What is the prime factorization of 51?

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 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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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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Answer:

Step-by-step explanation:

y(xy+1)

Answer:

xy^2+y = y(xy + 1)

Step-by-step explanation:

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:

90 degrees

Step-by-step explanation:

10 + 3 + 7 = 20

10/20 x 180 = 90 degrees

Hope this helped :)

Answer:

The largest angle is 90 degree[10]

Step-by-step explanation:

Let 10:3:7 be x

10x+3x+7x = 180 [ angle sum property of a triangle ]

20x = 180

x=180/20

 =9/1

 =9

10x=10*9=90

3x=3*9=27

7x=7*9=63

90>63>27

therefore the largest angle is 90 degree.

x^2 + (y – 3)^2 = 36

Step-by-step explanation:

The standard equation of a circle with center at (h, k) and radius r is

(x - h)^2 + (y - k)^2 = r^2.

If the center lies on the y-axis, then h = 0:  (x - 0)^2 + (y - k)^2 = r^2

If the circle diameter is 12, then the circle radius is 6, and so r^2 = 36

So, among the given equations, your

x^2 + (y – 3)^2 = 36 is correct (but only if you use " ^ " for exponentiation).

The required y-coordinate of system of equation is -3.

The second component of an ordered pair is a y-coordinate. The y-coordinate denotes the directional separation of the point from the x-axis when an ordered pair is graphed as the coordinates of a point in the coordinate plane. The ordinate is another term for the y-coordinate.

We have,

y = x/2 - 4 and y = -2x + 1

Equate both equation

x/2 - 4 = -2x + 1

x - 8 = -4x + 2

5x = 10

x = 2

Then,

y = -2x + 1

y = -2(2) + 1

y = -4 + 1

y = -3

Thus, required y-coordinate of system of equation is -3.

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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 :)

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:

Answer:180-128=52

Step-by-step explanation:

opposite supplementary angles

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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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.

Answer:

(a) 61.5%

Step-by-step explanation:

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

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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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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The Option that is common to the formation of all fossil fuels is: fossils are converted into carbon-rich fuels. The Option A is correct.

Fossil fuels are gotten from the decomposition of plants and animals. These fuels, which can be found in the Earth's crust and contain carbon and hydrogen, can be burned for energy. Fossil fuels include coal, oil, and natural gas.

Coal is a material that is typically found in sedimentary rock deposits where layers of rock and dead plant and animal matter are piled up. More than half of the weight of a piece of coal must come from fossilized plants. Oil was discovered as a solid material between layers of sedimentary rock, such as shale.

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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°

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

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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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:

6x-5= 7.62345791436

Step-by-step explanation:

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?

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:[tex]x=12[/tex]

Step-by-step explanation:

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).

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

The side lengths form a proportional relationship, and the ratios are given as follows:

17.955/11.97 = 14.565/9.71 = 5.415/3.61.

Similar triangles are triangles that share these two features presented as follows:

For this problem, the triangles are similar, as they have the same angle measures, and thus the side lengths form a proportional relationship, as the equivalent side lengths have a ratio of 1.5.

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The justification for step 1 in the solution process of equation 8x + 15 = 11x + 2 will be to substitute the negative sign before the number 13.

An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.

The equation is given below.

8x + 15 = 11x + 2

Simplify the equation for 'x', then we have

8x + 15 = 11x + 2

8x = 11x + 2 - 15

8x = 11x - 13

The justification for step 1 in the solution process of equation 8x + 15 = 11x + 2 will be to substitute the negative sign before the number 13.

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