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Therefore , the solution of the given problem of trigonometry comes out to be the exact value of tanθ in simplest radical form is:

tanθ  = 7/2.

connections between trigonometry and cubic slope The field of mathematics is believed to have been established around the fourth millennium BC, when scientists and professions came together. Many geometric problems can be resolved using precise mathematical techniques, and these techniques can also be used to predict the results of calculations. Trigonometry is the study of the six basic trigonometric operations.

Here,

We can use the Pythagorean theorem to find the length of the hypotenuse of the right triangle formed by the terminal side of the angle θ and the x and y axes.

The distance from the origin to the point (2,7) is the hypotenuse, so we have:

r = √{2²+7²} = √53

Since $\tan\theta$ is the ratio of the opposite side to the adjacent side, we have:

tanθ  = 7/2

Therefore, the exact value of tanθ in simplest radical form is:

tanθ  = 7/2.

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Answer:

We can use the following logarithmic identities to simplify the expression:

log a + log b = log (ab)

log a - log b = log (a/b)

n log a = log (a^n)

Using these identities, we can simplify the expression as follows:

1/2(log₂x + log₂y) - 5 log₂(x+6)

= 1/2 log₂(xy) - log₂(x+6)^5 (using the first two identities)

= log₂[(xy)^(1/2)/(x+6)^5] (using the third identity to combine the logarithms)

Therefore, the simplified expression is:

log₂[(xy)^(1/2)/(x+6)^5]

Step-by-step explanation:

A perpendicular line calculator online is a tool used to find the equation of a line that is perpendicular to a given line and passes through a given point.

A perpendicular line calculator online is a math tool used to find the equation of a line that is perpendicular to a given line and passes through a given point. To use this calculator, users input the slope and y-intercept of the given line, as well as the x- and y-coordinates of the given point.

The calculator then uses the formula for the slope of a perpendicular line to find the slope of the new line and calculates the y-intercept by plugging in the given point. This tool is useful in many applications, such as finding the equation of a perpendicular bisector, a perpendicular tangent line, or a perpendicular distance between two points.

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3x=108

and y= 54

by linear pair angle

the initial value problem dy/dt = 5y, y(0) = y0, the solution has a vertical asymptote at t = 4 only when y0 = 0, and the time interval of existence is the entire real line, (-∞, ∞).

The initial value problem given is: dy/dt = 5y, y(0) = y0

The solution to this differential equation is: y(t) = y0 × e⁽⁵t⁾

To find the value(s) of y0 for which the solution has a vertical asymptote at t = 4, we need to set t = 4 and solve for y0 such that the solution becomes infinite.

y(4) = y0 × e⁽⁵ˣ⁴⁾ = y0 × e²⁰

For the solution to have a vertical asymptote at t = 4, y0 × e²⁰ must be infinite. This means that y0 must be equal to 0.

Next, we need to determine the time interval of existence C<4 for the solution. The solution is continuous and differentiable for all values of t, so the time interval of existence is the entire real line, (-∞, ∞). Therefore, for the initial value problem dy/dt = 5y, y(0) = y0, the solution has a vertical asymptote at t = 4 only when y0 = 0, and the time interval of existence is the entire real line, (-∞, ∞).

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In this problem, the lower limit of integral is -3 and the upper limit of integration is 3.

We can use the formula for the surface area of a solid of revolution generated by a curve revolving around a given axis. The formula is S = 2π ∫ a b y dx, where a and b are the lower and upper limits of integration, and y is the height of the curve at x. In this problem, the lower limit of integration is -3 and the upper limit of integration is 3. Substituting y = 1/16(e^8x + e^-8x) into the equation gives S = 2π ∫ -3 3 (1/16(e^8x+e^-8x)) dx. Integral this expression gives S = 10512π.

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From the given information provided, the first three common denominators of 7/9 and 2/3 are 9, 18, and 27.

To find the common denominators of 7/9 and 2/3, we need to find the least common multiple (LCM) of their denominators.

The prime factorization of 9 is 3 x 3, and the prime factorization of 3 is 3.

The prime factorization of 2 is 2, and the prime factorization of 3 is 3.

The common factors are 3, so the LCM of 9 and 3 is 9.

Therefore, the common denominator of 7/9 and 2/3 is 9.

To find the next two common denominators, we can continue to find the LCM of the denominators with the added factor of 9.

The prime factorization of 18 (2 x 3 x 3) includes the prime factors of 9, so it is a common denominator.

The prime factorization of 27 (3 x 3 x 3) also includes the prime factors of 9, so it is another common denominator.

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Answer:

[tex] \sf \: a) \: 2x + 7y - 2 [/tex]

[tex] \sf \: c) \: 7y - 2 + 2x [/tex]

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The expression is,

→ -2x + 3 + 7y + 4x - 5

Let's simplify the expression,

→ -2x + 3 + 7y + 4x - 5

→ -2x + 4x + 7y + 3 - 5

→ (-2x + 4x) + (7y) + (3 - 5)

→ (2x) + 7y + (-2)

→ 2x + 7y - 2

→ 7y - 2 + 2x

Hence, option (a) & (c) is correct.

Step-by-step explanation:

-2x + 3 + 7y + 4x - 5 = 2x + 7y - 2

as addition is commutative (= can be done in any sequence of terms), the right answers are variations in the sequence of these 3 terms :

A and C are correct.

B and D disqualify themselves right away by including mixed terms of xy. you can never ever create such a mixed term just out of addition or subtraction of single x and y terms. you need multiplication to do that. but there is none.

The sale price of the green beans represents a decrease of 16.67% compared to the original price of the beans.

To find the percent increase or decrease in the price of a can of green beans during the sale, we need to compare the sale price with the original price.

During the sale, the green beans were sold at a rate of 3 cans for $1.25, or approximately 41.67 cents per can:

Sale price per can = $1.25 / 3 = $0.4167 ≈ 41.67 cents

The original price of a can of green beans was 50 cents.

To find the percent increase or decrease in the price, we can use the following formula:

Percent increase or decrease = ((New value - Old value) / Old value) x 100%

Substituting the values, we get:

Percent increase or decrease = ((0.4167 - 0.5) / 0.5) x 100%

Percent increase or decrease = (-0.0833 / 0.5) x 100%

Percent increase or decrease = -16.67%

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The value of volume 750 ml after converting to cups is 3.17 cups.

The conversion is useful when you need to measure liquids in cups instead of milliliters, especially if you are following a recipe that is written in cups instead of milliliters.

To convert 750ml to cups, you need to know that one cup is equal to 236.6ml. Knowing how to make the conversion can help you get the right measurements and produce accurate results in your cooking or baking. To do the conversion, divide 750 by 236.6 to get the answer in cups.

So, 750ml / 236.6ml per cup = 3.17 cups (rounded to the nearest hundredth).

Therefore, volume of 750ml is equivalent to 3.17 cups.

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Answer:310.45

Step-by-step explanation:

The equation for split times is 4x= 198.608  and the value of x is 49.652

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Let x be the split time

all 4 of the split times were the same.

4x= 198.608

=> x= 198.608/4 = 49.652

The equation for split times is 4x= 198.608  and the value of x is 49.652

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Answer: -20

Step-by-step explanation:

2(-1 x 3 - 7)

2(-3-7)

2(-10)

-20

Answer:

[tex]\huge\boxed{\sf -20}[/tex]

Step-by-step explanation:

= 2(xy - 7)

Put x = -1, y = 3

= 2[(-1)(3) - 7]

= 2(-3 - 7)

= 2(-10)

[tex]\rule[225]{225}{2}[/tex]

93 centimeter is approximately equal to 36.6142 inches ( rounded to four decimal places )

To convert 93 cm to inches, we can use the following formula:

1 cm = 0.393701 inches

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The length in inches = conversion factor × The length in centimeter

Substitute the values in the equation

93 cm = 93 x 0.393701

Multiply the numbers

= 36.6142 inches ( rounded to four decimal places )

Therefore, 93 centimeter is 36.6142 inches

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To calculate the standard deviation of the sampling distribution of p-hat, the answer will be 59 students.

By calculating,

600/10=60 and 59 students which is less than 10% of the population.

A sampling distribution, also known as a finite-sample distribution, in statistics is the probability distribution of a given random-sample-based statistic. The sampling distribution is the probability distribution of the values that the statistic takes on if an arbitrarily large number of samples, each involving multiple observations (data points), were used separately to compute one value of a statistic (such as, for example, the sample mean or sample variance) for each sample. Although only one sample is frequently observed, the theoretical sampling distribution can be determined.

Because they offer a significant simplification before drawing conclusions using statistics, sampling distributions are crucial in the field. They enable analytical decisions to be made based on the probability distribution of a statistic rather than the combined probability distribution of all the individual sample values

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The solution set of the given homogeneous system in parametric vector form is x = (0, 0, t), where t is a real number

Vectors are an important mathematical tool for representing complex data and equations. In this problem, we are given a homogeneous system of equations and asked to write the solution set in parametric vector form.

The homogeneous system consists of three equations: 3x₁ + 3x₂ + 6x₃ = 0, -6x₁ - 6x₂ - 12x₃ = 0, and -4x₂ + 4x₃ = 0. To solve this system, we need to use linear algebra techniques, such as Gaussian elimination, to find the solution set.

By using Gaussian elimination, we can reduce the system to a simpler system, which has the form x₁ = 0, x₂ = 0, and x₃ = t, where t is a real number. This can be written as a parametric vector form as x = (0, 0, t).

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The scalars c1 = 2/5, c2 = -3/5, and c3 = -8/5 satisfy the equation:

c1M1 + c2M2 + c3M3 = [ 2 3 ][ 1 2 ]

We want to find the scalars c1, c2, and c3 such that:

c1M1 + c2M2 + c3M3 = M

Substituting the given matrices:

c1[ 2 2 ] c2[ -1 1 ] c3[ 1 2 ] [ 2 3 ]

[ 1 1 ] [ 2 1 ] [ 3 1 ] [ 1 2 ]

Multiplying each scalar by its corresponding matrix:

[ 2c1 - c2 + c3 2c1 + 2c2 + 3c3 ]

[ c1 + 2c2 + 3c3 c1 + c2 + 2c3 ]

Setting the result equal to M:

[ 2c1 - c2 + c3 2c1 + 2c2 + 3c3 ] = [ 2 3 ]

[ c1 + 2c2 + 3c3 c1 + c2 + 2c3 ] [ 1 2 ]

This gives us two equations:

2c1 - c2 + c3 = 2

2c1 + 2c2 + 3c3 = 3

c1 + 2c2 + 3c3 = 1

c1 + c2 + 2c3 = 2

We can solve this system of equations using any method we prefer, such as elimination or substitution. Here, we will use elimination.

Subtracting the first equation from the second, we get:

3c2 + 4c3 = 1

Subtracting the third equation from fourth, we get:

c2 - c3 = 1

Multiplying second equation by 2, we get:

4c1 + 4c2 + 6c3 = 6

Subtracting first equation from this, we get:

5c2 + 5c3 = 4

Now we have three equations for c2 and c3:

3c2 + 4c3 = 1

c2 - c3 = 1

5c2 + 5c3 = 4

Solving for c2 and c3 using elimination, we get:

c2 = -3/5

c3 = -8/5

Substituting these values into the third equation, we get:

c1 = 2/5

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Answer:

1/2

Step-by-step explanation:

The numbers are: 1, 2, 4, 5, 7, 8, 9, 10

We see that only 7, 8, 9, and 10 are greater than 5

So, 4 possible numbers are greater than 5 in the total of 8 numbers.

So, the probability is 4/8 = 1/2

So, the answer is 1/2.

well, let's take a looksie at what it would  have been had there not been a sale, so at regular price the washer and dryer are just 685.96 + 475.70 = 1161.66, well hell how much is 4.25% of that?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{4.25\% of 1161.66}}{\left( \cfrac{4.25}{100} \right)1161.66} ~~ \approx ~~ 49.37[/tex]

now, since we know the appliances are going to be 20%, that means the appliaces sale price will be 100% - 20% = 80%, so 80% of the original price, well, we know the original price for those two is 1161.66, what's 80% of that?

[tex]\stackrel{\textit{80\% of 1161.66}}{\left( \cfrac{80}{100} \right)1161.66} ~~ \approx ~~ \stackrel{ sale~price }{929.33} \hspace{5em} \stackrel{\textit{4.25\% of 929.33}}{\left( \cfrac{4.25}{100} \right)929.33} ~~ \stackrel{ \textit{Paula's commission} }{\approx ~~39.5}[/tex]

well, Paula could have made 49.37, but she ended up with 39.5, 49.37 - 39.5 ≈ 9.87.

When comparing two numbers, there are a few different things you might be interested in: which is larger, which is smaller, or whether they are equal.

In this case, we can see that both numbers are negative, which means they are to the left of zero on the number line. In general, the further left a number is on the number line, the smaller it is. Therefore, we can say that:

-2.25 > -3

In other words, -2.25 is larger (closer to zero) than -3.

a) It is a continuous random variable.

b) It is a discrete random variable.

c) It is not a random variable nor discrete.

d) It is a continuous random variable

e)  It is a discrete random variable

f) It is a discrete random variable

A continuous variable has an uncountable range of possible values.

Any value falling inside an interval is acceptable.

They cannot be stated as decimal numbers and can only accept a discrete value. Counting is used to obtain them rather than measuring.

a). The height of a randomly selected giraffe is a continuous random variable.

b). The random variable is discrete. You can count how many people are sitting at a computer.

c). The gender of college students ⇒ Gender is categorical data. It is neither continuous nor discrete.

d). The number of people in a restaurant that has a capacity of 300 is a continuous random variable

e). The number of bald eagles in a country Since the number of people cannot be expressed as decimals, thus it is a discrete random variable

f). it is a discrete random variable as a number of people is a discrete count, which takes values such as 0 or 1 or 2.

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The mean and variance of the number x of unusable fasteners in a randomly selected box are about 150 and 150 respectively.

Poisson distribution is a distribution function useful for characterizing events with very low probabilities of occurrence within some definite time or space. It is used when the number of trials is very large and the probability of success is comparatively small.

In Poisson distribution, the mean is defined as:

λ = np

where n = number of items and p = probability of success

Given: n = 5000 and p = 3/100 = 0.03

Thus,  λ = np = 5000 * 0.03 = 150

Since the mean and variance are equal in Poisson distribution. Thus, the variance (σ²) =  150

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To find the equation of the tangent line to a curve at a given point, we will need the equation of the curve and the place where you want to locate the tangent line in order.

Calculate the derivative by differentiating the curve's equation. This will reveal the tangent line's slope at any point along the curve.

Put the derivative you discovered in step 1's derivative into the x-coordinate of the place where you wish to find the tangent line. This will reveal the tangent line's slope at that particular position.

To determine the equation of the tangent line, use the point-slope form of the equation of a line. A line's point-slope formula is written as y - y1 = m(x - x1), where (x1, y1) is the line's point and m is its slope. Both the slope of the line and the location on the line where you wish to find the tangent line are known to you from step 2.

Put the tangent line's equation in a simpler, more conventional form,        as y = mx + b.

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The probability that at least 3 children age 18 or under will be selected is 0.50

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Probability = sample space/total possible outcome

at least 3 children means x≥ 3

therefore ;

probability of atleast 3 children age 18 or under are selected =

.13+ .10 +.22 +.05

= 0.50

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The total price for paint with an 8.5% sales tax is $69.02928.

The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure.

Given:

Length = 14 feet

width = 17 feet

Height = 9 foot

So, the area of Four walls

= 2(14 x 9) + 2( 17 x 9)

= 2 x 126 + 2 x 153

= 252 + 306

= 558

Now, Area of ceiling

= lw

= 14 x 17

= 238

So, the total Area = 558 + 238 = 796

Now, the cost of painting room

= 796/350 x 28

= 63.68

and, After sales tax

= 63.68 + 0.085 x 63.68

= $69.02928

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The greatest percent change occurred in the first five-year period, between the first and second year, with a percent change of 60%.

Percentage is a number or ratio expressed as a fraction of 100.

We can calculate the percent change between two values using the following formula:

percent change = (new value - old value) / old value x 100%

To compare the percent change over a five-year period, we need to consider the percent change between each pair of values, as follows:

Percent change between the first and second year:

percent change = (320 - 200) / 200 x 100% = 60%

Percent change between the second and third year:

percent change = (400 - 320) / 320 x 100% = 25%

Therefore, the greatest percent change occurred in the first five-year period, between the first and second year, with a percent change of 60%.

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Exponential functions are mathematical functions that involve an exponent or power. There are two types of exponential functions: growth and decay.

1. Exponential Growth Functions: These functions have the form y = a*b^x, where a > 0 and b > 1. They model exponential growth, where the value of y increases rapidly as x increases. For example, the function y = 2^x is an exponential growth function, as the value of y doubles for each increase in x.

2. Exponential Decay Functions: These functions have the form y = a*b^x, where a > 0 and 0 < b < 1. They model exponential decay, where the value of y decreases rapidly as x increases. For example, the function y = (1/2)^x is an exponential decay function, as the value of y is halved for each increase in x.

Both types of exponential functions are important in many fields, including finance, biology, and physics. They are used to model phenomena such as compound interest, population growth, and radioactive decay.

The sequence of transformations performed by Isabella is Rotate 90° clockwise about the origin; translate 10 units down.

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.

Given that, Luther drew on his graph paper. After performing a series of transformations, Isabella drew. we need to find the transformations performed by Isabella,

We see, that, the sequence performed by Isabella is a rotation of 90°, from the origin, also the image is 10 units down to the original figure.

Hence, the sequence of transformations performed by Isabella is Rotate 90° clockwise about the origin; translate 10 units down.

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The complete question :-

From the given information the quadrilateral QUAD is a rectangle because opposite sides are of the same length and the adjacent sides are perpendicular to each other.

What is a quadrilateral?

A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry. A closed quadrilateral has four sides, four vertices, and four angles. It is a form of a polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees. The diagonals are obtained by joining the opposing vertices of the quadrilateral.

From finding the lengths of the sides of the quadrilateral, we can see that two sides of the quadrilateral have the same length and the other two sides have the same length.

QU

length = √20

slope = 2

UA

length = √5

slope = -1/2

AD

length = √20

slope = 2

DQ

length = √5

slope = -1/2

Now the lines QU and UA are perpendicular to each other since the product of slopes is -1.

So QU ⊥ UA

similarly,

AD ⊥ UA

AD ⊥ DQ

Also, the lines QU and AD as well as the lines UA and DQ are parallel to each other as the slopes are the same.

Therefore from the given information the quadrilateral QUAD, is a rectangle because opposite sides are of same length and the adjacent sides are perpendicular to each other.

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