the scale of a map is 1:50000 find the area in square km of a square field 4cm² on the map.​

Yes, the given pair of triangles are congruent by ASA rule.

In geometry, two triangles are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

Given are two triangles, labelling by names, (refer to the image attached)

Considering the triangles, Δ ABC and Δ DEC,

We have,

AC = DC [given]

∠ A = ∠ D [both are congruent]

∠ ACB = ∠ DCE [vertically opposite angles]

∴ Δ ABC ≅ Δ DEC

By ASA rule.

Hence, we can say, the given pair of triangles are congruent by ASA rule.

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Minimum value = 3 , Q₁ = 7.5 , Median = 10 , Q₃ = 13 and maximum value = 16 of the given data set.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

According to the question,

Minimum value of the given data set = 3

n = number of data set

First arrange the data in ascending order

3,4,6,7,8,9,10,10,12,12,13,13,15,16

Quartiles

Q₁ = [ (n+1)/4]th term

   = 14 +1 / 4

  = 3.75th term

  = 3th term + 0.75 ( 4th term - 3th term)

  = 6 + 0.75 (7 -6)

   = 6.75

As n is even,

Median = (N/2)th term

           = 14 /2

           = 7th term

          = 10

Q₃ = [3(n+1)/4]th term

   = 3 × 3.75

   = 11.25

   = 11th term +0.25( 12th term - 11th term)

   = 13 + 0.25 (13 -13)

   = 13

Maximum value = 16

Hence, Minimum value = 3 , Q₁ = 7.5 , Median = 10 , Q₃ = 13 and maximum value = 16 of the given data set.

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The complete question in attachment

To prove the isosceles triangle theorem, you must use the fact that the base angles of an equilateral triangle have equal measure, and then use the properties of isosceles triangles to show that the two angles opposite the equal sides are also equal.

To prove the isosceles triangle theorem, we can follow these steps:

Step 1: Draw an isosceles triangle with sides AB and AC of equal length.

Step 2: Draw a line from point A to point D, perpendicular to line BC.

Step 3: Use the definition of an isosceles triangle to state that ∠ABD and ∠ACD are congruent.

Step 4: Use the definition of a perpendicular line to state that ∠ADB and ∠ADC are congruent.

Step 5: Use the definition of a triangle to state that ∠BAC and ∠BAC are congruent.

Step 6: Use the Congruent Triangles Postulate to state that triangle ABD and triangle ACD are congruent.

Step 7: Use the definition of congruent triangles to state that ∠ABC and ∠ACB are congruent.

Step 8: Use the definition of an isosceles triangle to conclude that the isosceles triangle theorem is true.

Therefore, we have proven the isosceles triangle theorem, which states that the base angles of an isosceles triangle are congruent.

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Answer:

To get the average you add all numbers up then divide by the amount of numbers you have. In case it's 4 then you get your average dollar amount then you can calculate the amount for the years by multiplying it by 52 because there is 52 weeks in a year.

Microliters (µL) and liters (L) are both units of volume measurement. A microliter is a very small unit of volume, equivalent to one millionth of a liter. To convert microliters to liters, we can use a simple conversion factor.

The conversion factor is based on the fact that one liter is equivalent to one million microliters. Therefore, to convert microliters to liters, we divide the number of microliters by one million. This can be expressed as:

L = µL / 1,000,000

For example, if we have a volume of 500 µL that we want to convert to liters, we can use the formula above as follows:

L = 500 µL / 1,000,000

L = 0.0005 L

Therefore, 500 µL is equivalent to 0.0005 liters.

It is important to keep track of the units when making conversions and to use appropriate significant figures. Additionally, it is worth noting that microliters are often used in situations where very small volumes are involved, such as in medical or laboratory settings, whereas liters are used for larger volumes such as in the context of cooking or liquid measurements.

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Answer: x=6

Step-by-step explanation:

90-75=15

15-3=12

12/2=6

the little box means 90 degree angle

Answer:

x = 6

Step-by-step explanation:

Complementary angles:

If sum of two angles add up to 90°, they are called complementary angles.

          75 + 2x +3 = 90

               2x + 78 = 90

Subtract 78 from both sides,

                       2x = 90 - 78

                       2x = 12

Divide both sides by 2

                          x = 12÷2

                         x = 6°

2x + 3 = 2*6 + 3

           = 12 + 3

           = 15°

The two different possible values for height h and radius r for the cone is given by r = 2 inches , h = 6.746 inches

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the center of base) called the apex or vertex.

The volume of a cone is given by the equation

Volume of Cone = ( 1/3 ) πr²h

where r is the radius of the cone

h is the height of the cone

Surface area of the cone = πrl

where l = √ ( b² + r² )

Given data ,

Let the volume of the cone be represented as V

Now , the value of V = 28.26 inches³

Let the radius of the cone be r

Let the height of the cone be h

Volume of Cone = ( 1/3 ) πr²h

Substituting the values in the equation , we get

28.26 = ( 1/3 ) π ( r )² h

Multiply by 3 on both sides of the equation , we get

84.78 / π = r²h

26.986 = r²h

Now , when r = 2 inches

h = 26.986 / 4

h = 6.746 inches

And , when r = 3 inches

h = 26.986 / 9

h = 2.998 inches

Hence , the two values of radius and height of cone are solved

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Answer:

6x-5= 7.62345791436

Step-by-step explanation:

The bag that contains​ pennies, nickels,​ dimes, and quarters have the total amount of 5.26 dollars.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

A bag contains 50 coins

Now, Number of pennies = 14% of 50

                               = 0.14 × 50

                               = 7 pennies

and, Number of dimes  = 40% of 50

                             = 0.40 × 50

                             = 20 dimes

Number of nickels = 6 more than pennies

                              = 6 + 7

                             = 13 nickles

Number of quarters = Rest of the coins

                               = 50 - (7 + 20 + 13)

                               = 50 - 40

                              = 10 quarters

As we know,

1 penny = 0.01 dollar

7 pennies = 0.01 ×7  = 0.07 dollar

1 dime = 0.10 dollar

20 dimes = 0.10 × 20 = 2.00 dollar

1 nickel = 0.05 dollar

13 nickel = 0.05 × 13 = 0.65 dollar

1 quarter = 0.25 dollar

10 quarter = 0.25 × 10 = 2.50 dollars

Total value of the coins in the bag = 0.07 + 2.00 + 0.65 + 2.50

                                                           = 5.22 dollars

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The measure of {x} for each case is -

{ 1 } : x = 45

{ 2 } : x = 54.5

Given is a quadrilateral and a pentagon.

{ 1 } -

We can write -

2x + 3x + x + 90 = 360

6x + 90 = 360

6x = 270

x = 45                                  ... { 1 }

{ 2 } -

We can write -

5(2x - 1) = 540

2x - 1 = 108

2x = 109

x = 54.5                                     ... { 2 }

Therefore, the measure of {x} for each case is -

{ 1 } : x = 45

{ 2 } : x = 54.5

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The initial amount of stickers given to each of the volunteers was 4 stickers while the final amount given to each of them was 6 stickers.

We are told that Mai gave each of the five volunteers the same number of stickers. Thereafter, she gave each of them 2 stickers each and the total was 30 stickers.

If the initial amount given to them each was y, then we have;

5(y + 2) = 30

y + 2 = 6

y = 6 - 2

y = 4

Thus, we can say that the amount of stickers she gave each of them initially was 4 stickers while the amount she gave them in total after the extra ones was 6 each

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Answer:

The answer would be part C

Step-by-step explanation:

First we find the gradient by y2-y1/x2-x1

So it would be;

3-1/4-8

2/-4

-1/2

Now we put in the gradient and the points (4,3) in the equation y=mx+c;

3=-1/2(4)+c

3=-2+c

3+2=c

5=c

Finally we put c in the equation;

y=mx+c

y=-1/2x + 5

Answer:

The sale price of the shoes is $52.

Step-by-step explanation:

100-35=65

x    =     65

80   =    100

x=65*80/100

x=52

Have a good day :)

If x is a continuous random variable then P(x≥A) =  P(X>A). So, the correct option is C, i.e., P(X>A).

For a continuous random variable, the probability of X taking any specific value is zero, since there are infinitely many possible values that X could take. Instead, we calculate the probability that X falls within a certain range of values.

To find the probability that X is greater than or equal to A, we can use the cumulative distribution function (CDF) of X, denoted as F(X). The CDF F(X) gives the probability that X is less than or equal to a certain value x, i.e., F(X) = P(X ≤ x).

Now, since the event X ≥ A is the complement of the event X < A, we can use the complement rule to write:

P(X ≥ A) = 1 - P(X < A)

Using the definition of CDF, we get:

P(X ≥ A) = 1 - F(A)

Therefore, the probability of a continuous random variable X being greater than or equal to a certain value A is P(X>A) = 1 - F(A). This is the correct option C in the given question.

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Complete question is:

If x is a continuous random variable then P(x≥A)=

A. P(X<A)  

B. 1-P(X>A)

C. P(X>A)

D. 1-P(X≥A-1).

The angles Θ are:

Θ = 45°

Θ = 225°

If tan = 1, the angle can be found by taking the inverse tangent (or arctan) of 1.

Because tangent is positive in the first and third quadrants, we must examine angles ranging from 0° to 360° that fall within those quadrants:

We have the following in the first quadrant:

arctan(1) = 45° if tan = 1

We have the following in the third quadrant:

225° = tan = 1 + 180° = arctan(1)

As a result, the possible angles for are 45° and 225°, which satisfy the equation tan = 1.

As a result, the angles are:

Θ = 45°

Θ = 225°

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The sentence that describes the next step in the construction is; D: draw a line through points C and D

The steps that are used to bisect a line segment are;

1) Place the compass at one end of line segment.

2) Adjust the compass to slightly longer than half the line segment length

3) Draw arcs above and below the line.

4) Keeping the same compass width, draw arcs from other end of line.

5) Place ruler where the arcs cross, and draw the line segment.

From the given procedure and looking at the image, we can say that the next logical step would be to draw a line through points C and D

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Answer: The conversion of a raw score to a scaled LSAT score is a complex process that involves several steps. The Law School Admission Test (LSAT) is a standardized test used by law schools in the United States and Canada to assess applicants' critical thinking, reading comprehension, and analytical reasoning skills.

Here's a general overview of the process of converting a raw score to a scaled LSAT score:

- Raw score calculation: The raw score is the number of questions answered correctly on the LSAT. There is no penalty for incorrect answers, so it is in your best interest to answer every question, even if you are unsure of the correct answer.

- Equating: The LSAT is equated to account for differences in difficulty between test forms. This means that the raw scores of test-takers are adjusted so that the scaled scores are consistent across different test forms.

- Scaling: The raw scores are then scaled to a range of 120 to 180, with a median score of 150 and a standard deviation of 10. This scaling process allows for meaningful comparisons between test-takers, regardless of the difficulty of the specific test form they took.

It is important to note that the LSAT score is not based solely on the number of questions answered correctly, but also on the difficulty of the questions. This means that a high raw score on a particularly difficult test form may result in a lower scaled score than a lower raw score on a less difficult test form.

Step-by-step explanation:

The graph will show a proportional relationship if it is a linear function with an intercept of zero.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

Hence from the definition the features of the graph of a proportional relationship are given as follows:

The problem is incomplete, hence the procedure to verify if the graph is a proportional relationship is presented.

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Answer:

  1/3

Step-by-step explanation:

You want to know the ratio of the difference in median wait times to the IQR for the box plots shown.

The median is the line in the middle of the box. The medians are ...

The difference in median wait times is 11 -9 = 2 min.

The IQR is the difference between the upper end of the box and the lower end. The IQRs are ...

The ratio of the difference in medians to the IQR is ...

  (median difference) / (IQR) = (2 min)/(6 min) = 1/3

The difference in medians is 1/3 times the IQR.

__

Additional comment

The problem already tells you the difference of medians and the IQR, so all you need to do is express than as a ratio.

  difference = k × IQR

  k = difference/IQR = 2/6 = 1/3

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This can be solved by using the geometric mean theorem. The altitude drawn to the hypotenuse is the geometric mean of the lengths of the segments of the hypotenuse. The geometric mean is numbers for which this statement is true: a/x = x/b where a and b represent 2 numbers. So filling in a/x = x/b with the given information gives you 36/x = x/9. You can then solve by using the means-extremes property. x^2 = 324  

x = 18

The variable that the friends must consider when calculating the cost of the mountain bike tour is the number of hours they would be on the tour.

The group of friends will have to pay $ 90 to rent the equipment needed for the bike tour which means this is a cost that cannot change and so there is no need worrying about it as a variable.

The only variable that the friends should consider is the number of hours that they would need to go on the mountain bike tour as the total cost will increase based on the number of hours that they spend on the bike tour.

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The question is:

At the campground, the friends sign up to go on a mountain bike tour. It costs $90 to rent the equipment and $100 per hour for a group of four.

What variable must the friends consider when calculating the cost of the mountain bike tour?

The total number of beings surveyed is given by the equation A = 20

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the total number of beings surveyed be represented as A

Now , the percentage of beings preferred pisquet juice = 30 %

The number of beings who preferred pisquet juice = 6

Substituting the values in the equation , we get

( 30 ) % of A = 6   be equation (1)

On simplifying the equation , we get

( 30/100 )A = 6

Multiply by 100 on both sides of the equation , we get

30A = 600

Divide by 30 on both sides of the equation , we get

A = 600/30

A = 20

Therefore , the value of A is 20

Hence , the number of beings is 20

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The sentence that best describes the next step in the construction of a square inscribed in a circle include the following: D. draw a line through points C and D.

In Mathematics, a line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points. Additionally, a line segment typically has a fixed length.

In this scenario, the first step in the construction of a square inscribed in a circle is to draw line segment AB and then place your compass needle on any of the endpoints of line segment AB with arcs above and below, named line segment CD.

Furthermore, you should draw a straight line through point C and point D, wherein, line segment CD represent the perpendicular bisector of line segment AB.

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Answer:180-128=52

Step-by-step explanation:

opposite supplementary angles

Answer:

(a) 61.5%

Step-by-step explanation:

(a) $36.90/$60*100%= 61.5%

The triangular area abc, from the graph on the market for gasoline represents, D. the deadweight loss (or excess burden) created by the tax.

The cost of market inefficiency, which happens when supply and demand are out of balance, is known as a deadweight loss. When supply and demand are out of equilibrium, a deadweight loss arises, which impairs the efficiency of the market.

Deadweight losses may result from price floors, such as minimum wage and living wage regulations, price ceilings like price controls and rent restrictions, and taxation. A society's resource distribution may also become inefficient with a decline in commerce.

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Answer: This question is asking for the range of the graph, which is the set of all possible values of the dependent variable (y-coordinate) in the graph.

Based on the options given, the correct range is:

D x:-2,-1,0,2,5 Y: 0,2,1,0,2

The range of this graph is {0, 1, 2}.

Step-by-step explanation:

Using the conversion from microgram to milligram, we get, 10mcg is equal to 0.01mg.

1 mcg (microgram) is equal to 0.001 mg (milligrams). Therefore, to convert 10mcg to mg, we simply need to multiply 10 by 0.001:

10 mcg * 0.001 mg/mcg = 0.01 mg

So, 10mcg is equal to 0.01mg.

To explain further, the prefix "micro" means one millionth (1/1,000,000), while the prefix "milli" means one thousandth (1/1,000). Therefore, to convert a value from micrograms to milligrams, we need to divide the value by 1000 (or multiply by 0.001), because there are 1000 micrograms in a milligram. It is important to use the correct units when working with medication dosages, as small differences in dose can have significant effects on the patient's health.

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The simplified expression for this problem is given as follows:

18a³ - 4a²b² - 2b³.

The expression for this problem is defined as follows:

3a(6a² - 4ab²) + 8a²b² - 2b³.

Applying the distributive property to the term 3a(6a² - 4ab²) , we have that:

3a(6a² - 4ab²) = 18a³ - 12a²b².

Hence the expression can be written as follows:

18a³ - 12a²b² + 8a²b² - 2b³.

-12a²b² + 8a²b² are like terms, hence:

-12a²b² + 8a²b² = -4a²b².

Meaning that the simplified expression is given as follows:

18a³ - 4a²b² - 2b³.

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