An equilateral triangle has an altitude of 15 m. What is the perimeter of the triangle?
(A) 30√2 m
(B) 45 m
(C)30√3 m
(D)60√3 m.

The value of x is 80 degrees.

The correct answer is an option (A)

Consider the following figure.

Let us assume that the upper triangle be ABC and the lower triangle be NMC.

We can observe that both the triangles are isosceles triangles, because in both the triangles two sides are congruent.

Consider triangle ABC.

As the triangle is isosceles triangle, from the definition of  isosceles triangle ∠A = ∠B

So, ∠A = 65°

We know that the sum of all the angles of triangle is 180°

⇒ ∠A + ∠B + ∠C = 180°

⇒ ∠C = 180° - (65° + 65°)

⇒ ∠C = 180° - 130°

⇒ ∠C = 50°

We can observe that ∠ACB and ∠MCN are opposite angles.

So,  ∠MCN = 50°

Also, triangle MNC is also an isosceles triangle.

so, ∠C = ∠N

⇒∠N = 50°

We know that the sum of all the angles of triangle is 180°

⇒ ∠M + ∠N + ∠C = 180°

⇒ ∠M = 180° - (50° + 50°)

⇒ ∠M = 180° - 100°

⇒ ∠M = 80°

Therefore,  x = 80°

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Answer:

Step-by-step explanation:

3.8 liters = 38deciliters

Answer:

3.8 litres =38 deciliters

The measure of side AB of the triangle is given by equation AB = 3.5 cm

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be represented as ΔACE

Let the second triangle be represented as ΔBCD

The measure of side AC = 14 cm

The measure of side EC = 84 cm

The measure of side ED = 21 cm

Now , ΔACE is similar to ΔBCD

So , corresponding sides of similar triangles are in the same ratio

Substituting the values in the equation , we get

AB / AC = ED / EC

AB / 14 = 21 / 84

Multiply by 14 on both sides of the equation , we get

AB = ( 1/4 ) 14

AB = 3.5 cm

Therefore , the value of AB is 3.5 cm

Hence , the measure of side AB of triangle is 3.5 cm

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A function rule, if a carnival charges $6 to enter and $. 75 per ticket is f(x) = $6 + .75x

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input

According to the question,

carnival charges is $6

cost per ticket is $0.75

Let the number of person/tickets be x

and f(x) be the total cost

therefore the function is f(x) = $6 + 0.75x

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Using Cramers Rule, X = 10.34, Y = 0.85. See the computations below.

Cramer's rule is an explicit formula in linear algebra for solving a system of linear expressions with as many equations as unknowns, and it is true whenever the system has a unique solution.

Given:

10x - 4y = 100; ..................1) and

8x - 100y = -2; ...................2)

First things first, let's pick off the variables we will need for Cramer's equation:

Standard equation 1 = ax + by = c and Standard equation 2 = dx + ey = f. Therefore:

a = 10, b = -4, c = 100, d = 8, e = -100, f = -2

Step 1, calculate the denominator Delta (Δ):

Δ = a * e - b * d

Δ = (10 * -100) - (-4 * 8)

Δ = -1000 - -32

Δ = -968

Step 2, calculate the numerator for x

Numerator(x) = c * e - b * f

Numerator(x) = (100 * -100) - (-4 * -2)

Numerator(x) = -10000 - 8

Numerator(x) = -10008

X = Numerator (x) / Δ

x  = -10008/-968
x = 10.338842975207

x [tex]\approx[/tex] 10.34

y  =   Numerator(y)/Δ

y  =   -820/-968

y = 0.84710743801653

y [tex]\approx[/tex] 0.85

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(i) The average values for the variables andre, pri gpa, and act is sum of all the values divided by the total number of values.

(ii) The model atenderte 5 b0 1 b1 prigpa 1 b2act 1 u in equation form  is atenderte = b₀ + b₁ x prigpa + b₂ x act + u

(iii) The slope coefficients is  b₁ and b₂

(iv) The predicted atenderte if prigpa 5 3.65 and act 5 20 is atenderte = b₀ + b₁ x 3.65 + b₂ x 20 + u

(v) if student a has prigpa 5 3.1 and act 5 21 and student b has prigpa 5 2.1 and act 5 26, then the predicted difference in their attendance rates is  0.5

In this exercise, we will be exploring a regression model that predicts the attendance rate of students based on their academic performance variables. We will be using three variables to predict the attendance rate: "andre", "pri gpa", and "act". Here are the answers to the questions:

(i) To obtain the minimum, maximum, and average values for the variables "andre", "pri gpa", and "act", we need to first look at the data. The minimum value is the smallest value for each variable, the maximum value is the largest value for each variable, and the average value is the sum of all the values divided by the total number of values.

(ii) The regression model that predicts the attendance rate is written in equation form as

=> "atenderte = b₀ + b₁ x prigpa + b₂ x act + u".

This equation means that the predicted attendance rate (atenderte) is equal to the intercept (b₀) plus the product of the coefficient for "pri gpa" (b₁) and the value of "pri gpa" plus the product of the coefficient for "act" (b₂) and the value of "act".

(iii) The estimated slope coefficients (b₁ and b₂) tell us the expected change in the attendance rate for each one-unit increase in "pri gpa" or "act". If b₁ is positive, it means that as "pri gpa" increases, the attendance rate is expected to increase. Similarly, if b₂ is positive, it means that as "act" increases, the attendance rate is expected to increase.

(iv) To find the predicted attendance rate if "pri gpa" is 3.65 and "act" is 20, we can substitute these values into the regression equation:

atenderte = b₀ + b₁ x prigpa + b₂ x act + u

atenderte = b₀ + b₁ x 3.65 + b₂ x 20 + u

This will give us the predicted attendance rate for a student with "pri gpa" of 3.65 and "act" of 20. If there are any students in the sample with these values of the explanatory variables, then their actual attendance rate should be close to the predicted value.

(v) To find the predicted difference in attendance rates between student A (with "pri gpa" of 3.1 and "act" of 21) and student B (with "pri gpa" of 2.1 and "act" of 26), we can first use the regression equation to predict the attendance rates for each student:

Student A:

atenderteA = b0 + b1 x 3.1 + b2 x 21 + u

Student B:

atenderteB = b0 + b1 x 2.1 + b2 x 26 + u

Then, we can take the difference between the predicted attendance rates for each student:

=> atenderteA - atenderteB

=> 52.6 - 52.1 = 0.5

This will give us the predicted difference in attendance rates between the two students.

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If the functions be f(x) = 4x + 13 and g(x) = 10x − 2 then the expression (f + g)(x) be 4x + 11.

A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, while the set Y is known as the function's codomain. Initially, functions were just an idealized representation of the relationship between two changing quantities.

Given f(x) = 4x + 13 and g(x) = 10x − 2

We must add both functions to reflect the amount of time it takes to travel east and west in order to calculate the round-trip time.

Let the equation be (f + g)(x) = f(x) + g(x)

substitute the values in the above equation, we get

= (4x + 13) + (10x − 2)

simplifying the above equation, we get

= 4x + 13 + 10x − 2

= 4x + 10x − 2 + 13

= 4x + 11

Therefore, the expression (f + g)(x) be 4x + 11.

The completed question is:

The function f(x) represents the time it takes an airplane to travel east. The function g(x) represents the time it takes an airplane to travel west. Given f(x) = 4x + 13 and g(x) = 10x − 2, solve for (f + g)(x) to determine the total roundtrip time.

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Yes, both methods give the same result. The chain rule is used to differentiate a composite function, while the substitution method is used to differentiate a function after substituting a variable with its expression.

The chain rule is used to differentiate a composite function, which is a function of a function. To use the chain rule, we differentiate the inner function and multiply it by the derivative of the outer function. In this case, we would have

f(x) = ([tex]x^2 + 3x + 2[/tex]) and

g(x) = [tex]2x^3 + 5[/tex]

The derivative of f(x) would be 2x + 3 and the derivative of g(x) would be [tex]6x^2[/tex]. Taking the product of these two derivatives, we get

[tex]12x^3 + 18x^2[/tex],

which is the answer we get using the chain rule. The substitution method involves substituting a variable in a function with its expression. In this case, we substitute x with ([tex]x^2 + 3x + 2[/tex]). This gives us a new function that is a function of [tex]x^2 + 3x + 2[/tex]instead of x. We then differentiate this new function and the answer we get is the same as the one we got using the chain rule. Therefore, both methods give the same result and agree with each other.

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In a case whereby three numbers are in the ratio 2:3:5 and the sum of their cube is 34560 then the numbers are  12, 18, and 30.

The given Ratio of three numbers can be expressed as 2:3:5

Then we can represent the three numbers  as: 2x, 3x, and 5x.

We were given the Sum of their cubes as  34560

Thern we can cube them as 2x^3 + 3x^3 + 5x^3 =34560

The we will have 8x^3 + 27x^3 + 125x^3 =34560

Then we have 160x^3 = 34560

x^3 =34560/160

x= 6.

then we can find the values of the ratio as :

2x =( 2×6)

= 12

3x = (3×6 )

= 18

5x = (5×6 )

= 30

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The Malthusian law for population growth states that the rate of population growth is proportional to the current population size.

Mathematically, we can express this as:

dP/dt = rP

where P is the population size, t is time, and r is the growth rate.

Assuming a constant growth rate, we can integrate this equation to get:

ln(P) = rt + C

where C is an integration constant. We can solve for C using the initial population estimate:

ln(1200) = r(1980) + C

C = ln(1200) - r(1980)

Substituting the values of C and P from the second estimate (P=7500 in 2008), we get:

ln(7500) = r(2008) + ln(1200) - r(1980)

Solving for r, we get:

r = [ln(7500) - ln(1200)] / (2008 - 1980) = 0.0496

Using this value of r, we can predict the alligator population in 2020, which is 12 years after the second estimate (2008). We have:

ln(P) = rt + ln(7500)

ln(P) = 0.0496(12) + ln(7500) = 9.058

P = e^9.058 = 8656

Therefore, the estimated alligator population in the region in the year 2020 is 8656.

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Based on the distance covered by Zebra and Giraffe in mentioned time, the Zebra can be said to run faster.

Firstly, the question requires a candidate to be familiar with the concept of speed. We know that speed is associated with distance and time as -

Speed = distance/time

So, taking the case for Giraffe

Speed = 280/20

Performing division

Speed = 14 m/s

Taking the case of Zebra

Speed = 204/12

Performing division

Speed = 17 m/s

We see that in unit time or one second, the distance covered by the two animals is different. The one covering larger distance comparatively will be said to run faster. So, zebra runs faster.

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The table of question is attached in the picture.

The ratio of EP to PF is given as follows:

EP : PF = 2 : 7.

The ratio of EP to PF is obtained applying the proportions in the context of the problem.

Looking at the x-coordinates, we have that:

The ratio must necessarily be the same for the y-coordinates, hence the ratio is given as follows:

EP : PF = 4 : 14.

EP : PF = 2 : 7.

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PLEASE GIVE BRAINLIEST!

thank you and have a good day :)

Answer:

163/30

Step-by-step explanation:

4 3/5 in mixed number form would be 23/5

5/6 remains 5/6 as it is not greater than 1, therefore it cannot be simplified.

23/5 + 5/6

in order to add, we have to make the denominators alike. the least common multiple is 30. so we have to not just multiply the denominators by whatever results in 30, but also the numerators.

23 times 6 = 138

5 times 6 = 30

5 times 5 = 25

5 times 6 = 30

138/30 + 25/30

at this point, we can simply just add the numerators

163/30

i hope this helps

Each wand costs $83, found by dividing the total cost of $498 by the total number of items, 6 (4 cloaks and 2 wands), resulting in $498 / 6 = $83.

To solve for the cost of each wand, we first need to determine the cost of each item (cloak and wand) that Harry bought. We can represent the cost of each item as "x". Since Harry bought 4 cloaks, the total cost of the cloaks is 4 * x. Similarly, since he bought 2 wands, the total cost of the wands is 2 * x.

The total cost of the cloaks and wands that Harry bought was $498, so we can write the equation: 4 * x + 2 * x = $498. This equation represents the total cost of the 4 cloaks plus the 2 wands, which must equal $498.

Next, we can simplify the equation by combining like terms: 4 * x + 2 * x = 6 * x = $498.

Finally, we can find the cost of each item by dividing both sides of the equation by 6: x = $498 / 6 = $83.

Therefore, each wand costs $83.

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To buy down the quoted interest rate from 4.75% to 4.5% will cost Trystan and Kendall $4,800 after the down payment.

The down payment refers to the initial cash payment for the purchase of an item on mortgage.

The down payment is required by the financier to evaluate the buyer's financial readiness.

The cost of the new home = $300,000

Down payment = 20% or $60,000 ($300,000 x 20%)

Mortgage loan required = $240,000 ($300,000 - $60,000)

Bank quoted interest rate = 4.75%

Desired interest rate = 4.5%

Difference in interest rate = 0.25% (4.75% - 4.5%)

Rate of buy down of the quoted interest per point = 0.125%

The number of points to buy down the interest rate = 2 (0.25/0.125)

The cost of each point = 1% of $240,000 = $2,400

The total cost of 2 points = $4,800 ($2,400 x 2)

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In conclusion, the hospital needs to consider their staffing needs on a shift-by-shift basis, taking into account the number of patients and nurses' preferences.

Number  mathematical entity used to represent a quantity or magnitude it can be symbol or a combination of symbol used to denoted a quantity such as 2573 or 8 1 number are used in a variety of context including counting measuring and computing they are also used to denote the size or amount of something such as a number of people in a room or the number of apples in a basket number play an important role in mathematics including algebra geometry and calculus.

Based on the above figures, the hospital would require a staffing of approximately 62 nurses on Shift A, 93 nurses on Shift B, 68 nurses on Shift C, and 27 nurses on Shift D. This would equate to a total of 250 nurses, which is the number of nurses the hospital has on its staff.

The hospital can adjust the staffing needs by taking into account the amount of nurses needed to provide the necessary patient care. If the shift with the highest number of patients (Shift B) requires additional nurses, the hospital could move nurses from the shift with the lowest number of patients (Shift D). This would result in fewer nurses on Shift D, but would allow for more nurses on Shift B.

In order to ensure that nurses are working in a safe and comfortable environment, the hospital should also take into account the nurses' own preferences. If nurses prefer to work certain shifts, the hospital can adjust the staffing levels accordingly. This can help create a better work-life balance for the nurses, which can, in turn, improve their job satisfaction and performance.

In conclusion, the hospital needs to consider their staffing needs on a shift-by-shift basis, taking into account the number of patients and nurses' preferences. This way, they can maintain a safe and comfortable environment for their nursing staff, while also ensuring that they have enough nurses to provide the necessary care to their patient.

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Answer:

Step-by-step explanation:

Use PEMDAS to determine order of operations.

P = Parentheses

E = Exponents

M/D = Multiplication/Division

A/S = Addition/Subtraction

The operation in the parentheses must be performed first, which is the addition of 6.1 + 12.

The next operation to perform is multiplication, which is 415 times (6.1 + 12).

The last operation to perform is the subtraction of 415 times (6.1 + 12) from 8.3.

6.1 + 12 = 18.1

8.3 - 415(18.1)

8.3 - 7511.5 = -7503.2

The number that can each terms of the equation be multiplied by to eliminate the decimals before solving is 100

The equation is

5.6j + 0.12 = 4 + 1.1j

The equation is defined as the mathematical expression that shows the relationship between one expression and another expression with equal sign. The equation consist of mathematical operator like addition, subtraction, division and multiplication

The equation is

5.6j + 0.12 = 4 + 1.1j

Here three term has fractional part.

In 0.12 there are two digits after the decimal point to eliminate the decimal number we have to multiply the number with 100 .

Then the equation will become

560j + 12 = 400 + 110j

Therefore, the number is 100

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The given question is incomplete, the complete question is

Which number can each term of the equation be multiplied by to eliminate the decimals before solving?

5.6j + 0.12 = 4 + 1.1j

a) The probability of a defect is  0.0668.

b. The process standard deviation can be reduced to  0.0062.

c. The advantage of reducing process variation is more efficient and reliable production process, as it reduces the need for inspection and rework.

Probability is the measure of the likelihood of an event occurring. It is used in various fields such as finance, engineering, and manufacturing to analyze and predict outcomes.

One company that utilizes probability in its production process is Motorola. In this scenario, Motorola uses the normal distribution, also known as the Gaussian distribution, to determine the probability of defects in their production process.

The normal distribution is a probability distribution that is symmetric and bell-shaped. It is characterized by its mean and standard deviation. The mean represents the center of the distribution, while the standard deviation represents the spread of the distribution.

a. To determine the probability of a defect, we need to find the area under the normal distribution curve to the left or right of ounces. This area represents the probability of a defect occurring. We can use a standard normal distribution table or a calculator to find this area. The probability of a defect to four decimal places is approximately 0.0668.

If the production run is for 100 items, then the expected number of defects would be 0.0668 x 100 = 6.68. Since we cannot have fractional defects, we would round this number to the nearest whole number, which is 7.

b. If the process standard deviation is reduced to, then the probability of a defect will decrease. This is because a smaller standard deviation means the distribution is less spread out, and therefore, fewer items will fall outside the control limits.

To find the new probability of a defect, we would follow the same process as in part a. The probability of a defect to four decimal places is approximately 0.0062.

c. The advantage of reducing process variation is that it results in a larger distance between the mean and the control limits. This means that there is less chance of items falling outside the control limits, which in turn, reduces the probability of defects. This leads to a more efficient and reliable production process, as it reduces the need for inspection and rework. Additionally, it can lead to cost savings and improved customer satisfaction.

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The one who types the fastest is Morgan. hence, the correct option is A.

An equation is defined as an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation , the instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We have been given that equation y=39x

Which models the total number of words Alexa can type, where y is the number of words typed and x is the time in minutes.

The data shows the relationship for Morgan.

Then we can conclude that Morgan types the fastest.

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If the mechanic told Mr P that it will cost 50$ an hour to fix his car, then 50x will be the cost which Mr P has to pay.

An expression is combination of variables, numbers and operators.

Given that Mr P’s had some car issues and he took it into the car shop.

The mechanic told him that it will cost 50$ an hour to fix his car.

We need to find Mr P has to pay for car.

Let x represents the number of hours.

$50x represents the amount Mr P has to pay for car.

Hence, the expression 50x represents the cost Mr P has to pay for car.

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Answer:The price of 10 pounds of cheese is 15.84$

Step-by-step explanation:

It's simple

Answer:

Part A: Slope (m) = -75

Part B:

Point-slope form --- y - 1350 = -75(x - 2)

Slope-intercept form --- y = -75x + 1500

Standard form --- 75x + 1y = 1500

Part C: g(x) = -75x + 1500 (Just replace 'y' in y = mx + b with 'g(x)').

Part D: The balance in the bank account after 5 days equals $1,125.

Step-by-step explanation:

(Pertaining to Part D --- Plugging in variables):

To find the answer to Part D, we must first take the function notation equation from Part C and plug in the appropriate variables needed to find the balance in the bank account after 5 days. So, we plug in '5' for g(x), which would give us g(5). For the other x found in the equation, we also correspondingly replace it with '5'. Our equation now appears as g(5) = -75(5) + 1500.

Finally, we must solve this equation using the order of operations, which simplifies our equation to g(5) = -375 + 1500. We can simplify this further by adding 1500 to -375, giving us the final answer for Part D of $1,125 being the balance in the bank account after 5 days.

Hope that helps!!

Answer:

Part A: Slope (m) = -75

Part B:

Point-slope form --- y - 1350 = -75(x - 2)

Slope-intercept form --- y = -75x + 1500

Standard form --- 75x + 1y = 1500

Part C: g(x) = -75x + 1500 (Just replace 'y' in y = mx + b with 'g(x)').

Part D: The balance in the bank account after 5 days equals $1,125.

The type of sampling that Huw is using is called Convenience Sampling.

Explanation:

Convenience sampling is a non-probability sampling technique where the sample is selected based on ease of access and availability. In Huw's case, he is administering the questionnaire to people who happen to be in the town centre, which is convenient for him. The sample is not selected randomly, and therefore does not accurately represent the population as a whole. Convenience sampling is often used in quick, informal surveys where the researcher does not have the resources or time to conduct a more rigorous, randomized sampling method.

After cutting 9 pieces of ribbons, Diego made 14 pieces of wreaths with the remaining roll of ribbon.

For finding the pieces of wreaths we will first obtain the total meter required for 9 pieces of ribbon by multiplying 9 with 0.4 meter and then subtract it from the total meters of the roll of ribbons i.e., 12 meters and then divide the result with 0.6 meter.

Total meter required for 9 pieces of ribbon = 9x0.4 meter

                                                                        = 3.6 meters

Total meter of the roll of ribbon = 12 meters

Meter required per wreath = 0.6 meter per wreath

Meter of roll remaining for making wreaths = 12-3.6

                                                                        = 8.4 meters

Total number of wreath made from the remaining roll

= 8.4 meter / 0.6 meter

= 14 Wreaths

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We can estimate that there is about 1000 joules of kinetic energy in an average size helium balloon.

The amount of kinetic energy in an average size helium balloon can be estimated using the ideal gas law and the equipartition theorem.

Assuming the balloon is filled with helium at room temperature (around 298 K) and atmospheric pressure (around 1 atm), the volume of the balloon can be estimated to be around 0.5 m^3. The number of helium atoms in the balloon can be estimated using Avogadro's number, which is around 6.02 x 10^23.

Using the equipartition theorem, we can estimate the average kinetic energy of each helium atom in the balloon. At room temperature, each atom has an average kinetic energy of (3/2)kT, where k is the Boltzmann constant (1.38 x 10^-23 J/K).

Therefore, the total kinetic energy of the helium atoms in the balloon can be estimated as:

KE = (3/2)kT * N

where N is the number of helium atoms in the balloon.

Plugging in the estimated values, we get:

KE = (3/2) * (1.38 x 10^-23 J/K) * 298 K * 6.02 x 10^23

KE ≈ 9.95 x 10^2 J

Therefore, An average-sized helium balloon contains roughly 1000 joules of kinetic energy, according to our estimation. It's important to note that this is just an estimate, and the actual amount of kinetic energy in a helium balloon can vary depending on a number of factors such as the temperature, pressure, and size of the balloon.

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Rounding off the 1004.8 into 3 significant figures will give 1000.

Since significant figures are established as digits, they are also known as significant digits. By counting all of the values beginning with the first non-zero digit on the left, it is possible to determine the number of significant digits.  

For example, the number of significant figures in 567 is 3.
The number of significant figures in 2.671 is 4.  

Here we have a number    

1004.8 need to be rounded off for 3 significant figures  

Since 4 is less than 5 then the resultant number = 1000  

[ 4 and 8 neglected since 4 < 5]

Therefore,

Rounding off the 1004.8 into 3 significant figures will give 1000.

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Since the mode is the most frequently occurring data value so -

Option D : None of the alternatives is correct.

What is mode?

A mode is described as the value in a group of values that occurs more frequently. The value that appears the most frequently is called mode.

The distribution of the mean, median, and mode values will depend on how skewed the distribution is.

The total dependency of mean, median and mode of data is on the asymmetric form of the data.

As a result, mean or mode may be larger than or less than mode.

Therefore, the mode is neither large than mean or median and can never be larger than mean.

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