x² + 12x +32 = 0
lesser x =
greater x =

The trigonometric function simplified as a single expression is cosec² t .

The given trigonometric function is  : [tex]\frac{sin^2t+cos^2t}{sin^2t}[/tex]

We know from trigonometric identity : that sin²t +cos²t = 1

hence the given expression simplifies to 1 / sin²t

Again trigonometric ratios states that :

1 / sin t =  cosec t

∴ 1 / sin²t = cosec² t

Hence the trigonometric function is of the form cosec² t .

The right-angled triangle's angle and the ratios of its two side lengths are connected by the trigonometric functions, which are actual functions. They are also referred to as goniometric functions, circular functions, and angle functions .

The three trigonometric functions that are used in modern mathematics the most commonly are sine, cosine, and tangent. The less frequent cotangent, cosecant, and secant are their reciprocals.

Disclaimer: The complete question is :

simplify sin² ( t ) + cos ² ( t ) / sin ² ( t ) to an expression involving a single trig function with no fractions.

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We must calculate the standard deviation of the differences between the values in the matched pairs in order to build a confidence interval using those values.

The 95% confidence interval is another frequently used measure of accuracy. In order to calculate it, a range of values that is 95% likely to contain the true population mean must be created using the standard deviation.

According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, so to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.

Data dispersion in relation to the mean is quantified by a standard deviation, or σ. Data are said to be more closely clustered around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

The difference between the values in the matched pairs' standard deviation is calculated.

The complete question is:

To construct a confidence interval using matched pairs, we must compute the standard deviation of the ___ between the values in the matched pairs.

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We must calculate the standard deviation of the differences between the values in the matched pairs in order to build a confidence interval using those values.

What is the difference between standard deviation and confidence interval?

The 95% confidence interval is another frequently used measure of accuracy. In order to calculate it, a range of values that is 95% likely to contain the true population mean must be created using the standard deviation.

According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, so to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.

Data dispersion in relation to the mean is quantified by a standard deviation, or σ. Data are said to be more closely clustered around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

The difference between the values in the matched pairs' standard deviation is calculated

To construct a confidence interval using matched pairs, we must compute the standard deviation of the ___ between the values in the matched pairs.

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By solving the question, The equation has 2 valid solutions; no extraneous solutions that are x = 2,5

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

Equation is -

[tex]\sqrt{x - 1} - 5 = x-8[/tex]

adding 5 to both of the sides,

[tex]\sqrt{x - 1} = x-8+5[/tex]

[tex]\sqrt{x - 1} = x - 3[/tex]

squaring,

[tex]( x- 1) = (x-3)^{2}\\ x - 1 = x^{2} + 9 - 6x\\x^{2} - 7x + 10 = 0\\x(x-2)-5(x-2)=0\\x=2, 5\\[/tex]

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The roots of the quadratic equation are x = (3±2i)/2

The meaning of quadratic formula is a formula that gives the solutions of the general quadratic equation ax² + bx + c = 0

Given a quadratic equation, 4x²+13 = 12x

4x²-12x + 13 = 0

Quadratic formula =

x = [-b ± (√b²-4ac)]/2a

a = 4, b = -12 and c = 13

x = [12 ± (√(-12)² - 4*4*13)]/2*4

x = (12 ± 8i)/8

x = (3 ± 2i)/2

Hence, The roots of the quadratic equation are x = (3±2i)/2

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The correct option regarding the statement is given as follows:

A. There may be an association, but not a correlation unless the variables are quantitative. There could be a correlation between the average number of hours of TV watched per person and number of crimes committed per year. Even if there is a relationship, one does not cause the other.

The variables are classified as qualitative or quantitative as follows:

The relevance of the variables according to association and correlation are given as follows:

The variables in this problem are given as follows:

As they are qualitative variables, they can have association, and thus option A is correct.

The options are given by the image presented at the end of the answer.

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If we model the situation with a discrete dynamical system, with time interval

one day, we obtain the following:

[tex]\[x_{n+1} =\[x_{n}- \frac{3}{50}\[x_{n}[/tex]    ---------(1)

[tex]\[y_{n+1} =\[y_{n}+\frac{3}{50}\[x_n}-\frac{3}{100} \[y_{n}[/tex]

The amount of pollutant in Upper Lake tomorrow, [tex]\[x_{n+1}[/tex], is equal to the

amount of pollutant in Upper Lake today,[tex]\[x_{n}[/tex], minus the amount of pollutant which has flown into Lower Lake, via the river. The concentration of pollutant in Upper Lake today is [tex]\frac{\[x_{n}m^3}{50km^3}[/tex] The amount of water carried by the river to Lower Lake during the day is [tex]3km^3[/tex] This water contains

                                           [tex]3km^3\frac{\[x_{n}m^3}{50km^3}[/tex] [tex]=\frac{3}{50} {\[x_{n}m^3}[/tex]

of the pollutant. So the decrease of pollutant in Upper Lake is equal to [tex]=\frac{3}{50} {\[x_{n}}[/tex]  (measured in m3 , which are the correct units for the components of the state vector). This justifies Formula (1).

The change in the pollutant in Lower Lake consists of the inflow from

Upper Lake, which is [tex]\frac{3}{50}[/tex] , minus the outflow, which is [tex]{3}\frac{{\[y_{n}}}{100}[/tex] , because the concentration of the pollutant in Lower Lake is  [tex]\frac{{\[y_{n}}}{100}[/tex].

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Answer:

x=1,5

Step-by-step explanation:

X^2-6x+5<0

(x-5)(x-1)<0

x=1,5

Answer: (0, -3)

Step-by-step explanation:

You start from the x axis which is zero and then u go to the y axis and look for -3

The box and whisker plots and the IQR for each of the data set is given below.

A box and whisker plot has a rectangular box and two lines that connect from it on both sides, where:

The above stated values are referred to as the five-number summary of a data.

The interquartile range (IQR) = Q3 - Q1.

6. The five-number summary for the data set, 32, 34, 36, 37, 36, 37, 38, 37, 38 are:

The IQR is: 37.5 - 35 = 2.5

7. The five-number summary for the data set, 52, 52, 55, 55, 53, 56, 57, 57, 58 are:

The IQR is: 57 - 52.5 = 4.5

8. The five-number summary for the data set, 50, 51, 52, 58, 58, 59, 49, 50, 49 are:

The IQR is: 58 - 49.5 = 8.5

9. The five-number summary for the data set, 18, 16, 15, 19, 11, 14, 12, 14, 16 are:

The IQR is: 17 - 13 = 4

The box and whisker plot for each of the data set given is shown in the diagram below.

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The percent that is student's estimate off are, 40%.

What is percent?

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed. A % has no dimensions and no standard measurement.

Given:

A student has a container with a volume of 1. 5 liters.

She estimates the volume to be 0. 9 liters.

The student is off by

1.5 - 0.9 = 0.6

Now, the percent that is student's estimate off are,

(0.6 / 1.5) x 100 = 40%

Hence, by 40% is the student's estimate off.

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The output word of BATS into the machine, the output would be AZSR.

What is logical reasoning?

In logical reasoning, premises and the relationships between them are rigorously employed to infer conclusions that are suggested (or contended) by the premises and the relationships. Technology and artificial intelligence philosophy diagnoses various varieties of logical reasoning.

By using reasoning skills to take an unbiased look at any issue, logical questioning aids in reaching a logical conclusion about how to move forward. For instance, if we are having problems at work, we will use the information at our disposal and our logical thinking skills to solve the problem.

Explanation:

If the letter is ‘A’, it changes it to ‘Z’.

like the same way,

‘B’, it changes to ‘A’

‘A’, it changes to ‘Z’

‘T’, it changes to ‘S’

‘S’, it changes to ‘R’

Therefore, The output word of BATS into the machine, the output would be AZSR.

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The half-life of vanadium-48 is 16 days.

What is half life?

The half-life formula is used to determine the half-life of a material whose quantity is degrading or decreasing. When a substance degrades, the rate of decay varies depending on the quantity present. It is exceedingly challenging to determine the life of a decaying substance since when the quantity of the chemical decreases, the pace of decay likewise slows down. In order to offer the appropriate metrics to quantify the life of decomposing material, the half-life formula is applied.

According to law of radio active decay, IN=N

N-- amount of sample present

N1--- initial amount of sample

Decay 0 constant

Half life = 16 days

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[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$600\\ r=rate\to 3.3\%\to \frac{3.3}{100}\dotfill &0.033\\ t=years\dotfill &4 \end{cases} \\\\\\ A=600[1+(0.033)(4)] \implies A=600(1.132)\implies A = 679.2[/tex]

Answer: photo

Step-by-step explanation: picture

Answer:

2^2

Step-by-step explanation:

(2^7)/(2^5) = 2^(7 - 5) = 2^2

The rate of change of the function is -2.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the function are 3 and 5

The inputs of the function are 1 and 2.

We have,

We will find two points on the graph.

The points on the graph are:

(0, 5), (1, 3), and (2, 1)

We can choose any two points.

(0, 5) and (1, 3)

The rate of change of the function.

= (3 - 5) / (1 - 0)

= -2/1

= -2

Thus,

The rate of change of the function is -2.

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If one of the brightest stars in the sky is Sirius ​, which is part of the constellation Canis Major Sirius is 9 light years from the Earth. One light year=5.88 x 10^12 miles. The distance is 5.29 x 10^13 miles.

Distance can be defined as the length of an object or how far an object is from another object.

Given data:

9 light years

5.88 x 10^12 miles

Now let find the how far, in​ miles, is Sirius ​

Distance = 5.88 x 10^ 12 miles× 9  light year

Distance = 52,920,000,000,000

Distance = 5.29 x 10^13 miles

Therefore we can conclude that the distance is  5.29 x 10^13 miles.

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The value  of x and y is  3

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equals sign =. [2] [3] In other languages, the word equation and its cognates may have slightly different meanings; for example, in French, an équation is defined as containing one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.

Let the equations be

x + 3y = 8    ..............(1)

x + y = 2    ..............(2)

substracting equation 1 from 2

(x + 3y) - (x + y ) = 8 - 2

x + 3y - x + y = 6

3y - y = 6

2y =6

y = 6/2

y = 3

multiply the equation 2  with value of 3

x + y=2*3

x+y =6

x+3 = 6

x = 6 - 3

x = 3

Therefore the value of x and y is both are 3

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Answers:

Domain = {12, 10, 8, 6}

Range = {1, 3, 5, 7}

============================================

Explanation:

The domain is the set of allowed x inputs. Simply list the x coordinates of each point.

The range will have us list the y coordinates of each point. This shows the list of possible outputs.

Use curly braces for the domain and range because each is a set of values.

Optionally you can sort the values. I decided not to sort them to keep the same order of coordinates mentioned from left to right.

{12,10,8,6} sorts to {6,8,10,12}

If there were any duplicate items, in either domain or range, then you would erase them. Simply list each unique item once.

-------------------

Extra info:

The matrix cannot be inverted if any eigenvalue is 0, which also means that the determinant is zero. This suggests a linear dependence between the columns of A. As a result, A is not of full rank and is not invertible.

What does "linearly dependent" mean?

A set's ability to have at least one linear combination of its components equal to zero when the coefficients are taken from another provided set and at least one of those coefficients is not equal to zero.

                  This feature applies to matrices or vectors. adjective that depends on linearity.

What does it mean to be linearly dependent?

A group of non-zero vectors is said to be linearly dependent if at least one of them can be expressed as a linear combination of the others.

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Answer:

Step-by-step explanation:

Ok:

1. Use PEMDAS to solve equations(Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

First parentheses:

4(x−5)=20

4x-20=20

Second add subtract from both sides by isolating variable x!

4x-20=20

4x=40

4*x=40

x=40/4

x=10

3. Answer: x=10

As we dilate rectangle ABCD by a scale factor of 1/2 and use E as the center, the coordinates of the point D' = (2, -1).

A rectangle is a quadrilateral in Euclidean plane geometry with four right angles.

The coordinates of the rectangle's points A'B'C'D' are as follows:

A' = the point's coordinates (-2, -1)

B' = the coordinates of the point (-2, 1)

C' = the coordinates of the point (2, 1)

D' = the coordinates of the point (2, -1)

Using the point P as the chart's origin, we get;

The coordinates of point B are (-4, 2), and the coordinates of point C are (4, 2).

Given that the sides are parallel to each other, the coordinates of point A = (-4, -2) The coordinates of point D = (4, -2)

We have; given that the sides are parallel to the axis.

The segment length AB = 2 - (-2) = 4

The segment length BC = 4 - (-4) = 8

The segment length CD = 2 - (-2) = 4

The segment length AD = 4 - (-4) = 8

As a result, a 1/2 dilation yields;

The segment length A'B' = AB/2 = 4/2 = 2

The segment length B'C' = BC/2 = 8/2 = 4

The segment length C'D' = CD/2 = 4/2 = 2

The segment length A'D' = AD/2 = 8/2 = 4

Point A' coordinates = Point A/2 coordinates = (-4, -2)/2 = (-2, -1)

= (-4, 2)/2 = (-2, 1) (-2, 1)

The coordinates of the point B' = (-2, 1) The coordinates of the point C' = (4, 2)/2 = (2, 1)

C' = the coordinates of the point (2, 1)

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     2. There is not sufficient evidence to support the claim that the average percentage of readers who own a particular make of car is above 53%

What is null and alternative hypothesis??|
The alternative hypothesis of a test expresses your research's prediction of an effect or relationship, whereas the null hypothesis of a test always predicts no effect or no association between variables.

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The equation (x - 3)² / 144 + (y - 5)² / 196 = 1 is the standard form of the ellipse.

Herein we know the main features of a vertical ellipse, that is, the center and the lengths of its axes. The standard form of the equation of the ellipse:

(x - h)² / a² + (y - k)² / b² = 1, b > a

Where:

If we know that (h, k) = (3, 5), a = 12, b = 14, then the standard form of the equation of the ellipse is:

(x - 3)² / 12² + (y - 5)² / 14² = 1

(x - 3)² / 144 + (y - 5)² / 196 = 1

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Answer:

Both angles are 56°

Step-by-step explanation:

These angles are vertical angles and vertical angles are congruent

5x + 1 = 6x -10  Subtract 5x from both sides

1 = x -10  Add 10 to both sides

11 = x  Plug this back into one of the expressions to find the measurement of the angels

5x + 1

5(11) + 1

55 + 1

56  or

6x - 10

6(11) -10

66 - 10

56

The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the coefficient of determination.

What is coefficient of determination?

The effectiveness of a statistical model in forecasting a result is shown by the coefficient of determination (R²). The dependent variable in the model is a representation of the result.

R² can have a value of 0 or 1, with 1 being the maximum achievable. Simply said, a model's R² will be closer to 1 the more accurate its predictions are.

R² is a more precise measure of goodness of fit. The amount of volatility in the dependent variable that the model can account for.

You can typically tell whether your linear regression data's R² is high or low by graphing it. The graphs below, for instance, display two sets of simulated data:

Dots represent the observations.

The line of best fit, or predictions of the model, is displayed as a black line.

Purple lines represent the deviations (the residuals) between the data and their expected values.

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1. Both segments have the slopes = 1/2.

2. Slope of CD = -1/3.

Slope of CD = -1/3.

Slope of zipline = -1/3.

3. ΔAHE, ΔBID, and ΔCGF are the slope triangles.

Slope of the line = 1/2.

4. See attachment for the slope triangles drawn.

The slope of the line = 3/5

A slope triangle can be described as an imaginary triangle that is drawn on a coordinate plane, whereby, the hypotenuse of the triangle is the line we are interested in finding the slope, and the legs represent the rise and run of the line that is used to calculate the slope.

The slope formula = rise/run.

1. Slope of segment RT = rise/run = 2/4 = 1/2

Slope of segment TV = rise/run = 1/2

The slopes of both segments are equal.

2. Choosing points C and D, the slope of CD = rise/run = -1/3.

Choosing points B and C, the slope of CD = rise/run = -2/6 = -1/3.

The slope of the zipline is: -1/3.

3. The slope triangles are ΔAHE, ΔBID, and ΔCGF.

Slope of the line = rise/run = 2/4 = 1/2.

4. The slope triangles drawn is in the image attached below.

The slope of the line = rise/run = 3/5

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The line integral ∫CF⋅dr = ∫(df/dx)dx + ∫(df/dy)dy + ∫(df/dz)dz

A gradient fiield is a function of the form F = ∇f where f is a scalar field and

∇= gradient function = (d/dx)i + d/dyj + d/dzk.

So, F =  [(d/dx)i + d/dyj + d/dzk]f

A line integral is the integral along a line. It is given by ∫F⋅dr = ∫Fxdx + ∫Fydy + ∫Fzdz

Since F=F(x,y,z) is a gradient field with F=∇f, S is a level surface of f, and C is a curve on S.

We desire to find the line integral ∫CF⋅dr.

Since the gradient field = ∇f, we have that

F =  [(d/dx)i + d/dyj + d/dzk]f

F(x, y, z) =  (df/dx)i + df/dyj + df/dzk

Now, the line integral along the curve C is ∫CF⋅dr

Since ∫F⋅dr = ∫(Fxi + Fyj + Fzk).(dxi + dyj + dzk)

= ∫[(df/dx)i + df/dyj + df/dzk].(dxi + dyj + dzk)

= ∫(df/dx)dx + ∫(df/dy)dy + ∫(df/dz)dz

So, we see that the line integral ∫CF⋅dr = ∫(df/dx)dx + ∫(df/dy)dy + ∫(df/dz)dz

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