The measure of angle 1 is greater than 97° and at most 115°. Graph the possible values of x. (9x + 7)

We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.

The test statistic needed to test the claim that whether a subject lies or does not lie is independent of the polygraph test indication is the chi-square statistic.

In this case, the grand total is 90. The row totals are 57 and 33, and the column totals are 42 and 48. The expected frequencies are as follows:

The chi-square statistic is calculated as 0.177. The p-value for the chi-square statistic is calculated using a chi-square table. The degrees of freedom for the chi-square table are the number of rows minus 1, multiplied by the number of columns minus 1.

Since the p-value is greater than 0.05, we fail to reject the null hypothesis. We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.

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Answer:

Hence, the \(y(t)=e^{-2 t}\left(\frac{75}{74} \cos 6 t+\frac{75}{148} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t))\end{array}\) and approximately value of \(y(t)\) is \(-0.844\).

Given :

 \(my''+cy'+ky=F(t), y(0)=0, y'(0)=0,\)

Where  \(m=2\) kilograms

           \(c=8\) kilograms per second

           \(k=80\) Newtons per meter

          \(F(t)=20\sin (6t)\) Newtons

Explanation :

(1)

Solve the initial value problem. \(y(t)\)

   \(my''+cy'+ky=F(t), y(0)=0, y'(0)=0,\)

\(\Rightarrow 2y''+8y'+80y=20\sin (6t)\)

\(\Rightarrow y''+4y'+40y=10\sin (6t)\)

Auxilary equations :\(F(t)=0\)

\(\Rightarrow r^2+4r+40=0\)

\(\Rightarrow r=\frac{-4\pm\sqrt{4^2-4\times 1\times 40}}{2\times 1}\)

\(\Rightarrow r=\frac{-4\pm\sqrt{16-160}}{2}\)

\(\Rightarrow r=\frac{-4\pm\sqrt{-144}}{2}\)

\(\Rightarrow r=\frac{-4\pm12i}{2}\)

\(\Rightarrow r=-2\pm6i\)

The complementary solution is \(y_c=e^{-2t}\left(c_1\cos 6t+c_2\sin 6t\right)\)

The particular Integral, \(y_p=\frac{1}{f(D)}F(t)\)

\(y_{y} &=\frac{1}{D^{2}+4 D+40} 25 \sin (6 t) \\\\ y_{y} &=\frac{25}{-6^{2}+4 D+40} \sin (6 t) \quad\left(D^{2} \text { is replaced with }-6^{2}=-36\right) \\\\y_{y} &=\frac{25}{4 D+4} \sin (6 t) \\\\y_{y} &=\frac{25}{4(D+1)} \sin (6 t) \\\\y_{y} &=\frac{25(D-1)}{4(D+1)(D-1)} \sin (6 t) \\\\y_{y} &=\frac{25(D-1)}{4\left(D^{2}-1\right)} \sin (6 t) \\\\y_{y} &=\frac{25(D-1)}{4(-36-1)} \sin (6 t) \\\\y_{y} &=-\frac{25}{148}(D-1) \sin (6 t) \\y_{y} &=-\frac{25}{148}\left(\frac{d}{d t} \sin (6 t)-\sin (6\)

Hence the general solution is :\(y=y_c+y_p=e^{-2t}(c_1\cos 6t+c_2\sin 6t)-\frac{25}{148}(6\cos 6t-\sin 6t)\)

Now we use given initial condition.

\(y(t) &=e^{-2 t}\left(c_{1} \cos 6 t+c_{2} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\\y(0) &=e^{-\alpha 0)}\left(c_{1} \cos (0)+c_{2} \sin (0)\right)-\frac{25}{148}(6 \cos (0)-\sin (0)) \\\\0 &=\left(c_{1}\right)-\frac{25}{148}(6) \\\\c_{1} &=\frac{75}{74} \\\\y(t) &=e^{-2 t}\left(c_{1} \cos 6 t+c_{2} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\\)

\(y^{\prime}(t)=-2 e^{-2 t}\left(c_{1} \cos 6 t+c_{2} \sin 6 t\right)+e^{-2 t}\left(-6 c_{1} \sin 6 t+6 c_{2} \cos 6 t\right)-\frac{25}{148}(-36 \sin (6 t)-6 \cos (6 t)) \\\\y^{\prime}(0)=-2 e^{0}\left(c_{1} \cos 0+c_{2} \sin 0\right)+e^{0}\left(-6 c_{1} \sin 0+6 c_{2} \cos 0\right)-\frac{25}{148}(-36 \sin 0-6 \cos 0) \\\\0=-2\left(c_{1}\right)+\left(6 c_{2}\right)-\frac{25}{148}(-6) \\\\0=-2 c_{1}+6 c_{2}+\frac{75}{74} \\\\0=-2\left(\frac{75}{74}\right)+6 c_{2}+\frac{75}{74} \\\\\)\(\begin{array}{l}0=-\frac{150}{74}+6 c_{2}+\frac{75}{74} \\\\\frac{150}{74}-\frac{75}{74}=6 c_{2}\end{array}\)

\(\begin{array}{l}c_{2}=\frac{25}{148}\\\\\text { Substitute } c_{1} \text { and } c_{2} \text { in } y(t) \text { . Then }\\\\y(t)=e^{-2 t}\left(\frac{75}{74} \cos 6 t+\frac{75}{148} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t))\end{array}\)

(2)

\(y(t)=e^{-2 t}\left(\frac{75}{74} \cos 6 t+\frac{75}{148} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\y(t)=\left(\frac{75}{74} e^{-2 t} \cos 6 t+\frac{75}{148} e^{-2 t} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\y(t)=\frac{75}{74}\left(e^{-2 t}-1\right) \cos 6 t+\frac{25}{148}\left(3 e^{-2 t}+1\right) \sin 6 t \\\\|y(t)| \leq \frac{75}{74} e^{-2 t}-1|\cos 6 t|+\frac{25}{148}\left|3 e^{-2 t}+1\right||\sin 6 t| \\\\\)

\(|y(t)| \leq \frac{75}{74}\left|e^{-2 t}-1\right|+\frac{25}{148}\left|3 e^{-2 t}+1\right| \\\\\lim _{t \rightarrow \infty} y(t) \leq \lim _{t \rightarrow \infty}\left\{\frac{75}{74}\left|e^{-2 t}-1\right|+\frac{25}{148}\left|3 e^{-2 t}+1\right|\right\} \\\\\lim _{t \rightarrow \infty} y(t)=\left\{\frac{75}{74}\left|\lim _{t \rightarrow \infty}\left(e^{-2 t}-1\right)\right|+\frac{25}{148}\left|\lim _{t \rightarrow \infty}\left(3 e^{-2 t}+1\right)\right|\right\} \\\)

\(\lim _{t \rightarrow \infty} y(t)=\left\{\frac{75}{74}(-1)+\frac{25}{148}(1)\right\}=-\frac{75}{74}+\frac{25}{148}=-\frac{-150+25}{148}=-\frac{125}{148} \approx-0.844\)

Answer:

sec 30° = 1/cos 30° = 2.

Step-by-step explanation:

The secant function (sec) is the reciprocal of the cosine function. So, sec(x) = 1/cos(x). The value of cosine at 30 degrees is sqrt(3)/2, and its reciprocal is 2/sqrt(3), which can be simplified to 2. Hence, sec(30°) = 2.

Answer:

x = 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

2(x + -5) + x = x + (-6)

Step 2: Solve for x

Answer:

x=2 ( see Image below)

Step-by-step explanation:

cancel equal terms on both sides of the equation

2(x-5)=-6

move the constant to the right -hand side and change its sign

2x= -6 +10

Calculate the sum

2x=4

divide both sides of the equation by 2

x=2

Answer: b) $60.56 per year of age

Step-by-step explanation: If the scatterplot of two variables shows a line and the correlation between them is strong, we can calculate a regression line.

Regression line is a line graph that best fits the data. Like any other line, its formula is given by

y = mx + b

with

m being the slope

b the y-intercept

The slope of the line, correlation and standard deviations of the two variables have the following relationship:

\(m=r\frac{S_{y}}{S_{x}}\)

where

r is correlation

\(S_{y}\) is standard deviation for the y data

\(S_{x}\) is standard deviation for the x data

For our problem:

r = 0.34

\(S_{y}=\) 2850

\(S_{x}=\) 16

Calculating

\(m=0.34(\frac{2850}{16})\)

m = 60.56

Slope for the regression line of annual income per year of age is 60.56.

Answer:

Step-by-step explanation:

(-4*5 - 1) + (-4)

(-20 - 1) - 4

-21 - 4

-25

when A = 49, the value οf s is apprοximately 1.0535.

The sequence where each wοrd is varied by anοther by a cοmmοn ratiο is knοwn as a geοmetric prοgressiοn οr geοmetric sequence. When we add a cοnstant (which is nοt zerο) tο the term befοre it, the sequence's subsequent term is created. The fοllοwing symbοls stand in fοr it: a, ar, ar2, ar3, ar4, etc.

Geοmetric Prοgressiοn (GP), a fοrm οf sequence in mathematics, is a series in which each subsequent term is created by multiplying each preceding term by a set integer, knοwn as a cοmmοn ratiο. A geοmetric sequence οf integers that fοllοws a pattern is anοther name fοr this develοpment.

Starting with the fοrmula \(A = 1 - 82/s^{36\), we can sοlve fοr s by substituting the given value οf A and then sοlving fοr s:

\(A = 1 - 82/s^{36\)

\(49 = 1 - 82/s^{36\)(substituting A = 49)

\(50 = 82/s^{36\) (adding 1 tο bοth sides

\(50s^{36} = 82\) (multiplying bοth sides by \(s^{36\))

\(s^{36} = 82/50\) (dividing bοth sides by 50)

\(s^{36}= 41/25\)

s ≈ 1.0535

Therefοre, when A = 49, the value οf s is apprοximately 1.0535.

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The range is the best measure of variability for this data, and its value is 4.

The line plot displays the number of roses purchased per day at a grocery store, with the data values ranging from 0 to 4 (since there are no dots above 4).

The best measure of variability for this data is the range, which is the difference between the maximum and minimum values in the data set. In this case, the minimum value is 0 and the maximum value is 4, so the range is:

Range = Maximum value - Minimum value = 4 - 0 = 4

Therefore, the range is the best measure of variability for this data, and its value is 4.

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Answer:

Area of parallelogram is: 56 square yards.

Step-by-step explanation:

We are given:

Height of parallelogram = 7 yd

Base of parallelogram = 8 yd

We need to find area of parallelogram

The formula used is: \(Area\:of\: parallelogram = Base*Height\)

Putting values and finding area of parallelogram

\(Area\:of\: parallelogram = Base*Height\\Area\:of\: parallelogram = 7*8\\Area\:of\: parallelogram = 56\)

So, Area of parallelogram is: 56 square yards.

The rays and lines in the picture are as follows;

rays: BD, AC and AB

lines: AC

A ray is a part of a line that has one endpoint and goes on infinitely in only one direction.

A ray is named using its endpoint first, and then any other point on the ray

A line segment has two endpoints.

Therefore, the rays and lines are as follows:

rays: BD, AC and AB

lines: AC

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Answer:

120 degrees

Step-by-step explanation:

Rsm right?

f(x) = 3x^2 - 11x -20

To find the zeros of the function, first we factor the expression as follows:

f(x) = (3x + 4)(x - 5)

Now we equal the expression to zero:

(3x + 4)(x - 5) = 0

If the expression is equal to zero, that means at least one of the factors is equal to zero, so:

3x + 4 = 0, then x = - 4/3

or

x - 5 = 0, then x = 5

The zeros of the function are:

(-4/3, 0) and (5, 0)

(a)the common ratio = 2

(b)the 6th term​ = 64

How to find the common ratio and 6th term ?

        Here, the common ratio = r

                   the first term = a = 2

(a)the common ratio

\(a +ar^{2} = 10\\\\2(1+r^{2} ) = 10\\\\(1+r^{2} ) = 5\\\\r^{2} =4\\\\r = 2\)

The common ratio (r) = 2

(b)the 6th term​

\(a_{n}=ar^{n-1} \\\\a_{6}=ar^{6-1} \\\\a_{6} =2(2^{5} )\\\\a_{6}=64\)

Thus ,the 6th term​ = 64

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Using thie model ,The answer is D. 27.

To calculate 9÷1/3 using the model below, we can imagine dividing the green rectangle into thirds vertically. Each third would contain 3 cells.

Then, we can see that there are a total of 9 cells in the rectangle. Since we are dividing by 1/3, we need to find out how many sets of 1/3 are in 9.

We can see that there are 3 sets of 1/3 in each row (since each row contains 3 cells, which are thirds). So, in total, there are 3 rows of 3 sets of 1/3, which gives us:

9÷1/3 = 3 rows x 3 sets of 1/3 = 9 sets of 1/3 = 27

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Answer:

A.

The graph shows trigonometric functions intercept the x-axis at minus 3, 0.2, and 3.5 units also pass parallel to the g of the x-axis.

Answer:

x = 14

Step-by-step explanation:

110 + 5x = 180

-110 -110

5x = 70

divide by 5 on both sides

x = 14

to find y add 70 + 40 + missing angle = 2y

missing angle is 70 because 70+40+70 = 180

so 2y = 110

y = 55

Answer:

x=14

y=55

Step-by-step explanation:

5x and  110 form a straight line so they add to 180

5x+110 =180

5x = 180-110

5x = 70

Divide by 5

5x/5 = 110/5

x = 14

We know the exterior angle of a triangle is equal to the sum of the two opposite interior angles

40 + 5x = 2y

Substitute in 14 for x

40 +5(14) = 2y

40 + 70 = 2y

110 = 2y

Divide by 2

110/2 =2y/2

55 = y

Set A is a subset of set B if every element of A is also an element of B

If every element of set A is also an element of set B, then set A is a subset of set B. This is expressed in symbols as A B or. For example, suppose you’re representing all of the nations in the globe, and set A represents Finland and Greece, while set B represents all of Europe.

If a set A is a subset of a larger set B, the circle representing set A is drawn within the circle representing set B.

If sets A and B share certain components, we can symbolize them by drawing two overlapping circles.

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Answer:

A

Step-by-step explanation:

\( \frac{4x - 3}{7} \)

Replace y with x.

\(x = \frac{4y - 3}{7} \)

Solve for y.

\(7x = 4y - 3\)

\({7x + 3}{} =4 y\)

\( \frac{7x + 3}{4} = y\)

To solve this problem, we need to use Charles's law, which states that, at constant pressure, the volume of a sample of gas is directly proportional to its temperature.

The law can be expressed mathematically as:

\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{ \frac{V_1}{T_1}=\frac{V_2}{T_2} } \end{gathered}$} }\)

Where:

Now we obtain the data to continue solving:

Now, we will convert the temperatures to Kelvin:

\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_1=220 \ ^{\circ}C+273=493 \ Kelvin} \end{gathered}$} }\)

\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_2=40 \ ^{\circ}C+273= 313 \ Kelvin} \end{gathered}$} }\)

Now we solve for V₂:

\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2=\frac{V_1T_2}{T_1 } } \end{gathered}$} }\)

Where:

Now, we substitute the values in the formula:

\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2=\frac{(0.5 \ L\times313\not{k} )}{493\not{k} } } \end{gathered}$} }\)

\(\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2\approx0.32 \ Liters } \end{gathered}$} }}\)

Answer:

Kindly check explanation

Step-by-step explanation:

Given that:

Number of donuts consumed in a month = y

Age = x

Regression equation obtained :

y=47-1.36x

Meaning of slope of the regression line ;

Comparing the regression equation obtained with the general equation of a linear regression line ;

y = mx + c; where m = slope of the regression line

Hence, the value of slope in the equation is = - 1.36

Thus, the slope can be interpreted as ; The number of donuts consumed in a month is expected to decrease by 1.36 for per(1) increase in age x of consumer.

The slope means that the number of donuts reduces by 1.36 as people get older.

A linear equation is in the form:

y = mx + b;

where y, x are variable, m is the slope of the line and b is the y intercept.

Let y represent the number of donut ate by the customers in a month and x represent their age

Given the regression line:

y = 47 - 1.36x

The slope means that the number of donuts reduces by 1.36 as people get older.

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Using proportions we can find,

6. The weight of the adult bear = 750 pounds.

7. The measure of each angles are: 10°, 75° and 95°

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole.

According to the definition of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilized.

Here in the question,

The weight is in the ratio = 3:1000

The average birth weight = 12 ounces = 3/4 pounds.

Now the weigh of adult bear = 1000 × 3/4 = 750 pounds.

In the second part the angles are in the ratio, 2:15:19.

So, 2x+ 15x + 19x = 180

x = 180/36

x = 5

Hence, the measure of each angles are: 10°, 75° and 95°

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Answer:

0.408

Step-by-step explanation:

Convert -6.8 and -0.06 to 34/5 and 3/50(The math explains why)
\(0 - 68/10 \times 0 - 3/50\\0 - 34/5 \times (-3)/50\\= 51/125\\= 0.408\)

Answer: 0.408

Step-by-step explanation:

Answer:

2.2

Step-by-step explanation:

(1.85 x 2) - 1.50

...............

Answer: C. A=[1,3,5,7,9] thats the answer

Step-by-step explanation:

If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.

Here in the figure attached below,

Given two triangles ΔABC and ΔDEF

Also given that,

ΔABC and ΔDEF are congruent to each other.

Given AC = 4cm

Since both triangles are congruent ,

Side AC is congruent to DF

Therefore DF = 4cm (based on SSS theorem).

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Answer:

a number, r, added to 6

Step-by-step explanation:

a number, r, added to 6

Answer:

a number, r, added to 6

Step-by-step explanation:

a number, r, added to 6

Answer:

11. x = 32.6°

12. x = 27.0

Step-by-step explanation:

Question 11

\(\sin(\theta)=\dfrac{\textsf{opposite side}}{\textsf{hypotenuse}}\)

Given:

\(\implies \sin(x)=\dfrac{7}{13}\)

\(\implies x=\sin^{-1}\left(\dfrac{7}{13}\right)\)

\(\implies x=32.6\textdegree \textsf{ (nearest tenth)}\)

Question 12

\(\sin(\theta)=\dfrac{\textsf{opposite side}}{\textsf{hypotenuse}}\)

Given:

\(\implies \sin(64\textdegree)=\dfrac{x}{30}\)

\(\implies x=30\sin(64\textdegree)\)

\(\implies x=27.0\textsf{ (nearest tenth)}\)

Answer:

15

Step-by-step explanation:

27÷1.8=15

The horizontal transformations are defined as follows:

cos(ax).

They are classified as follows:

The vertical transformations are defined as follows:

acos(x).

They are classified as follows:

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