Karen has two dogs. The larger dog weighs 1. 4 pounds more than the smaller dog. The combined weight of the two dogs is 12. 6 pounds

The pass rate in the afternoon subgroup is greater than 1, we cannot draw a reliable conclusion without further investigation or clarification of the data.

To compare the probability that a student will pass the challenge in the morning with the probability that a student will pass the challenge in the afternoon, we need to calculate the proportion of students who passed in each subgroup.

The proportion of students who passed the challenge in the morning subgroup is:

Pass rate in the morning subgroup = Number of students who passed in the morning subgroup / Total number of students in the morning subgroup

Pass rate in the morning subgroup = 40 / 60

Pass rate in the morning subgroup = 0.67

The proportion of students who passed the challenge in the afternoon subgroup is:

Pass rate in the afternoon subgroup = Number of students who passed in the afternoon subgroup / Total number of students in the afternoon subgroup

Pass rate in the afternoon subgroup = 50 / 40

Pass rate in the afternoon subgroup = 1.25

that the pass rate in the afternoon subgroup is greater than 1, which is not possible as probabilities must be between 0 and 1. This implies that there might be a data error.

Assuming the data is correct, we can conclude that the probability of passing the challenge in the afternoon subgroup is higher than the probability of passing the challenge in the morning subgroup. However, since the pass rate in the afternoon subgroup is greater than 1, we cannot draw a reliable conclusion without further investigation or clarification of the data.

for such more question on probability

https://brainly.com/question/24756209

#SPJ4

Answer:

To evaluate this expression, we need to follow the order of operations, which is commonly remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction):

1. Start with any operations inside parentheses. There are no parentheses in this expression.

2. Evaluate any exponents. There are no exponents in this expression.

3. Evaluate multiplication and division, from left to right. In this expression, we have:

7 + (35/3) + 5 - (7 + (35/3) / (3 - 5))

= 7 + (35/3) + 5 - (7 + (11.67) / (-2))

= 7 + (35/3) + 5 - (7 - 5.835)

= 7 + (35/3) + 5 + 5.835 - 7

= 15.835 + (35/3) - 7

4. Finally, evaluate addition and subtraction, from left to right:

15.835 + (35/3) - 7

= 15.835 + 11.67

= 27.505

Therefore, the value of the expression is 27.505.

Step-by-step explanation:

Here is an example table for tracking the flowers stocked in the flower shop, based on the information provided in Question 4, Part I:

A flower is the reproductive structure found in flowering plants.

Flower Type Color Initial Quantity

Roses          Red 50

Roses          Pink 30

Tulips         Yellow 25

Tulips          Red 20

Lilies         White 40

Lilies          Pink 15

In this table, each row represents a specific flower type and color, and the initial quantity of that flower type and color that the shop stocks. This table can be used to track inventory levels and monitor when certain types and colors of flowers need to be restocked.

Additional columns can be added as needed to track other information, such as supplier information, purchase dates, or prices.

To know more about Flowers:

https://brainly.com/question/12236356

#SPJ4

The volume of the top half of the cone (in terms of π) is 4π whose height is 6 inches and radius is 4 inches.

The volume of the top half of the cone (in terms of π) is 4π whose height is 6 inches and radius is 4 inches.

It is a physical quantity that is typically expressed in cubic units, such as cubic centimeters (cm³) or cubic meters (m³).

When the cone is sliced in half by a horizontal plane, the resulting cross-section is a circle with radius 2 inches. This circle has half the diameter of the original base of the cone, which means that it has half the area. We can use this fact to find the volume of the top half of the cone.

The original cone has height 6 inches and radius 4 inches, so its volume is given by:

V = (1/3)π(4²)(6) = (1/3)π(96) = 32π

When the cone is sliced in half, the top half has volume equal to half the volume of the original cone that lies above the horizontal plane. The height of this top half can be found using similar triangles: the radius of the top half is half the radius of the original cone, so the height of the top half is half the height of the original cone. Therefore, the height of the top half is 3 inches.

The radius of the top half is given as 2 inches, which means that its volume is:

V = (1/3)π(2²)(3) = (1/3)π(12) = 4π

Therefore, the volume of the top half of the cone (in terms of π) is 4π.

To know more about volume visit:

brainly.com/question/23477586

#SPJ1

Commission is usually calculated as a percentage of the selling price of a product or service. Therefore, the correct answer is option B, where the commission is calculated as (percent commission) x (selling price). For example, if the commission rate is 5% and the selling price is $100, the commission earned would be $5, calculated as follows:

Commission = (5%)( $100) = $5

This means that the salesperson or agent would earn $5 in commission for selling the product or service at a price of $100. The commission rate can vary depending on the type of product or service and the agreement between the parties involved.

To learn more about selling price refer to:

brainly.com/question/4125821

#SPJ4

A sequence An is defined recursively by the equation aₙ = 0.5( aₙ₋₁ + aₙ₋₂ ) for n ≥ 3

First five terms of this sequence are 14, 14, 14, 14, 14 respectively.

A sequence is an ordered list of numbers. Like 1,2,3,.... The three dots implies to continue forward by following the pattern. Each number in the sequence is called a term. We have a sequence 'aₙ' and it is defined as aₙ = 0.5( aₙ₋₁ + aₙ₋₂ ) for n≥ 3 and

First term of sequence, a₁ = 14

second term of sequence, a₂ = 14

We have to determine value of first five terms of sequence.

Third term of sequence, n = 3

a₃ = 0.5( a₂ + a₁ )

=> a₃ = 0.5( 14 + 14)

=> a₃ = 0.5 × 28 = 14

Forth term of sequence, n = 4

a₄ = 0.5( a₃ + a₂ )

=> a₄ = 0.5( 14 + 14 ) = 14

Fifth term of sequence, n= 5

a₅ = 0.5( a₄ + a₃ )

=> a₅ = 0.5( 14+ 14) = 14

Hence, required terms are obtained and sequence is 14,14,14,14,..... ( constant sequence).

For more information about sequence, visit :

https://brainly.com/question/28036578

#SPJ4

Complete question:

A sequence, An is defined recursively by an = 0.5(an-1 + an-2) for n ≥ 3, where a1 = 14 and a2 = 14. Find the first five terms of the sequence.

Alexander would have to pay $15 to buy 2 pounds of walnuts with the coupon. The expression is cost = ($8/pound) x pp - $1.

The functional connection between cost and output is referred to as the cost function. It examines the cost behaviour at various output levels under the assumption of constant technology. An essential factor in determining how well a machine learning model performs for a certain dataset is the cost function. It determines and expresses as a single real number the difference between the projected value and expected value.

Given that, the price per pound of walnuts is $8.

2 pounds x $8/pound = $16

Alexander would get $1 off the final amount.

Thus,

$16 - $1 = $15

So Alexander would have to pay $15 to buy 2 pounds of walnuts with the coupon.

The expression for the cost can be written as:

cost = ($8/pound) x pp - $1

Hence, Alexander would have to pay $15 to buy 2 pounds of walnuts with the coupon. The expression is cost = ($8/pound) x pp - $1.

Learn more about algebraic expressions here:

https://brainly.com/question/24875240

#SPJ1

Step-by-step explanation:

2.1 Factoring 3x2-2x-23

The first term is, 3x2 its coefficient is 3 .

The middle term is, -2x its coefficient is -2 .

The last term, "the constant", is -23

Step-1 : Multiply the coefficient of the first term by the constant 3 • -23 = -69

Step-2 : Find two factors of -69 whose sum equals the coefficient of the middle term, which is -2 .

-69 + 1 = -68

-23 + 3 = -20

-3 + 23 = 20

-1 + 69 = 68

Answer:

8.41

Step-by-step explanation:

8.14+3.45=11,59

20-11,59=8.41

Answer:

Step-by-step explanation:

You ask yourself, "600 is 30% of how many students?". In equation form this looks like:

600 = .30x

Divide both sides by .30 and you'll get that the number of students is 2000

Therefore, the fair price of one raffle ticket is $2.60, which is slightly less than the amount Raul paid ($3).

a) The fair price of one raffle ticket is $3. This is because 500 tickets were sold at this price and one prize of $200 is to be awarded. Therefore, the 500 tickets collected add up to $1,500, while the prize to be awarded is $200. The net amount to be divided among all the ticket holders is $1,300.

b) The fair price of one raffle ticket is $2.60. This is calculated by dividing the total prize money of $200 by the total number of tickets sold (500). Therefore, 500 tickets multiplied by $2.60 gives a total prize money of $1,300 which is equal to the total ticket sales of $1,500 less the prize money of $200.

For more such ticket related questions

https://brainly.com/question/107024

#SPJ11

value of variable x is 65 degree.

A straight line is a geometric object that extends infinitely in both directions and has a constant slope or gradient. It is the shortest distance between two points, and it can be described by an equation in the form of y = mx + c, where m is the slope or gradient of the line and c is the y-intercept.

The term "supplementary angles" refers to two angles whose sum is equal to 180 degrees. In other words, if angle A and angle B are supplementary angles, then:

∠A +∠B = 180 degrees

To find value of x

A straight line's angle total is 180°.

2x+50°=180°

2x=130°

x=65

Hence, value of variable x is 65 degree.

To know more about variable, visit:

https://brainly.com/question/17344045

#SPJ1

Answer:

4

Step-by-step explanation:

(is the equation below x - 7 or x +7, I am working with x + 7)

9+ (2x - 6) is equivalent to x + 7

9 + (2x - 6) = x + 7

Open the bracket

9 + 2x - 6 = x + 7

2x + 3 = x +7

Subract 3 from both sides

2x = x + 4

Subtact x from both sides

X = 4

Confirm if the equation in the question is x +7 or x - 7

Answer:

Step-by-step explanation:

45342

If the volume of a right cone is 3,525, then the height of the cone is approximately 5 units.

We can use the formula for the volume of a cone to solve for the height of the cone:

V = (1/3)πr²2h

where V is the volume of the cone, r is the radius (half of the diameter), and h is the height of the cone.

Given that the diameter of the cone is 30 units, the radius is 15 units. Substituting this and the volume V = 3525, we get:

3525 = (1/3)π(15)²2h

3525 = 225πh/3

h = 3(3525)/(225π)

h ≈ 5

Therefore, the height of the cone is approximately 5 units.

Learn more about cone here:

https://brainly.com/question/29767724

#SPJ4

3.31 is an estimate for the radius of the circle.

The circle fοrm is a clοsed twο-dimensiοnal shape because every pοint in the plane that makes up a circle is evenly separated frοm the "centre" οf the fοrm.

Each line tracing the circle cοntributes tο the fοrmatiοn οf the line οf reflectiοn symmetry. In additiοn, it rοtates arοund the center in a symmetrical manner frοm every perspective.

he radius of the circle, we need to use the formula for the area of a sector, which is:

Area of sector = (θ/360) x π x r

the radius of the circle "x" for now, and set up an equation using the given information

51.3 = (120/360) x π x

Simplifying this equation, we get:

= (51.3 x 360)/(120 x π)

x² ≈ 10.95

x ≈ √10.95

x ≈ 3.31

Learn more about circle

brainly.com/question/29142813

#SPJ1

Answer:

The remainder when 5x3 + 2x2 - 7 is divided by x + 9 is -692.

Explanation:

We can use long division to divide 5x^3 + 2x^2 - 7 by x + 9:

-5x^2 + 43x - 385

x + 9 | 5x^3 + 2x^2 + 0x - 7

5x^3 + 45x^2

--------------

-43x^2 + 0x

-43x^2 - 387x

--------------

387x - 7

Therefore, the remainder when 5x^3 + 2x^2 - 7 is divided by x + 9 is 387x - 7.

Hope this helps, sorry if this is wrong! :]

The formula would be: =BINOM.DIST(3,9,0.25,TRUE) + BINOM.DIST(2,9,0.25,TRUE) + BINOM.DIST(1,9,0.25,TRUE) + BINOM.DIST(0,9,0.25,TRUE). Probability of this outcome is 0.372.

The probability of drawing at most three spade cards when drawing nine cards with replacement from a standard 52-card deck is 0.628. This probability was calculated using the binomial distribution formula in Microsoft Excel. The formula takes into account the number of trials (nine), the probability of success (drawing a spade card), and the number of successes desired (at most three). The result shows that there is a relatively high likelihood of drawing at least four spade cards, as the probability of this outcome is 0.372.

Learn more about probability here: brainly.com/question/30034780

#SPJ4

a)  approx 0.562$$

When playing backgammon, the doubling cube is an important feature that allows players to increase the stakes of the game. Imagine playing with a "tripling cube" instead, with faces of 3, 9, 27, 81, 243, and 729. Using the analysis given for the doubling cube, we can compute the probability of winning above which a triple should be accepted.To determine the probability of winning above which a triple should be accepted, we need to use the formula derived from the analysis of the doubling cube:$$P_w = \frac{q^2}{1-2q^2}$$where Pw is the probability of winning, and q is the probability of losing. We can substitute 1-q for p, the probability of winning, to get:$$P_w = \frac{(1-p)^2}{1-2(1-p)^2}$$Now, we need to modify this formula to account for the tripling cube. If we triple the current stakes, then we have effectively tripled the value of the doubling cube. In other words, if the current stakes are 1, then the value of the tripling cube is 3. If the current stakes are 2, then the value of the tripling cube is 9. More generally, if the current stakes are n, then the value of the tripling cube is 3^n. Using this information, we can modify the formula as follows:$$P_w = \frac{q^{3^n}}{1-2q^{3^n}}$$. This is the formula we need to use to compute the probability of winning above which a triple should be accepted. We can solve for q using the quadratic formula:$$q = \frac{1\pm\sqrt{1-4(1-2P_w)(-P_w^{3^n})}}{2}$$The value of q we want is the smaller one, because we want to compute the probability of losing. Once we have q, we can substitute it into the formula for Pw to get the probability of winning above which a triple should be accepted. Example Suppose we have a backgammon game with a current stake of 4, and we are considering accepting a triple from our opponent. Using the formula above, we can compute the probability of winning above which a triple should be accepted as follows:$$n = \log_3{3^2} = 2$$$$P_w = \frac{q^{3^2}}{1-2q^{3^2}}$$$$q = \frac{1-\sqrt{1-4(1-2P_w)(-P_w^{3^2})}}{2}$$$$q = \frac{1-\sqrt{1-8P_w^9}}{2}$$$$q = \frac{1-\sqrt{1-8(0.5)^9}}{2}$$$$q \approx 0.515$$$$P_w = \frac{q^{3^2}}{1-2q^{3^2}}$$$$P_w = \frac{(0.515)^9}{1-2(0.515)^9}$$$$P_w \approx 0.562$$. Therefore, if we have a probability of winning greater than 0.562, then we should accept the triple.

  Learn more about probability

  brainly.com/question/30034780

  #SPJ4

a) The probability of that happening is P(W1 = 1, W2 = 2) = P(W1 = 2, W2 = 1) = p1p2.

b) P(W1 = 1)P(W2 > 1) + P(W1 = 1)P(W2 > 2) + P(W1 = 2)P(W2 > 3) + ...= p1(1 - p2) + p1(1 - p2)p2 + p1p2(1 - p2) + ...= p1(1 - p2)(1 +p2 + p22 + ...) = p1(1 - p2)/(1 - p2)2= p1/(1 - p2)2

c) The probability that their minimum value is k is P(min(W1, W2) = k) = P(W1 = k, W2 > k) + P(W1 > k, W2 = k) = p1(1 - p2)k-1p2 + p2(1 - p1)k-1p1

d) The probability that their maximum value is k is P(max(W1, W2) = k) = P(W1 = k, W2 = k) + P(W1 = k, W2 > k) + P(W1 > k, W2 = k) = p1p2k-1 + p1(1 - p2)k-1 + p2(1 - p1)k-1

a) P(W1 = W2)The probability that W1 = W2 is 0. If W1 and W2 have different values, then W1 is equal to either 1 or 2. The probability of that happening is P(W1 = 1, W2 = 2) = P(W1 = 2, W2 = 1) = p1p2. The probability of that happening is P(W1 = 1, W2 = 2) = P(W1 = 2, W2 = 1) = p1p2.b) P(W1 < W2)The probability of W1 being less than W2 is P(W1 = 1, W2 = 2) + P(W1 = 1, W2 = 3) + P(W1 = 2, W2 = 3) + ... This may be written as P(W1 = 1)P(W2 > 1) + P(W1 = 1)P(W2 > 2) + P(W1 = 2)P(W2 > 3) +...= p1(1 - p2) + p1(1 - p2)p2 + p1p2(1 - p2) + ...= p1(1 - p2)(1 + p2 + p22 + ...) = p1(1 - p2)/(1 - p2)2= p1/(1 - p2)2

d) Distribution of min(W1, W2)If W1 and W2 are independent geometric random variables with parameters p1 and p2, respectively, then the probability that their minimum value is k is P(min(W1, W2) = k) = P(W1 = k, W2 > k) + P(W1 > k, W2 = k) = p1(1 - p2)k-1p2 + p2(1 - p1)k-1p1e) Distribution of max(W1, W2)If W1 and W2 are independent geometric random variables with parameters p1 and p2, respectively, then the probability that their maximum value is k is P(max(W1, W2) = k) = P(W1 = k, W2 = k) + P(W1 = k, W2 > k) + P(W1 > k, W2 = k) = p1p2k-1 + p1(1 - p2)k-1 + p2(1 - p1)k-1

Learn more about Independent Geometric Variables

brainly.com/question/30480240

#SPJ11

Answer:

a) x = 20

b) x = 9

Step-by-step explanation:

  a)     [tex]\boxed{\bf Mean =\dfrac{sum \ of \ all \ the \ data}{Number \ of \ data}}[/tex]

          [tex]\dfrac{16 +x + 3 + 14 +57}{5}=22\\[/tex]

                                 x + 90 = 22*5

                                 x + 90 = 110

                                         x = 110 - 90

                                        x = 20

b)

         [tex]\bf \dfrac{4 + x + 5 +6 + 1}{5} = 5[/tex]

                          x + 16   = 5 * 5

                            x + 16 = 25

                                   x = 25 - 16

                                   x = 9

Answer:

Step-by-step explanation:

[tex]D=\frac{\theta}{360} \times2\times\pi \times r[/tex]

[tex]D=\frac{60}{360} \times2\times\pi \times 42[/tex]

    [tex]=\frac{1}{6} \times84\times\pi[/tex]

    [tex]=12\pi cm^2[/tex]

Answer:

A)  [tex]15x^2+22x+8[/tex]

B)  Degree 2, Quartic Expression

C)  The dimensions of the rectangle are polynomials. When multiplied together, the area of the rectangle is also a polynomial.

Step-by-step explanation:

A)  The formula for area of a rectangle is Area = L * W. The length and width are represented by (3x+2) and (5x+4). So we can say that

[tex]Area = (5x+4)(3x+2)[/tex]

Use FOIL to multiply the the polynomials. First, Outside, Inside, Last

[tex]Area = (5x)(3x) + (5x)(2) + (3x)(4) + (2)(4)\\Area = 15x^2 + 10x + 12x + 8\\Area = 15x^2 + 22x + 8[/tex]

The expression that represents the area of the rectangle is

[tex]15x^2 + 22x + 8[/tex].

B)  The degree of the expression is 2, because two is the highest power of x. The classification of the expression is quadratic because the graph of the expression is a parabola.

Degrees vs. Classification

Degree 0:  Zero Polynomial or Constant

Degree 1:  Linear (line)

Degree 2:  Quadratic (parabola)

Degree 3: Cubic

Degree 4: Quartic

...

C)  Closure property for polynomials applies to addition, subtraction, and multiplication. It means that the result of multiplying two polynomials will also be a polynomial. Part A demonstrates polynomial closure under multiplication because the dimensions of the rectangle are polynomials and so is the area.

Answer:

[tex]14in^2[/tex]

Step-by-step explanation:

Volume of a rectangluar prism = Length x Width x Height

Volume, Length, and Width is given now we can solve for Height, y

[tex]V = l * w * h[/tex]

[tex]3in^3 = 1in * 1in* h[/tex]

[tex]h = 3in[/tex]

Surface area of a rectangular prisim is A = 2(wl +hl +hw)

A = [tex]2(1in * 1in + 3in * 1in + 3in * 1in)\\2(1 in^2+ 3 in^2+ 3in^2)\\2(7in^2)\\14in^2[/tex]

Hope this helps!

Brainliest is much appreciated!

Therefore , the solution of the given problem of equation comes out to be  y = 0.5x²- 3

The foundation of a model of linear regression is the equation y=mx+b. The inclination is B, and the y-intercept is m. Although it is true that y and y are separate parts, the the above sentence is frequently referred to as a "mathematics problem with two variables". Y=mx+b is the formula for a singular system of equations, where m denotes the gradient and b the y-intercept. The equation is Y=mx+b, where m denotes slopes and b denotes the y-intercept.

Here,

=> x  y

  -4  5

   -2  -1

   0  -3

    2  -1

To find : the equation which passes through the point

=> y = 0.5x²- 3

We can see,

=> y = 0.5(-4)² - 3

=> y = 8 -3

=> y =5

To know more about linear equation visit:

https://brainly.com/question/11897796

#SPJ1

Part A:

The equation Y = 10X + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Therefore, in this equation, the slope is 10 and the y-intercept is 5.

The slope represents the rate of change in the monthly rate of the gym membership. For every one unit increase in the number of months, the monthly rate will increase by $10. The y-intercept represents the initial cost of joining the gym, which is $5.

Part B:

To find out how much money Justin saves the first month by joining the gym at the discounted price, we need to calculate the difference between the regular price and the discounted price for the first month.

The regular price for the first month can be found by plugging in X = 1 into the equation Y = 15X + 20, which gives Y = 35.

The discounted price for the first month can be found by plugging in X = 1 into the equation Y = 10X + 5, which gives Y = 15.

Therefore, Justin saves $20 (35 - 15) the first month by joining the gym at the discounted price rather than the regular price.

Part C:

The system of equations is:

Y = 10X + 5 (discounted price)

Y = 15X + 20 (regular price)

The solution to the system of equations is (-3, -25), which means that if X = -3, then Y = -25 is a solution to both equations. However, this solution is not possible in this situation because X represents the number of months, which cannot be negative. Therefore, the point (-3, -25) is not a valid solution.

Robert is currently 10 years old.Given that five years ago Sharon was twice as old as Robert was then, we can set up the following equation: y + 5 = 2(y)

We are given the information that Sharon is five years older than Robert, and five years ago Sharon was twice as old as Robert was then. This means we can create a system of equations to solve for Robert's age.

Let x = Robert's current age

Let y = Robert's age five years ago

Given that Sharon is five years older than Robert, we can set up the following equation:

x + 5 = Sharon's current age

Given that five years ago Sharon was twice as old as Robert was then, we can set up the following equation:

y + 5 = 2(y)

Solving the first equation for x, we get x = Sharon's current age - 5. Substituting this into the second equation, we get:

y + 5 = 2(Sharon's current age - 5)

Solving this equation for y, we get y = (Sharon's current age - 5)/2.

Since Sharon is five years older than Robert, Sharon's current age is x + 5. Substituting this into our equation for y, we get:

y = (x + 5 - 5)/2

Simplifying this equation, we get y = x/2. This means that Robert's age five years ago was half of his current age.

Since we know that Robert is currently 10 years old, Robert's age five years ago was 5. Therefore, Robert is currently 10 years old.

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

Answer:

Let x be the number of hopts and y be the number of totts.

The first statement relates to the total amount of money expected to be made:

3x + 7y ≥ 84

This inequality states that the total revenue from selling hopts and totts should be at least $84.

The second statement relates to the total number of units expected to be sold:

x + y ≤ 24

This inequality states that the total number of hopts and totts sold should be at most 24 units. Therefore, the system of inequalities in standard form is:

3x + 7y ≥ 84

x + y ≤ 24

where x ≥ 0 and y ≥ 0 (since we cannot sell a negative number of hopts or totts).

Answer: Let "x" be the number of hopts that Farmer Naxvip plans to sell, and let "y" be the number of totts that she plans to sell. Then we can write the following system of inequalities to model the relationships between the amounts of hopts and totts:

3x + 7y >= 84

x + y <= 24

The first inequality represents the condition that Farmer Naxvip expects to make at least $84, while the second inequality represents the condition that she expects to sell at most 24 units.

Brainliest Appreciated! (:

(a) The solution of the equation is √6 + 2.

(b) a = 10 and b = 2, and the solution of the equation is √10 + 7.

((a) To solve this equation, we need to isolate the term with the variable x on one side and move all other terms to the other side.

Let's start by simplifying each term using the fact that;

√24 = √(4 × 6) = 2√6,

√96 = √(16 × 6) = 4√6,

√108 = √(36 × 3) = 6√3, and

√12 = √(4 × 3) = 2√3.

Then, we have:

x√24 + √96 = √108 + x√12

2x√6 + 4√6 = 6√3 + 2x√3

2(√6 + 2√3) = (x√3 + 2x√6)

2√6 + 4√3 = x(√3 + 2√6)

Now, we can equate the coefficients of √6 and √3 on both sides to get a system of equations:

2 = x

4 = 2x

Solving this system, we find that x = 2 and therefore a = 6 and b₁ = 2.

So, the solution of the equation is √6 + 2.

(b) To solve this equation, we also need to isolate the term with the variable x on one side and move all other terms to the other side.

Let's start by squaring both sides of the equation to eliminate the square roots:

(x√40)² = (x√5 + √10)²

40x² = 5x² + 10 + 2x√50 + 10

35x² - 20 = 2x√50

Now, we can square both sides again to eliminate the remaining square root:

(35x² - 20)² = (2x√50)²

1225x⁴ - 1400x² + 400 = 0

This is a quadratic equation in x². We can solve it using the quadratic formula:

x² = (1400 ± √(1400² - 4 × 1225 × 400)) / (2 × 1225)

x² = (1400 ± 200) / 245

x² = 2 or x² = 8/7

Since x² cannot be negative, we have x² = 2 and therefore x = √2.

Substituting this value of x back into the original equation, we have:

x√40 = x√5 + √10

√80 = √10 + √10

√80 = 2√10

So, a = 10 and b = 2, and the solution of the equation is √10 + 7.

Learn more about integers here: https://brainly.com/question/17695139

#SPJ1