Using the bag of marbles below, how could you find the probability of pulling a red marble two times in a row? After pulling the first red marble, you do NOT replace it in the bag before pulling the second one. Each marble has equally chance of being pulled

A. 5/7 multiplied by 5/7
B. 5/7 multiplied by 4/6​

the number of coupons sent to potential members was 228.

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

According to the problem, the total number of coupons sent out was 266. Therefore, we can write an equation based on the information given:

x + 6x = 266

Simplifying and solving for x, we have:

7x = 266

x = 38

Therefore, the number of coupons sent to existing members was 38. To find the number of coupons sent to potential members, we can multiply this number by 6:

6x = 6(38) = 228

Therefore, the number of coupons sent to potential members was 228.

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To make 20 litres of the cranapple mixture, Taylor should combine 8 litres of apple juice and (20 - 8) = 12 litres of cranberry juice.

Let's assume that Taylor mixes x liters of apple juice and (20 - x) liters of cranberry juice to make 20 liters of the cranapple mixture.

The price of the used apple juice is $0.85 and the price of the used cranberry juice is $1.25 (20 - x).

The mixture is supposed to be sold for exactly what the ingredients cost, or $1.09 per litre, according to the problem. As a result, the total cost of the juice used to create the mixture must be equivalent to the price at which it is sold.

[tex]0.85x + 1.25(20 - x) = 1.09(20)[/tex]

[tex]0.85x + 25 - 1.25x = 21.8-0.4x = -3.2x = 8[/tex]

Verification:

[tex]0.85(8) + 1.25(12) = 10.8[/tex]

Verify:

1.09(20) = 21.8

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The events of choosing a jack or a spade out of a standard deck of cards are not mutually exclusive.

Mutually exclusive events are events that cannot happen at the same time. In other words, if one event occurs, the other cannot.

In a standard deck of cards, there are four jacks and thirteen spades. One of the jacks is also a spade (the jack of spades). Therefore, it is possible to choose a card that is both a jack and a spade at the same time.

Since the events are not mutually exclusive, the probability of choosing a jack or a spade is the sum of the probabilities of each event minus the probability of both events occurring:

P(jack or spade) = P(jack) + P(spade) - P(jack and spade) = 4/52 + 13/52 - 1/52 = 16/52 = 4/13

Therefore, the events of choosing a jack or a spade out of a standard deck of cards are not mutually exclusive.

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The magnitude of the electric force upon an electron at point B is 8.16 x 10^-20 N, and it would accelerate in the direction opposite to the electric field, or -7.

The upon an electron at point B can be calculated using the formula F = qE, where F is the force, q is the charge of the electron, and E is the electric field magnitude. The charge of an electron is 1.6 x 10^-19 C, and the electric field magnitude at point B is 0.51 V/m. Therefore, the magnitude of the electric force is:

F = (1.6 x 10^-19 C) (0.51 V/m) = 8.16 x 10^-20 N

To determine the direction in which the electron would accelerate at point B, we need to consider the direction of the electric field. The electric field direction at point B is not given in the table, but we can assume that it is the same as the direction at point A, which is 7.

Therefore, the electron would accelerate in the direction opposite to the electric field, or -7.

The vector indicating the direction in which the electron would accelerate at point B can be drawn as follows:

<--- (electron)

In conclusion, the magnitude of the electric force is 8.16 x 10^-20 N, and it would accelerate in the direction opposite to the electric field, or -7.

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Answer:

x = 27

Step-by-step explanation:

x - 21 = 6 ( add 21 to both sides to isolate x )

x = 27

The answer is going to be 27 as x so 27 - 21 = 6 to check you can do 6 + 21 which would equal to 27 so that’s the answer.

Therefore, x = 27

Answer:

Proofs attached to answer

Step-by-step explanation:

proofs attached to answer

The probability of reaching into the box and randomly drawing the chip numbered 146 is 0.0027 or 1/364.

Probability is the chance or likelihood of an event taking place.

In this case, we are trying to determine the probability of drawing a chip numbered 146 from a box containing 364 plastic chips numbered 1 through 364.

To solve this, we will use the formula:

probability of an event = number of favorable outcomes / total number of possible outcomes.

Let's find out the favorable and total number of outcomes.

Favorable outcomes: The number of chips numbered 146 is only one.

Therefore, the number of favorable outcomes is 1.
Total number of outcomes: There are 364 plastic chips numbered 1 through 364 in a box.

Therefore, the total number of outcomes is 364.
Hence, the probability of reaching into the box and randomly drawing the chip numbered 146 can be calculated using the formula:

probability of an event = number of favorable outcomes / total number of possible outcomes.

Thus, the probability of drawing the chip numbered 146 is:

Probability = 1/364 or 0.0027 (rounded to four decimal places).

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Simone built 7 toy cars and 7 toy airplanes to make a total of 14 toys.

Simone could have built 7 toy cars and 7 toy airplanes to make a total of 14 toys.

To confirm this, we can add the number of toy cars and toy airplanes:

7 toy cars + 7 toy airplanes = 14 toys

Since Simone built the same number of toy cars and toy airplanes, dividing 14 by 2 would also give us the number of each type of toy:

14 toys ÷ 2 = 7 toys each (7 toy cars and 7 toy airplanes)

Therefore, we can conclude that Simone built 7 toy cars and 7 toy airplanes to make a total of 14 toys.

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6Aonly valid solution is 5π/4 on the interval [0, 2π]

63,cos x = sin x - 1 is x = 30°

To solve the following trigonometric equations, follow the steps given below:sec x + 1 = tan xcos x = sin x - 12π is the solution to the trigonometric equation sec x + 1 = tan x on the interval [0, 2π]. Let's try to solve the given equation:sec x + 1 = tan xLet's use the identity for secant and tangent in terms of cosine and sine:sec x = 1/cos xtan x = sin x / cos xSubstitute these into the given equation:1/cos x + 1 = sin x / cos xThe denominator of the right-hand side can be cleared by multiplying both sides by cos x. This gives:1 + cos x = sin xMultiplying both sides by 2 gives:2 + 2 cos x = 2 sin xNow we can use the Pythagorean identity:1 = sin^2 x + cos^2 xto solve for cos x in terms of sin x.cos^2 x = 1 - sin^2 xcos x = ± √(1 - sin^2 x)We can choose the negative root in the interval [0, π] since we need cos x ≤ 0 with tan x ≥ 0.Substitute this expression for cos x in the equation we derived earlier:2 - 2 √(1 - sin^2 x) = 2 sin xSimplify the equation and square both sides:4 sin^2 x - 4 sin x - 4 = 0sin x = (4 ± √32)/8 = (1 ± √2)/2We choose the solution sin x = 1 - √2/2 in the interval [0, π] since we need sin x ≤ 0 with cos x ≤ 0.Substitute this value of sin x into our expression for cos x:cos x = -√(1 - sin^2 x) = -√(1 - (1 - √2/2)^2) = -√(3/2 + √2/2)This value of cos x gives us the solution x = 5π/4, which is in the interval [0, 2π]. Therefore, the only valid solution is 5π/4 on the interval [0, 2π].cos x = sin x - 1sin x - cos x = 1We can use the Pythagorean identity to solve for sin x in terms of cos x:sin^2 x = 1 - cos^2 xsin x = ± √(1 - cos^2 x)Substitute this into the equation:sin x - cos x = 1± √(1 - cos^2 x) - cos x = 1Square both sides:1 - 2 cos x + cos^2 x = 1 - cos^2 xcos x = 1/2Substitute this value of cos x into our expression for sin x:sin x = ± √(1 - cos^2 x) = ± √(3/4) = ± 1/2We choose the solution sin x = 1/2 since sin x is positive and we need sin x - cos x = 1.Substitute these values of sin x and cos x into the identity we derived at the beginning:sin x - cos x = 1sin 30° - cos 30° = 1/2 - √3/2Therefore, the solution to the equation cos x = sin x - 1 is x = 30°.

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The density of the metal sculpture is 6.32 grams per cm³

Density can be defined as the quotient between mass and volume so we can just use the simple formula:

Density = mass/volume

And here we know the two values that we need to use as inputs in the formula above, these values are:

mass = 7.9kg

volume = 1250 cm³

We want the density in grams, then we can rewrite the mass as:

mass = 7.9kg = 7,900 g

Now just take the quotient between the two given quantities, we will get:

Density = 7,900g/1250 cm³ = 6.32 g/cm³

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If Central angle BAC of circle A measures 23/20 π T radians. Arc BC has a length of 63.48 centimeters. The radius of the circle A is: 55.2cm.

In this case, we know the length of arc BC is 63.48 cm and the central angle BAC measures 23/20 π radians.

Now let find the radius of circle A:

So:

63.48π = (23/20 π)/2π × 2πr

63.48π = 1.15 rπ

Divide both side by 1.15

r = 63.48 /1.15

r =55.2 cm

Therefore we can conclude that the radius of circle A is approximately 55.2 centimeters.

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The complete question is:

Central angle BAC of circle A measures 23/20 π T radians. Arc BC has a length of 63.48 centimeters. What is the radius of the circle? The radius of circle A is

Answer:

angle 1 = 54° because this angle is a vertical angle of 54°, and vertican angles are always the same.

angle 2 = 126° because straight line = 180°, and there we have 54°, so 180-54=126°

angle 3 = 126° because this angle is vertical angle to 126°

angle 4 = 121° because this angle is alternative interior angle of the sum of the angles 12(54) and 67°

angle 5 = 59° because angle 5 and angle 4 makes a straight line, staring line = 180°, and 180°-angle 4(121°)= 59°

angle 6 = 121° because this anle is vertican angle of 121°

angle 7 = 59 because this angle is vertical angle of 59°

angle 8 = 59° because this angle is corresponding to angle 5 (59°), and corresponding angles are always the same

angle 9 = 54° because this angle is corresponding angle to 54°

angle 10 = 67 because angle 10, 9 and 8 creates straight line, straight line = 180°, angle 9(54) + angle 8(59)=113, and 180°-113°=67°, that means that angle 10 = 67°

angle 11 = 59 because this angle is corresponding to angle 7 (59°)

angle 12 = 54° because this angle is corresponding angle to angle 1 (54°)

that is it :)

According the question, after simplifying an expression Jacksοn will spend $3.1.

Tοtal refers tο an entire οr cοmplete amοunt, and the verb "tο tοtal" means tο cοmbine twο numbers οr tο destrοy anything. In mathematics, yοu add integers tο get the tοtal; the οutcοme is the tοtal. The result οf adding 8 and 8 is 16.

The terms "quantity οf mοney" and "a sum οf mοney" are interchangeable.

Here, we have

Given:  Twο friends shοp fοr fresh fruit. Jacksοn buys a watermelοn fοr $6.25 and 4 pοunds οf cherries. Tim buys a pineapple fοr $3.15 and 3 pοunds οf cherries.

Jacksοn buys a watermelοn fοr $6.25 and 4 pοunds οf cherries.

Cοst οf 4 pοunds οf cherries = 4p

Nοw,

Cοst οf fruits tο Jacksοn = 6.25+4p   (in dοllars)

Tim buys a pineapple fοr $3.15 and 3 pοunds οf cherries.

Cοst οf 4 pοunds οf cherries = 3p

Nοw,

Cοst οf fruits tο Tim = 3.15+3p   (in dοllars)

Amοunt spent by Jacksοn mοre than Tim = (Cοst οf fruits tο Jacksοn)-(Cοst οf fruits tο Tim)

=  6.25+4p -(3.15+3p)

= 3.1 + p

p = 3.1

Hence, Jacksοn will spend $3.1.

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Answer:

categorical data

Step-by-step explanation:

thanks for the question

please mark me brainless

Answer: I believe it is categorical

The velocity of the ball after 2 seconds is 412 feet per second.

The position function for free-falling objects is s(t) = -16t^2 + v0t + S0, where t is the time, v0 is the initial velocity, and S0 is the initial position. In this case, the initial velocity v0 is -19 feet per second and the initial position S0 is the top of a 482-foot building.

To find the velocity after 2 seconds, we can plug in the time t = 2 into the equation and solve for the velocity v:

s(t) = -16t^2 + v0t + S0

s(2) = -16(2)^2 + (-19)(2) + 482

s(2) = -32 -38 + 482

s(2) = 412

Therefore, the velocity of the ball after 2 seconds, after calculation, is 412 feet per second.

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The equation which accurately represents the statement as given are; 4.9x - (-3) = 12.8; 3 + 4.9x = 12.8; and 12.8 = 4.9x + 3.

As evident from the task content; the given statement is; Negative 3 less than 4.9 times a number, x, is the same as 12.8.

Therefore, we have ;

4.9x - (-3) = 12.8

Or by evaluation;

3 + 4.9x = 12.8

Or by rearrangement;

12.8 = 4.9x + 3.

On this note, the equations which represent the given word phrase are; 4.9x - (-3) = 12.8; 3 + 4.9x = 12.8; and 12.8 = 4.9x + 3.

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Answer:

Based on the given input-output pairs (2,8), (3,11), and (4,14), it appears that the rule for this function table is to multiply the input by 3 and then add 2 to get the output. In other words, for an input x, the output is given by the function f(x) = 3x + 2.

The cylinder has a volume of about 30.55 cubic feet. Consequently, option D, which is 30.55 cubic feet, is the right response.

As a result, the product of the base area and height can be used to determine the cylinder's volume. The volume of any cylinder with base radius "r" and height "h" equals base times height. A cylinder's volume is therefore equal to r²h cubic units.

We use the following formula to determine a cylinder's volume:

V = πr²h

The height of the cylinder is 3.8 feet, according to the issue description.

The distance in feet between two points on the circular base that pass through the centre is designated as the 3.2 feet segment.

When these values are added to the formula, we obtain:

V = π(1.6)²(3.8)

V ≈ 30.55 cubic feet

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Answer:

option D, which is 30.55 cubic feet, is the right response.

Step-by-step explanation:

Answer:

x>-7

Step-by-step explanation:

matrix A was expressed in the form, a=[a c] [b d] find the value of a - b + c + d. 5x+7y=7 3x-2y=9. That is

a =5, c=7; and b=3, d=-2

a - b + c + d = 5 - 3 + 7 + (- 2) = 7

The given equations are

5x + 7y = 7

3x - 2y = 9

As a matrix equation,

A = [5 7

      3 - 2]

X = [x

       y]

C = [7

      9]

That is

a =5, c=7; and b=3, d=-2

a - b + c + d = 5 - 3 + 7 + (- 2) = 7

A matrix equation is an equation of the structure Hatchet = b, where An is an m × n matrix, b is a vector in R m, and x is a vector whose coefficients x 1, x 2,..., x n are obscure.

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the complete question is :

If the following system of equations was written as a matrix equation in the form AX = C,? and matrix A was expressed in the form, a=[a c] [b d] find the value of a - b + c + d. 5x+7y=7 3x-2y=9.

The abbreviated fοrmula is therefοre [tex]\dfrac{1}{3}[/tex]. Thus, option B is correct.

Estimates that cοmbine jοining, deactivating, but instead randοm divide shοuld be prοduced with shifting variables. If they banded tοgether, they cοuld dο the fοllοwing: a mathematical cοnundrum, sοme data, and sοftware. A statement οf truth cοntains fοrmulas, cοmpοnents, and arithmetic prοcedures like adding, subtractiοns, οmissiοns, and grοupings. It is pοssible tο assess and analyse bοth wοrds and sentences.

Here,

We add the expοnents οf twο expοnents multiplied by the same basis. As a result, we have:

=> [tex]3^{(2/5) } \times 3^{(-7/5) }= 3^{(2/5 - 7/5)}[/tex]

We need tο identify a cοmmοn denοminatοr fοr the expressiοns 3(2/5) and 3(-7/5) in οrder tο make it simpler, since it is the least cοmmοn multiple is 5:

=> [tex]3^{\tfrac{2 - 7}{5} }[/tex]

=> [tex]3^{\tfrac{-5}{5} } = 3^{-1}[/tex]

3⁻¹ = [tex]\dfrac{1}{3}[/tex]

The abbreviated fοrmula is therefοre [tex]\dfrac{1}{3}[/tex]. Thus, option B is correct.

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The volume of air in liters is in the room is 29901.7 litre.

Dimension :

s 11. 0 ft x 12. 0 ft x  8 ft

Volume = l * b ' h

V = 11.0 * 12.0* 8.0

V = 1056 cu. ft.

Covert of unit

1 cu. ft = 28.316 litre

1056 cu. ft. = 1056 * 28.316 litre

1056 cu. ft. = 29901.7 litre

Thus, the volume of air in liters is in the room is 29901.7 litre.

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The pressure on a brake pad has an area of 0.35 m² and a force of 21 N applied on it is equals to the 60N/m².

We have, area of a brake pad, A

= 0.35 m².

Force applied on brake pad, F = 21 N, we have to determine the value of pressure. Pressure is defined as the force acting perpendicularly on a unit area of the object. The standard unit of pressure is Pascals = 1 N/m². Pressure, force and area relation : pressure is calculated as the force divided by the area where the force is applied. So, in this case we have both force and area. That is pressure is, P = applied force/Area, so pressure on brake pad, P = 21 Newton/0.35 m²

=>[tex] P = \frac{2100}{35}[/tex]N/m²

=> P = 60 N/m²

Hence, the required pressure value is 60 N/m².

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Complete question:

A brake pad has an area of 0.35 m² and has a force of 21 N applied to it what’s the pressure in N/m².

The points are vertices of an isosceles triangle by using distance formula.

What is distance formula?

The xy-plane distance formula can be used to determine the distance between two points.

We know that the distance formula is

d = [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

Using this, we get

⇒AB = [tex]\sqrt{(7 -3)^{2} +(8 -4 )^{2} }[/tex]

⇒AB = [tex]\sqrt{(4)^{2} +(4 )^{2} }[/tex]

⇒AB = √16 + 16

⇒AB = √32

Similarly,

⇒AC = [tex]\sqrt{(11 -3)^{2} +(4 -4 )^{2} }[/tex]

⇒AC = [tex]\sqrt{(8)^{2} +(0 )^{2} }[/tex]

⇒AC = √64

⇒AC = 8

Similarly,

⇒BC = [tex]\sqrt{(11 -7)^{2} +(4 -8 )^{2} }[/tex]

⇒BC = [tex]\sqrt{(4)^{2} +(4 )^{2} }[/tex]

⇒BC = √16 + 16

⇒BC = √32

Since. AB = BC, so it is an isosceles triangle as in isosceles triangle, two sides are equal.

Hence, the given points are the vertices of an isosceles triangle.

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To make a scatter plot of the data from each table, begin by assigning the x-axis to represent the values from one of the tables and the y-axis to represent the values from the other table. Then plot each pair of values onto the graph, creating a "scatter" of points. To draw a trend line, look for the general pattern in the data points and draw a line that best fits them. To find the equation of the trend line, use the formula y = mx + b, where m is the slope of the line and b is the y-intercept. To find the slope of the line, use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line. To find the y-intercept, plug the slope and any point on the line into the equation y = mx + b and solve for b.

The given data is as follows: 5, 66, and 9. We can plot these values in a scatter plot by following the steps mentioned below:Step 1: Plot the given data points on the Cartesian plane. Step 2: Find the equation of the line of best fit/trend line. We can use the least-squares regression method to find the line of best fit/trend line. This method gives us the equation of a line that best represents the relationship between two variables. In this case, the two variables are X and Y. Step 3: Draw the trend line on the scatter plot. Step 4: Write the equation of the trend line. The equation of the line of best fit/trend line is in the form of y = mx + c, where m is the slope of the line, and c is the y-intercept. . However, we can still draw a line of best fit/trend line that passes through the data points. The equation of the line of best fit/trend line can be found using the least-squares regression method. Using this method, we get the equation of the line of best fit/trend line as: y = -10.33x + 71.33Therefore, the equation of the trend line is y = -10.33x + 71.33.

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The value of the segment MN is 18 units

Similar triangles are triangles that have the same shape but possibly different sizes in proportions

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

AB=24 , AD=14 , and MQ=10.5

Given that the triangles are similar, we have the following ratio

AB : AD = MN : MQ

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

24 : 14 = MN : 10.5

Make MN the subject

MN = 10.5 * 24/14

Evaluate

MN = 18

Hence, the value of MN is 18

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Answer:

£681.95

Step-by-step explanation:

131.78% of £517.49

131.78% = 1.3178

We take

517.49 x 1.3178 = £681.95

So, the answer is £681.95

Number of chocolate bars that Ron eat is 30

To solve the problem, we can work backwards from the information provided and use variables to represent unknown quantities.

Let's start with Betty, who ate 10 chocolate bars. We know that Billy had half as many as Betty, so we can represent Billy's chocolate bars as:

Billy = 1/2 × Betty

Billy = 1/2 × 10

Billy = 5

Next, we know that Bob ate 5 more chocolate bars than Billy, so we can represent Bob's chocolate bars as:

Bob = Billy + 5

Bob = 5 + 5

Bob = 10

Finally, we know that Ron eats 3 times as many chocolate bars as Bob, so we can represent Ron's chocolate bars as:

Ron = 3 × Bob

Ron = 3 × 10

Ron = 30

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[tex]\dfrac{\mathcal{P}_{1}}{\mathcal{P}_{2}} = \dfrac{h_{1}}{h_{2}} \iff \dfrac{37.8}{\mathcal{P}_{2}} = \dfrac{6}{15}[/tex]

[tex]\mathcal{P}_{2} = \dfrac{37.8(15)}{6} \implies \bf \mathcal{P}_{2} = 94,5 \ inches\\[/tex]

Two triangles are similar. The perimeter of the larger triangle is 94.5 inches.

SOLUTION:

Given, Two triangles are similar.  

The height of the smaller triangle is 6 inches and the corresponding height of the larger triangle is 15 inches.  

The perimeter of the smaller triangle is 37.8 inches.

We have to find what is the perimeter of the larger triangle?

We know that, for similar triangles, ratio of heights = ratio of perimeters.

[tex]\sf{Then,} \ \frac{height\ of \ 1st \ triangle}{height\ of \ 1st \ triangle} = \frac{perimeter \ of \ 2nd \ triangle}{perimeter \ of \ 2nd \ triangle}[/tex]

[tex]\sf{\frac{6}{15} =\frac{37.8}{perimeter\ of \ 2nd \ triangle}[/tex]

[tex]\sf{Perimeter} \ of \ 2^{nd \ triangle} \ \times6=37.8\times15[/tex]

[tex]\sf{Perimeter} \ of \ 2^{nd \ triangle} =37.8\times\frac{15}{6}=37.8\times\frac{5}{2} =\frac{189}{2} =94.5[/tex]

Hence, the perimeter of the larger triangle is 94.5 inches

Answer:

48 tiles are required.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

To solve for the area of a rectangle, we use this expression:

(Let l = length, w = width and a = area)

Inserting the dimensions of the hall:

Each tile has an area of:

To find the number of tiles needed to cover the hall, we can divide the area of the hall by the area of each tile:

Therefore, 48 tiles are required to cover the rectangular hall.