Which term is missing when using the square root method

Answer:

The tangent of theta is -1/3.

Explation step-by-Step

The tangent of theta is -1/3. This is calculated as follows:

cot theta = -√3

cot theta = 1/tan theta

-√3 = 1/tan theta

-1/3 = tan theta

They are similar by the property of SAS and the factor by which the triangle grows is 1.25

The number 2755 flights were scheduled.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Recently many airlines have had to cancel flights in a single day.

Republic airlines had to cancel 416 flights representing 15.1% of the airlines' scheduled flights.

The number of flights scheduled,

= 416 x 100/ 15.1

= 41600/15.1

= 2754.96

≈ 2755

Therefore, 2755 flights were scheduled.

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The volume of the soil that it holds in cubic yards is 11.1.

A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.

Given:

A raised flower bed is 25 feet long 8 feet wide and 1.5 feet deep.

In yards,

a raised flower bed is 8.33 yards long, 2.67 yards wide, and 0.5 yards deep.

The volume of the soil that it holds,

= 8.33 x 2.67 x 0.5

= 11.10 cubic yards.

Therefore, the volume is 11.1 cubic yards.

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Storm moving toward austin at speed of -10 mph.

To find the speed of the storm at 4:00 PM, we need to find the rate of change of the distance of the storm from Austin at that time. To do this, we can use the derivative of the function s(t) = 5 + 14t - 3t^2, which represents the distance of the storm from Austin.

s'(t) = 14 - 6t

At t = 4 hours, or 4:00 PM, the speed of the storm is given by:

s'(4) = 14 - 6 * 4

s'(4) = 14 - 24

s'(4) = -10 mph

So, the storm will be moving at 10 mph towards Austin at 4:00 PM.

Therefore, the answer is: 6. storm speed = -10 mph, storm moving toward Austin.

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The value of the sin(2θ) is given as follows:

-24/25.

We are given the cosine of the angle, hence the following identity must be considered:

sin²(θ) + cos²(θ) = 1.

Considering the value of the cosine, the value of the sine is obtained as follows:

sin²(θ) + (3/5)² = 1

sin²(θ) = 16/25

sin(θ) = -4/5 -> apply the square root, angle in the fourth quadrant is negative.

Then the sine of twice the angle is obtained as follows:

sin(2θ) = 2sin(θ)cos(θ)

Hence:

sin(2θ) = 2 x (-4/5) x (3/5) = -24/25.

Meaning that the correct option is the third option.

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The number of ways that at least two of the freshmen are at the ends of the line and at least two of the sophomores are standing next to each other will be 9.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

A debate team consists of 5 freshmen and 4 sophomores. (Everyone is distinguishable.)

⇒ (3 x 3)

⇒ 9

The number of ways that at least two of the freshmen are at the ends of the line and at least two of the sophomores are standing next to each other will be 9.

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The equation which can be used to model this situation is equals to the h = 1.9t + 14 , where h represents the water level , t represents the time in minutes.

We have, A water tank which is filled with water. Before pumping the water,

The level i.e., high of water in water tank

= 14 inches

After 20 minutes, the level of water in tank = 52 inches

We have to determine the equation to model this situation in form of time "t" in minutes. Let "h" be level of water increases from initial point/ level in t minutes. As the change in water level from initial to after 20 minutes = 52 inches - 14 inches = 38 inches

That is, water level increased 38 inches in 20 minutes. Then rate of increase in level = 38/20 = 1.9 inches per minutes

Now, the for time 't' the equation is formed by multiplying the rate of chenge of water level with 't' and adding initial water level.

=> h = 1.9t + 14

which is linear equation in two variables,i.e., h and t . Hence,the required equation model is h = 1.9t + 14 .

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The addition of the given fraction numbers 3(3/8) and 7(3/4) is, 89/8

Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.

Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.

Given that,

Two fraction numbers,

3(3/8) and 7(3/4)

The addition of two fraction number is,

⇒  3(3/8) + 7(3/4)

In simple form it can be written as,

⇒   24+3/8 + 28+3/4

⇒    27/8 + 31/4

LCM Of 8 & 4

=  8

⇒  27/8 + 31×2/4×2

⇒  27/8 + 62/8

⇒  (27 + 62)/8

⇒   89/8

Hence, the result is 89/8

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The value of x in the triangle is 23.83

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

A right triangle

The value of x can be calculated using the following tangent equation

tan(40) = 20/x

Make x the subject of the equation

x = 20/tan(40)

Evaluate

x = 23.83

Hence, the value of x is 23.83

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The area of the parallelogram with vertices p(3, 3, 2), q(5, 6, 4), r(9, 10, 12), and s(7, 7, 10) is √336≈18.34 units.

A unique variety of quadrilateral made up of parallel lines is called a parallelogram. A parallelogram can have any angle between its neighboring sides, but it must have opposite sides that are parallel for it to be a parallelogram.

Calculate the length of PQ → Position vector of Q - Position vector P

PQ→ (5-3)i + (6-3)j + (4-2)k

PQ→ 2i + 3j + 2k

Calculate the length of PS →Position vector of S - Position vector P

PQ→ (7-3)i + (7-3)j + (10-2)k

PQ→ 4i + 4j + 8k

Area of parralelogram = [tex]\left[\begin{array}{ccc}i&j&k\\2&3&2\\4&4&8\end{array}\right][/tex]

= √16² + 8² + 4²

=√336

=18.34 units

The area of a parallelogram is the region bounded by the parallelogram's four sides. It is measured in square units like cm2, m2, and inch2 and can be computed if we know the size of the parallelogram's base and height.

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The total area of all of the pieces is;

Total Area = 4x + 4y + 3xy + 6x² + y²

Area is the amount of space occupied by a 2-dimensional figure. It is the quantity that measures the number of unit squares that cover the surface of a closed figure. The word 'area' means a vacant surface. The area of a shape is calculated with the help of its length and width. Length is unidimensional and measured in units such as feet (ft), yards (yd), inches (in), etc.

From the diagrams, we have the following shapes;

Rectangle (x,1) = 4 x X x 1

Rectangle (y,1) = 4 x y x 1

Rectangle (x,y) = 3 x x x y

Square (x,x) = 6 x X x X

Square (y,y) = 1 x y x y

Total Area = 4x + 4y + 3xy + 6x² + y²

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The area of the given region that is enclosed by a cardiod r = 20+20sinθ, is 600π

A definite integral is a formal calculation of area beneath a function, using infinitesimal slivers or stripes of the region.

Given that, we need to find an area for region that is enclosed by a cardiod

r = 20+20sinθ

Using definite integral,

[tex]\frac{1}{2}\cdot \int _0^{2\pi }\left(20+20\sin \left(\theta\right)\right)^2d\theta[/tex]

= [tex]\frac{1}{2}\cdot \int _0^{2\pi }\left(400+400\sin^2 \left(\theta\right)+800sin\theta\right)d\theta[/tex]

= [tex]\frac{1}{2}\cdot \int _0^{2\pi }\left(400+400(\frac{1-cos2\theta}{2})+800sin\theta\right)d\theta[/tex]

= [tex]\frac{1}{2}\cdot \int _0^{2\pi }\left(600+200cos2\theta}+800sin\theta\right)d\theta[/tex]

= [tex]\frac{1}{2}\cdot \:1200\pi[/tex]

= [tex]600\pi[/tex]

Hence, the area of the given region that is enclosed by a cardiod

r = 20+20sinθ, is 600π

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In a poker hand consisting of 5 cards, the probability of holding 3 kings is   0.0009 .  

The probability of holding 3 kings in a poker hand of 5 cards can be calculated as follows:

The number of ways to choose 3 kings from a deck of 4 kings is= ⁴C₃ = 4.

The number of ways to choose 2 other cards from the remaining 48 cards is = ⁴⁸C₂ = 1128.

The total number of 5-card hands from a standard deck of 52 cards is = ⁵²C₅ = 2598960.

So , the probability of holding 3 kings in a 5 card hand is

⇒ (4 × 1128)/2598960

⇒ 4512/2598960  .

⇒ 0.00085148 .

Therefore , probability of holding 3 kings in a 5card hand is approximately 0.0009 .

The given question is incomplete , the complete question is

In a poker hand consisting of 5 cards, find the probability of holding  3 kings .

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Step-by-step explanation:

1 ounce = 28 grams

48 ounce = 1344 grams

So, 1344 grams would be in a 48-ounce sample.

The equation of the line is passing through a point (6, 2) and is perpendicular to the line 3x-2y = 7 is y = -2x/3 + 8

The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point

Given that, a line is passing through a point (6, 2) and is perpendicular to the line 3x-2y = 7, we need to find the equation of the line,

The line is

3x-2y = 7

Converting into slope-intercept form,

3x-2y = 7

2y = 3x - 7

y = 3x/2 - 7/2

We know that, the slopes of two perpendicular lines are negative reciprocal of each other,

Therefore, the slope of the asked line = -2/3

Therefore, the equation of the asked line is, y = -2x/3 + c....(I)

Put x = 6 and y = 2 in equation to find c,

2 = -4 + c

c = 8

Therefore, put c = 8 in equation (i)

y = -2x/3 + 8

Hence, the equation of the line is passing through a point (6, 2) and is perpendicular to the line 3x-2y = 7 is y = -2x/3 + 8

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The amount of money Intel pay Bally is given by the equation A = $ 8,232

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount be represented as A

Now , the equation will be

The total invoice amount = $ 14,000

The trade discount given by Intel = 40 %

So , the amount of discount = trade discount x total invoice amount

Substituting the values in the equation , we get

The amount of discount = ( 40/100 ) x 14000

The amount of discount = 0.4 x 14000

The amount of discount = $ 5600

So , the amount after 40 % discount = total invoice amount - amount of discount

Substituting the values in the equation , we get

The amount after 40 % discount = 14,000 - 5,600

The amount after 40 % discount = $ 8,400

And , 2/10 means 2%discount if the amount received within 10 days

So , the amount after 2 % discount = amount after 40 % discount - ( 2/100 ) x amount after 40 % discount

Substituting the values in the equation , we get

The amount after 2 % discount A = 8400 - 0.02 x 8400

The amount after 2 % discount A = $ 8400 - $ 168

The amount after 2 % discount A = $ 8,232

Hence , the amount is $ 8,232

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A total of 11 classes should be suggested to construct a frequency distribution.

A value's frequency is the number of times it occurs or takes place. In a frequency table, a list of objects is presented together with the frequency of each item.

The quantity of observations that take place during a specific predetermined timeframe is the frequency of a class interval. Therefore, if 20 individuals between the ages of 5 and 9 are found in the data from our study, the frequency for the 5–9 age range is 20.

The frequencies of each category are represented individually in a frequency graph; the frequencies of each category are shown cumulatively.

By doing so, we are able to analyze the data's distribution in greater detail than we could have done by using a frequency polygon and performing statistics.

If k is the number of classes and n is the number of observations, then for number of classes we should select the smallest k such that  

[tex]2^k > n[/tex] ( 2 to k rule)

In our case, the no. of observations is 2000

i.e.

2¹⁰ = 1024 < 2000

With this,

2¹¹ = 2048 > 2000

Thus, A total of 11 classes should be suggested to construct a frequency distribution.

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Answer:

Below

Step-by-step explanation:

145 yr / 29 yr/double = 5 doubles

6595 x 2 ^5 = 211 040  ppl

In order to calculate the exact closed form bound of the number of times function F is called in each code segment, we need to consider the number of times F is called in each line of code.

For the initial call of F(n^2), the number of times F is called depends on the value of n. To calculate the exact number of calls for any value of n, we can use a recursive approach, starting from the top line of code and working our way down.

For example, for n=4, the initial call of F(16) will call F(4), which will then call F(1) four times, for a total of 5 calls. For n=8, the initial call of F(64) will call F(16), which will call F(4) four times and F(1) sixteen times, for a total of 20 calls.

Thus, for any value of n, the exact closed form bound of the number of times function F is called is given by the formula [1]:

Where the number of terms in the summation is equal to the number of times n is divided by 4 before it reaches 1.

For example, for n=16, the summation will have four terms (n=16, n=4, n=1), and for n=32, the summation will have five terms (n=32, n=8, n=2, n=1).

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Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

The dilation of the image means expanding the image or reducing the image. In this case, the two figures will be similar in shape but not necessarily in size. In dilation, the new shape remains the same even if the original is larger or smaller.

According to the figure AB=1. AC=4

A'B' = 3, A'C' = 12

FAB'=3AB [A'C' = BAC

So, the scale factor is 3

Dilation is a method for producing comparable numbers. By increasing distances by the scale factor, each point is extended outwards from the center point D. (If the scale factor is more than one, go outwards.)

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Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

The dilation of the image means expanding the image or reducing the image. In this case, the two figures will be similar in shape but not necessarily in size. In dilation, the new shape remains the same even if the original is larger or smaller.

A. [tex]$T(x, y) \rightarrow(-x, -y)$[/tex]

This is a reflection to the origin that does not preserve angles or aspect proportions. Therefore, triangle ABC under this transformation does not resemble that image.

Example: [tex]$T(x, y) \rightarrow(x, x-y+1)$[/tex]

This is a shear transformation that does not preserve angles or aspect ratio. Therefore, triangle ABC under this transformation does not resemble that image.

C. [tex]$T(x, y) \rightarrow(x+3, y)$[/tex]

This is a translation that preserves angles and aspect ratio. So the triangle ABC under this transformation resembles that image.

D. [tex]$T(x, y) \rightarrow(0.2x, 4y)$[/tex]

This stretches by a factor of 0.2 in the x direction and 4 in the y direction, preserving angle and horizontal proportions. So the triangle ABC under this transformation resembles that image.

E. [tex]$T(x, y) \rightarrow(2x, 2y)$[/tex]

This is a stretch by a factor of 2 in both the x and y directions, preserving the proportions of the angles and sides. So the triangle ABC under this transformation resembles that image.

F. [tex]$T(x, y) \rightarrow(3x, 4y)$[/tex]

This stretches by a factor of 3 in the x direction and 4 times in the y direction, preserving the proportions of angles and sides. So the triangle ABC under this transformation resembles that image.

Therefore, the similarity-preserving transformations between triangle ABC and its image are C, D, E, and F. 

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what is a discrete variable and example?

Discretized variables require a certain amount of time to count. Consider counting the coins in your pocket as an example. Your bank account's funds can be counted. The balances in each person's bank accounts might also be added up. Even if it may take some time to count the last thing, it is still a countable item.

what is a Continuous Variable and example?

Counting continuous variables would literally take an eternity. In actuality, you would reach "forever" and never reach the end of the list. Consider age as an example. Age cannot be measured. why not Considering that it would take an eternity? For instance,

Twenty-five years, ten months, two days, five hours, four seconds, four milliseconds, eight nanoseconds, 99, and so on.

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The full question would be just part 1.

Explain the difference between a discrete variable and a continuous variable.

The cost of students ticket is $37.5and the cost of general admission is $187.5.

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.

Assume s be the students tickets cost and g be the general admission cost.

From the given information,

⇒  s + g = 225             ..(1)

 5s + 7g = 1500         ..(2)

From equation (1),

s = 225 - g

Plug the value of s in equation (2)

5(225 - g) + 7g = 1500

1125 - 5g + 7g = 1500

                  2g = 1500 - 1125

                  2g = 375

                    g = 187.5

Plug g = 125 in equation (1),

s + 187.5= 225

        s = 225 - 187.5

        s = 37.5

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The predicted end-of-year value of the portfolio can be calculated as follows:

What is a mathematical expression?

A statement, at least two variables or integers, and one or more arithmetic operations make up a mathematical expression. This mathematical procedure makes it possible to multiply, divide, add, or subtract quantities. The expression structure is as follows: Expression: Math Operator, Number/Variable, Math Operator

s = $200

b = $100

1.08s = 1.08 * $200 = $216

1.02b = 1.02 * $100 = $102

Therefore, the predicted end-of-year value of the portfolio is $216 + $102 = $318.

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Answer:

8

Step-by-step explanation:

It would be best if you put in the calculator. Have a good day.

The correct option is (A).

The following statements follows logically from the statements is there are students who are taking art but not literature.

"None of the students taking literature are taking physics."

So: if you are student taking literature, then you are not taking physics.

⇒TL=Taking Literature

⇒TP=Taking Physics

⇒TA=Taking Art

⇒TR=Taking Rhetoric

P1: TL ==> not TP

TP ==> not TL

"but several of the students taking physics are taking art."

So: some of the students taking physics are also taking art.

Q1: TP-some-TA

TA-some-TP

"In addition, none of the students taking rhetoric are taking physics."

So: if you are a student taking rhetoric, then you are not taking physics.

P2: TR ==> not TP

TP ==> not TR

Answer choice (A) states: "There are students who are taking art but not literature."

So: some students who are taking art are not taking literature.

(A): TA-some-not TL

not TL-some-TA

Can we logically infer this from the statements above? Yes.

Remember we can combine a quantifier statement with a Sufficient & Necessary statement if the right-hand side variable of the quantifier statement is the same as the sufficient condition of the Sufficient & Necessary statement. We have that with P1 and Q1.

So, we can combine Q1 to P1 like so: TA-some-TP ==> not TL to infer: TA-some-not TL, so the correct option is (A).There are students who are taking art but not literature.

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The expression that  represents the total number of points Victoria scored in the basketball games for the whole season is,

5x + 9.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.

Given:

Victoria scored a total of 9 points in the first basketball game of the season.

She scored 5 points per game in each of the other x basketball games she played that season.

That means, 5x is the score.

The expression that  represents the total number of points Victoria scored in the basketball games for the whole season is,

5x + 9.

Therefore, the expression is 5x + 9.

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The complete question:

Victoria scored a total of 9 points in the first basketball game of the season. She scored 5 points per game in

each of the other x basketball games she played that season.

Which of the following expressions represents the total number of points Victoria scored in the basketball games for the whole season?

The perimeter of a parallelogram P=102mm.

The perimeter of a parallelogram is defined as the total length of the boundaries, surrounding it. The sum of all the sides of a parallelogram is known as the perimeter of a parallelogram.

The formula for the perimeter of a parallelogram:

P=2(a+b).

There are some properties of a parallelogram:

The given information is slant height is 17, height is 24 and breadth is 27.

substitute the given values in the above formula.

P=2*(24+27)

P=2*(51)

P=102.

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The value for n(A ∩ [tex]B^c[/tex]) is {3}

Option D is the correct answer.

A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.

We have,

Set A = {1, 3}

Set B = {1, 7}

U = {1, 3, 5, 7}

[tex]B^c[/tex] = U - B = {3, 5}

A ∩ [tex]B^c[/tex].

= Numbers that are common to both A and [tex]B^c[/tex].

= {3}

Thus,

n(A ∩ [tex]B^c[/tex]) = {3}

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Answer:

7x^3 + 2x^2 - x

Step-by-step explanation:

To subtract the two expressions (9x^3-4x^2+2x) and (2x^+6x^2-3x), we will need to line up the terms with the same exponent and subtract them.

(9x^3-4x^2+2x) - (2x^+6x^2-3x)

= (9x^3 - 2x^3) + (-4x^2 + 6x^2) + (2x - 3x)

= 7x^3 + 2x^2 - x

So the result of the subtraction is 7x^3 + 2x^2 - x

Please note that if you want to simplify the result further, you can combine like terms.