The 95% Bayesian coverage interval is (2.041, 2.889).

c) The Bayesian method provided much better results compared to traditional methods because it takes into account previous knowledge of the dielectric constant, rather than just relying on the experimental data.

a) To find an estimate of the dielectric constant y and a 95% confidence interval using standard statistical methods, we can use the sample mean and standard deviation of the experimental data.

The sample mean of the experimental data is:

(2.749 + 2.866 + 2.420 + 1.637)/4 = 2.437

The sample standard deviation of the experimental data is:

√(((2.749 - 2.437)² + (2.866 - 2.437)² + (2.420 - 2.437)² + (1.637 - 2.437)²)/(4 - 1)) = 0.399

To find the 95% confidence interval, we can use the t-distribution with n-4 degrees of freedom. The t-value for a 95% confidence interval with 4 degrees of freedom is 2.776.

The 95% confidence interval is then:

2.437 +/- (2.776 × 0.399) = (1.638, 3.236)

b) To find a Bayesian estimate of the dielectric constant using the previous knowledge of the theoretical value and a factor, we can use the following formula:

μ × y = (K × [tex]e[/tex] + n × y)/(K + n)

Using the given values, the Bayesian estimate of the dielectric constant is μy = (10 × 2.50 + 4 × 2.437)/(10 + 4) = 2.465

μ × y +/- (t × √(V/n + q))

Using the given values and the t-value for a 95% confidence interval with 4 degrees of freedom (2.776), the 95% Bayesian interval is:

2.465 +/- (2.776 × √(1/4 + 0.25)) = (2.041, 2.889)

c) The Bayesian method provided much better results compared to traditional methods because it takes into account previous knowledge of the dielectric constant, rather than just relying on the experimental data. By incorporating the theoretical value and a weighting factor, the Bayesian estimate of the dielectric constant is more accurate and has a narrower confidence interval compared to the estimate obtained using just the experimental data.

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(a)     [tex]p_{n} =p_{n-1}-0.4p_{0} +n[/tex]

(b)       [tex]n = {\frac{p_{n-1} -p_{n} }{0.4p_{0}} }[/tex]

Given,

         Initial salmon population [tex]p_{0}=5000[/tex]

         Extraction rate = 40% per year

(a) Formula for recursion,

         For the first year,

                [tex]p_{1} =p_{0} -0.4p_{0}+n[/tex]

         For the second year,

                [tex]p_{2} =p_{1} -0.4p_{0} +n[/tex]

         For the n'th year,

               [tex]p_{n} =p_{n-1}-0.4p_{0} +n[/tex]

(b) The value of n,

        From the above equation,

                [tex]p_{n} =p_{n-1}-0.4p_{0} +n[/tex]

                  [tex]n = {\frac{p_{n-1} -p_{n} }{0.4p_{0}} }[/tex]

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Each year, 40% of the salmon population is extracted from a farming pond.

a. The recursion to describe Pn is Pn = 0.6 Pn-1 + N.

b. The value of N is 3000.

According to the recursion equation, the quantity of fish at the start of the nth year. Pn, is equal to 0.6 times the quantity at the start of the year before, Pn-1, plus the constant quantity of wild salmon that is restocked every year, N.

b. We can set the recursion equation equal to the initial population of 5000 fish in order to get the value of N that ensures the quantity of fish stays constant at the start of each year. Now we have the equation.

0.6Pn-1 + N = 5000. Solving for N gives us N = 3000.

Therefore, a. Pn = 0.6 Pn-1 + N. b.  3000.

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a. The blue line represents g(x) = 250,000csc(π30x).

b. g(5) = 25,000 km. This is the distance of the comet from Earth after 5 days.

c. The minimum distance between the comet and Earth is 250,000 km, which occurs when x = 0. This corresponds to the constant csc(π30x).

d. The equation has a vertical asymptote at x = 30/π.

a. Graph g(x):

To graph g(x), we can plot several points on the interval [0,35] and then connect them to form a graph of the function. For example, we can plot the points (0,250,000), (5,50,000), (10,25,000), (15,16,667), (20,12,500), (25,10,000), (30,8,333) and (35,7,143). Connecting these points will give us a graph of the function g(x).

b. Evaluate g(5):

The value of g(5) can be found by plugging in x = 5 into the equation: g(5) = 250,000 csc(π30*5) = 50,000 km. This means that after 5 days, the comet will be 50,000 km away from Earth.

c. Minimum distance between the comet and Earth:

The minimum distance between the comet and Earth can be found by taking the derivative of the equation and setting it to 0.

d. Vertical Asymptotes:

The vertical asymptotes of g(x) occur at x = 0 and x = 30. This means that the comet approaches an infinitely large distance from Earth at x = 0 and x = 30.

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The length of segment AY is 16.7 ft if the length of segment BC is 16.7 ft

From the question, we have the following parameters that can be used in our computation:

BC = 16.7 ft

The measures of the angles are not given

However, the marks on the side lengths imply that:

Using the above as a guide, we have the following:

AY = BC

This is because these segments are parallel segments

Recall that parallel segments are equal segments

Substitute the known values in the above equation, so, we have the following representation

AY = 16.7

Hence, the length of AY is 16.7 ft

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Division problem with quotient of 3 and a remainder of 28 are-

The given data is-

To estimate:

division problem?

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The dimensions that could be the measurements of a similar triangle are; base = 7.8 cm and height = 18 cm

Two triangles are said to be similar provided that they have the same ratio of corresponding sides and an equal pair of corresponding angles.

Now, we are given the side lengths of the triangle as a base length of 3.9 cm and a height of 9 cm.

Thus, this means that a similar triangle will have same ratio of side lengths. Thus;

If new height is h and new base is b, then we have;

9/h = 3.9/b

Thus,

h/b = 9/3.9

If we multiply the right side top and bottom by 2, then we have;

h/b = 18/7.8

18 and 7.8 cm could be similar dimensions.

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Step-by-step explanation:

3x - 3y=3 which means 3x=3+4y

3x/3=3/3+4y/3 devide both sides by 3 to find c

x=1+4/3y we solve x instead of y

3(1+4/3y)-4y=3 replace x instead of y

Any value of y makes the equation True.

The complete answer for the verbal expression into an algebraic inequality is  [tex]\frac{n}{-3} +5 \geq 12[/tex] .

What are inequality?

In arithmetic, the relationship between 2 values that are not equal is outlined by inequalities. difference means that not equal. Generally, if 2 values don't seem to be equal, we tend to use “not equal (≠)”.

Main body:

First, let's call "a number": n

"The quotient" means we are dividing.

Therefore, "the quotient of a number and -3" can be written as:

n÷ -3

now we need to add 5 to the expression ,

[tex]\frac{n}{-3} +5[/tex]

The quotient of a number and -3 plus 5 is at least 12.

so the expression found out till is equal to at least 12 which means sign used is " ≥"

Hence , the complete answer is  [tex]\frac{n}{-3} +5 \geq 12[/tex] .

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Evaluating the expression a² + b ÷ 3 for each set of given values we have

The expressions are evaluated using substitution as done below

for a = 4, b=3

substituting the the values of a and b

= a² + b ÷ 3  

= 4² + 3 ÷ 3

= 16 + 1

= 17

For a=2, b=21

substituting the the values of a and b

= a² + b ÷ 3

= 2² + 21 ÷ 3

= 4 + 7

= 11

For a = 3, b = 6

substituting the the values of a and b

=  a² + b ÷ 3

=  3² + 6 ÷ 3

= 9 + 2

= 11

substituting the values yielded the results as 17, 11 and 11

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The graph representation of the given distribution is attached below.

The term graph in math refers the visual representation of the collection of data that has the x and y coordinate values.

Here we have given that Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams and we need to find the graphical representation of the distribution.

Here by using the values in the foregoing ANOVA table are quickly produced by the calculator, including the test statistic and the p-value of the test calculator shows :

=> F=0.66853555

=> p = 0.530548

And the FACTOR df =2 and SS=23.212

=> MS = 11.606

Here  the ERROR df = 12

=> SS=208.324

=>  MS = 17.36

Here by using the f distribution for the test of three different means.

Then the value of the test statistic (F-value) is 0.668 and the p -value for the test is 0.5301

When we plot the graph for the distribution then we get he graph like the following.

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Complete Question :

An application is using a two-dimensional list defined as follows: 1. Write a statement that creates an empty two-dimensional list named values with 4 rows and 3 columns. 2. Write nested loops that get an integer value from the user for each element in the list, for example: values= [[1, 2, 3], [10, 20, 30], [100, 200, 300],[1000, 2000, 3000]] 3. Write a function named row_values that accepts values as argument and returns the sums of each row and displays the result as a list named row 4. Write a function named column_values that accepts values as arguments and returns the sums of each column and displays the result as a list named column 5. Write a function called sum_values that sums all the elements of the array and displays the result.

Sum of rows : [ 6, 60, 600, 6000 ]

Sum of columns : [ 1111, 2222, 3333]

Sum of all elements : 6666

The nested loops are :

Enter a number at row 0, and column 0 : 1

Enter a number at row 0, and column 1 : 2

Enter a number at row 0, and column 2 : 3

Enter a number at row 1, and column 0 : 10

Enter a number at row 1, and column 1 : 20

Enter a number at row 1, and column 2 : 30

Enter a number at row 2, and column 0 : 100

Enter a number at row 2, and column 1 : 200

Enter a number at row 2, and column 2: 300

Enter a number at row 3, and column 0 : 1000

Enter a number at row 3, and column 1 : 2000

Enter a number at row 3, and column 2 : 3000

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The graph (created with MS Excel) of the height the box is lifted to the number of times Brennan turns the crank to lift the box which is the graph of the proportional relationship, y = x, is attached.

A proportional relationship is one in which one variable (the output variable) is a constant multiple of the another variable known as an input variable.

The number of times Brennan turns the crank = x

The height to which the box is lifted = y

The points on the graph are; (15, 15), and (45, 45)

The ratio of the y-values to the x-values is 15/15 = 45/45 = 1, which indicates that the relationship is a proportional relationship

A point on the graph of a proportional relationship is the point (0, 0), therefore, the points on the graph are; (0, 0), (15, 15), and (45, 45)

Please find attached the graph of the proportional relationship between the number of times Brennan turns the crank to the height to which the box is lifted created with MS Excel

The relationship between the variables x and y is; y = x

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Answer:

-2

Step-by-step explanation:

By using division, it can be concluded that

Number of math problem she can be able to complete within given time is  [tex]24 \div \frac{2}{3}[/tex]

This is the required expression

What is division?

Division is the process by which value of single unit can be calculated from the value of multiple unit.

The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.

There is a well known formula for division

Divisor x Quotient + Remainder = Dividend.

This is a word problem on division

Zareen has 24 minutes to work on her math homework

Fraction of time taken to do each sum =[tex]\frac{2}{3}[/tex]

Number of math problem she can be able to complete within given time is

[tex]24 \div \frac{2}{3}[/tex]

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A 95% % lower confidence bound for the true average proportional limit stress of all such joints is 8.01.

In the given question, a sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.52 mpa and a sample standard deviation of 0.78 mpa.

We have to calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints.

Sample size: n = 13

Sample mean: x’ = 8.52 mps

Sample standard deviation: s = 0.78 mps

95% lower confidence bound for the true average proportional limit stress of all such joints

Level of Significance (α) = 1-95% = 5% = 0.05

α/2 = 0.025

So the value of t(α/2) = 1.8

The confidence interval = x’± t(α/2)*s/√n

Now putting the value:

The confidence interval = 8.41± (1.8)*(0.78)/√12

The confidence interval = 8.41± (1.8)*(0.226)

The confidence interval = 8.41± 0.4068

The confidence interval = (8.41- 0.4068, 8.41+ 0.4068)

The confidence interval = (8.01, 8.82)

A 95% % lower confidence bound for the true average proportional limit stress of all such joints is 8.01.

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The right question is:

A sample of 12 joint specimens of a particular type gave a sample mean proportional limit stress of 8.41 mpa and a sample standard deviation of 0.78 mpa.

Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (Round your answer to two decimal places.)

To answer this question we need to make use of Linear Programming

The solution is:

x = 170 units

y = 345 units

z(max) = 2235 rupees

To solve a linear programming problem, we need to formulate the model  

The Objective Function

Let´s call x the number of product 1 manufactured

and y the number of product 2 manufactured

Then the Objective Function is:

z = 3× x + 5×y    to be maximize

The set of constraints are:

                             D1           D2

                           ( min. )     ( min. )

Product  1 (x)          1               3

Product 2 (y)          2              2            

Availability            860        1200

First constraint:

Time available in D1:  860 minutes

1×x  +  2×y  ≤ 860

Second constraint:

Time available in D2: 1200 minutes

3×x  +  2×y  ≤ 1200

General constraint:   x ≥ 0  ;  y ≥ 0   integers ( we will assume only complete products at the end of the period no fractions )

Then the model is:

z = 3× x + 5×y    to be maximize

Subject to:  

1×x  +  2×y  ≤ 860

3×x  +  2×y  ≤ 1200

x ≥0   y ≥ 0   integers

With the help of Avtomat we get the solution:

x = 170 units

y = 345 units

z(max) = 2235 rupees

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Answer:

Choice D : x > - 1

Step-by-step explanation:

Left hand side (LHS) of the inequality can be siimplified

[tex]2\left(x-3\right)-5x = 2x - 6 - 5x = -3x -6\\\\[/tex]

Inequality becomes

[tex]-3x-6 < x-2[/tex]

Move x to the left side and -6 to the right side:

[tex]-3x - x < -2 + 6\\\\-4x < 4\\\\[/tex]

Multiply both sides by -1(the inequality sign changes to >)

[tex]4x > -4\\\\[/tex]

Divide both sides by 4:
[tex]x > -1[/tex]

The number line corresponding to this is the fourth choice

The measure of the angle S is 112° in the following parallelogram.

What is parallelogram?

A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of a polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. In a parallelogram, the opposing sides are of equal length, and the opposite angles are of equal size. A parallelogram has adjacent angles that add up to 180 degrees.

Given, ∠T= 11x + 2

∠V = 10x + 8

From the above definition, opposite angles are equal

So, ∠T = ∠V

or, 11x + 2 = 10x + 8

or, 11x - 10x = 8 - 2

or, x = 6

∠V= 10x + 8 = 10*6 + 8 = 68 degree

From the above definition, adjacent angles add up to 180 degrees

∠V + ∠S = 180°

or, 68° + ∠S =180°

or, ∠S = 180° - 68° = 112°

Hence, the measure of the angle S is 112°.

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The equation of line passes through the points (1, -4) and (4, 5) will be;

⇒ y = 3x - 7

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (1, -4) and (4, 5).

Now,

Since, The equation of line passes through the points (1, -4) and (4, 5)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (5 - (-4)) / (4 - 1)

m = 9 / 3

m = 3

Thus, The equation of line with slope 3 is,

⇒ y - (-4)= 3 (x - 1)

⇒ y + 4 = 3x - 3

⇒ y = 3x - 3 - 4

⇒ y = 3x - 7

Therefore, The equation of line passes through the points (1, -4) and (4, 5) is given as;

⇒ y = 3x - 7

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The gallons after 8 hours will be 3400 gallons.

Expression refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

Numbers, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations.

In this case, the reactor coolant tank is being filled with coolant at the rate of 400 gallons per hour with t>0 measure in hours.

Therefore, the gallons after 8 hours will be:

= 200 + 400(8)

= 200 + 3200

= 3400 gallons.

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Answer:

Equation 1 - x + 4y = 12

Equation 2 -  2x + 4x = 16

Cost of 1 Cheeseburger - $4

Cost of 1 Taco - $2

Step-by-step explanation:

Cheeseburger(x) and Taco(y)

x + 4y = 12 and 2x + 4y = 16

x = - 4y + 12

2(- 4y + 12) + 4y = 16

- 8y + 24 + 4y = 16

- 4y = - 8

y = 2

x + 4(2) = 12

x + 8 = 12

x = 4

The correct statement about histograms is given as follows:

d. All of these choices are true.

An histogram is a graph that shows the number of times each element of x was observed.

Each element is said in case that the histogram can represent element by element, but in the case of distribution with a wider range of possible output values, the histogram is divided into classes, and then the histogram shows the number of observations that were observed for each class, which cover the complete range of observations, meaning that the histogram is a summary of interval data.

The above paragraph, in case the histogram covers a wide range of data, means that all the statements in this problem are correct, and thus option d is correct.

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Value is a discontinuity is undefined when [tex]x=-5[/tex] or [tex]x=3[/tex] The answer is then the third choice. [tex]\frac{x^2+7 x+1}{x^2+2 x-15}=\frac{x^2+7 x+1}{(x+5)(x-3)}[/tex]

What is discontinuity?

A discontinuous function is a graph function that is not linked to any other functions. If the left-hand limit of f(x) and the right-hand limit of f(x) both exist but are not equal, then the function f(x) is said to have a discontinuity of the first sort at x = a.

A zone within the earth where a sudden change in physical properties, such as the velocity of earthquake waves, occurs. Such a zone marks the boundary between the different layers of the earth, as between the core and mantleSee also Mohorovičić discontinuity.

In mathematics, functions, and applications, continuous functions are crucial. Not all functions, nevertheless, are continuous. A function is said to have a discontinuity at that point in its domain if it is not continuous elsewhere in its domain.

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he group g and the positive integer n = 3 satisfy the conditions given in the problem.

Let g be the 6th group isomorphic to the rotationally symmetric group of regular hexagons. Let n = 3.

Since |g| = 6, it is clear that n |g|. Split. However, the action of g on any set cannot have orbitals of magnitude 3. To see this, note that the order of each element of g is either 1, 2, or 3. If an element of g has degree 1, then its orbit under the action of g is the element itself with magnitude 1.

If the elements of g have degree 2, then the orbitals under the action of g have magnitude 2. If the elements of g have degree 3, then the orbitals under the action of g have magnitude 3. However, g only has order elements. Since it is of order 3 (that is, a rotation of 120 degrees), the effect of g cannot have an orbit of magnitude 3.

Hence, the group g and the positive integer n = 3 satisfy the conditions given in the problem.

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The horizontal and vertical asymptotes for the function f(x) =6/(-2x +1) is equal to y = 0 and x = 1/2 respectively.

Graph is attached.

As given in the question,

Given function is :

f(x) =6 /(- 2x +1)

f(x) = y

Degree of the numerator is zero

Degree of the denominator is 1.

Degree of denominator is greater than the degree of numerator.

Function represent the horizontal asymptotes for y =0

To get the vertical asymptotes equate denominator equals to zero

(- 2x +1) = 0

⇒2x = 1

⇒x = 1/2

Vertical asymptotes is given by x =1/2.

Graph is attached.

Therefore , the horizontal and vertical asymptotes for the given function is equal to y=0 and x =1/2 respectively.

The above question is incomplete, the complete question is:

Graph the rational function. f(x) =6 /(- 2x +1) Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-function button X.

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We got sales revenue= $31500, cost of goods sold =$8300 and gross profit =$23200

The income that someone earn from his product and services before the deduction of any charges or expenses.

All direct and indirect cost needed to make a product such as raw materials, transportation cost and labor cost is called cost of goods sold.

The profit earns by a business organization after deducting all the costs associated with manufacturing and selling products.

we calculated gross profit by using the formula, Gross profit= sales revenue- cost of goods sold.

We calculate cost of goods sold by using the formula

beginning inventory + purchases during the period - ending inventory

= 550×24+950×28-900×35

costs of goods sold =$8300

given, number of units sold = 900

average sales price per unit= $35

Now sales revenue= 900 × $35

                                =$31500

Now gross profit= $31500-$8300

                                 $23200

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a) The maximum height of the rock is of: 5.50 metres.

b) The time that the rock was in the air is of: 2.12 seconds.

c) The distance which the rock landed is of: 12.72 meters.

The height of the projectile is modeled using a quadratic function, as follows:

y = -4.905t² + v(0)sin(60)ºt + h(0).

The parameters are given as follows:

Considering the values of these parameters, the function is given as follows:

y = -4.905t² + 10.39t.

The coefficients are given as follows:

a = -4.905, b = 10.39, c = 0.

The maximum height is obtained as the y-coordinate of the vertex, as follows:

Hmax = -(10.39² - 4(4.905)(0))/(4(-4.905)) = 5.50.

The rock hits the ground when:

y = 0.

Hence:

-4.905t² + 10.39t = 0

t(-4.905t + 10.39) = 0.

4.905t = 10.39

t = 10.39/4.905

t = 2.12 seconds.

The horizontal distance is given as follows:

x = v(0)cos(60º)t

Hence:

x = 12 x 0.5 x 2.12 = 12.72 meters.

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The expression [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex] as a single fraction is [tex]\frac{9a-11}{20}[/tex]

What is algebraic expression ?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

According to question

⇒     [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex]

⇒   taking LCM of 4, 5 = 20

now [tex]\[\frac{4(4+6a)-5(1+3a)}{20}[/tex]

⇒ (16 +24a - 5 - 15a)/20

⇒ ((24a - 15a) - (16-5))/20

⇒ (9a - 11)/20

hence, the expression  [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex] as a single fraction is [tex]\frac{9a-11}{20}[/tex]

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Step-by-step explanation:

Hope u get it x=3×3

x=9

It didn't include in the photo

[tex]340.11[/tex] or [tex]\frac{32651}{96}[/tex].

[tex]\frac{(\frac{309*317}{9-4+7})}{8x3}[/tex]

[tex]\frac{(\frac{309*317}{9-4+7})}{24}[/tex]

[tex]\frac{(\frac{309*317}{12})}{24}[/tex]

[tex]\frac{(\frac{97953}{12})}{24}[/tex]

[tex]\frac{(8162.75)}{24}[/tex]

[tex]340.11[/tex] or [tex]\frac{32651}{96}[/tex].