1. Given CR bisects ∠A C D , find x.

The measurement of all the angles in the given geometrical image are mentioned below.

Given is a figure as shown in the image.

We can write the following equations -

∠1 + ∠2 + (8x - 8)° + (3x + 17)° = 360°

and

(8x - 8)° = (3x + 17)°                               {Vertically opposite angles}

8x - 3x = 17 + 8

5x = 25

x = 5

So -

8x - 8 = 8 x 5 - 8 = 32°

3x + 17 = 3 x 5 + 17 = 32°

So -

∠1 + ∠2 + (2 x 32) = 360°

2∠1 + 64 = 360

2∠1 = 296

∠1 = 148° = ∠2                                   {Vertically opposite angles}

∠6 = ∠1 = 148°

∠3 = 32°

∠5 = (180 - 148) = 32°

∠4 = 148°

∠6 = 148°

∠5 = 32°

Now -

(4y + 44) + (6y + 46) = 180°

10y + 90 = 180

10y = 90

y = 9

So -

(4y + 44) = 4 x 9 + 44 = 36 + 44 = 80

∠8 = 80°

Now -

6y + 46 = 6 x 9 + 46 = 100°

∠10 = 100°

∠11 = 80°

∠7 = ∠10 = 100°

∠7 = 100°

∠11 = ∠12 = 80°

∠12 = 80°

Therefore, the measurement of all the angles in the given geometrical image are mentioned above.

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Using the concept of percentage, she earned a total of $1091 last week

A percentage is a number or ratio that can be expressed as a fraction of 100. Percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

To determine the amount she earned last week, we need to calculate the amount in commission and add it with her weekly salary.

She received 3% commission on her sales and she made a sale of $29700.

Let's find 3% of 29700

3 / 100 = x / 29700

0.03 = x / 29700

x = 29700 * 0.03

x = 891

The amount she earns will be 891 + 200 = 1091

Janelle earned $1091 last week

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Confidence interval for the mean score of all students is (91.679, 98.321)

Given:

Sample mean = 95

Standard deviation = 6.6

The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.

We have to construct a 99% confidence interval for the mean score of all the students.

Sample Standard Error =

[tex]\frac{Standard Deviation}{\sqrt{n} } \\= \frac{6.6}{\sqrt{30} }[/tex]

= 1.205

t-value for the 99% confidence interval = 2.756

(use the t-tables for this)

Margin of error = 2.756 x 1.205 = 3.321

If you are asked to report the confidence interval, you should include the upper and lower bounds of the confidence interval.

So, for the 99% confidence interval:

(95 - 3.321, 95 + 3.321) = (91.679, 98.321)

This is the final confidence interval.

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Tan P expressed as a fraction in simplest terms is 15/29

Trigonometric Identities are defined as equalities involving trigonometry functions and also holds true for all the values of variables given in the equation.

There are five types of trigonometric identities;

From the information given, we have that;

Opposite side = 15

Adjacent side = 29

But the tangent trigonometric identity is;

Tan P = opposite/adjacent

Substitute the value

Tan P = 15/29

Hence, the value is 15/29

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The maximum force on the rectangular floor tile is 32 N.

Force is the product of mass and acceleration.

To calculate the maximum force, we use the formula below

Formual:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the maximum force is 32 N.

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Mindy needs to place the painting at 2.125 feet away from each side of the wall.

The horizontal distance of two side of a wall is defined as width and the vertical distance is called length of wall.

We need to place the paint at an equal distance from each side of wall (horizontal distance).

suppose Mindy will place the paint at x feet away from each side of wall.

for both side she counts 2x feet

width of wall =12.25 feet

width of painting= 8 feet

now, 8+ 2x = 12.25

   2x= 4.25

  x=2.125 feet

hence, Mindy will place the paint at 2.125 feet away from each side horizontally.

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The graph of the compound inequality can be seen in the image at the end.

Here we have a compound inequality which is:

4x + 7 ≤ -37

5x + 3 > -7

First we need to isolate x in both of these inequalities, on the first one we will get:

4x + 7 ≤ -37

4x ≤ -37 - 7

4x≤ -44

x ≤ -44/4

x ≤ -11

The other inequality gives:

5x + 3 > -7

5x > -7 - 3

5x > -10

x > -10/5

x > -2

So the compound inequality is:

x > -2

x ≤ -11

To graph this we need to have a open circle at x = -2, and we need to graph a line to the right. And a closed circle at x = -11 and a line that goes to the left.

The number line is below

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Newsweek performed a poll in which 500 American parents were asked the question, “Would you prefer to have your child taught by a male or female for grades K-2?” 95% confidence interval for the poll is

(38.88%, 41.12%)

Generally, To construct a 95% confidence interval for the poll, we need to first calculate the margin of error. The margin of error for a poll is a measure of the precision of the estimate and is calculated based on the sample size, the level of confidence, and the standard deviation of the population.

In this case, the sample size is 500, the level of confidence is 95%, and the standard deviation of the population is unknown. We can approximate the standard deviation using the sample proportion of 40% as an estimate of the population proportion.

Using these values, the margin of error can be calculated as follows:

Margin of error = z * standard error

Where z is the critical value from the standard normal distribution for the desired level of confidence (in this case, 1.96 for a 95% confidence interval) and the standard error is calculated as:

Standard error = √(p * (1 - p) / n)

Where p is the sample proportion (40% in this case) and n is the sample size (500 in this case).

Substituting these values into the formula for the margin of error, we get:

Margin of error = 1.96 * √(0.4 * (1 - 0.4) / 500)

= 1.96 * sqrt(0.16 / 500)

= 1.96 * √(0.000032)

= 1.6 * 0.005656854

= 0.011168

So the margin of error for this poll is approximately 0.011168 or 1.12%.

To construct the 95% confidence interval, we need to add and subtract the margin of error from the sample proportion. The 95% confidence interval for the poll is, therefore:

40% ± 1.12%

= (38.88%, 41.12%)

This means that we can be 95% confident that the true population proportion of parents who would prefer to have their child taught by a male in grades K-2 lies within the interval between 38.88% and 41.12%.

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In the current year, Bonnie sells stock valued at $60,000 to Linda for $15,000. Later that year, Bonnie gives Linda $25,000 in cash. Bonnie's taxable gifts from these transfers total a) $55,000.

Shares, also known as stocks, are securities that represent partial ownership of the issuing company. A unit of stock is called a "share" and allows the holder to receive a portion of the company's assets and profits equal to the number of shares held.

shares are traded primarily on stock exchanges and form the basis of many individual investor portfolios. Stock trading must comply with government regulations designed to protect investors from fraud.

Taxable Gifts:

Gifts valued at $75 or more are taxable.

Non-cash gifts of small value (less than $75 annually) to employees. Holiday turkeys are tax exempt.

tax-free value is capped at $1,600 for all her awards for one year.

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Answer:

D. x=4

Step-by-step explanation:

32. m<1=m<2 ==> angle bisectors divide an angle into two equal angles

m<2=m<RQP

m<1=m<SQP

m<RQP+m<SQP=m<SQR

m<2+m<1=m<SQR

m<2+m<2=m<SQR

(2+7x)+(2+7x)=16x-4

2+7x+2+7x=16x-4

2+2+7x+7x=16x-4

4+14x=16x-4

4-4+14x=16x-4+4

4+4+14x=16x-4+4

14x+8=16x

14x-14x+8=16x-14x

8=2x

x=8/2

x=4 ==> D

Answer:

Look at the image

Step-by-step explanation:

You can solve the problem like in the image

The value of x for which l is parallel to m is 41°

An angle is a figure in Euclidean geometry made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. The meeting of two planes can also create an angle. These are referred to as dihedral angles. The angle formed by the rays lying perpendicular to the two intersecting curves at their point of intersection can likewise be used to establish an angle between two intersecting curves.

In the depicted figure, l and m are parallel. A transversal crosses parallel lines, creating the appropriate angles. The angles created when two parallel lines cross any other line, whether they are corresponding or matching corners to the transversal.

(3x-43)°=80°

3x=80°+43°

3x=123°

x=41°

Therefore, the value of x is 41°

Hence, the value of x for which l is parallel to m is 41°.

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The area of square is 100 square centimeter.

What is square?

A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles. It can also be explained as a rectangle with two adjacent sides that are of equal length.

Given:

A square has sides 10 centimeters long.

We have to find the area of square.

Since,

Area of square = (side)^2

Here side of square is 10cm

So,

Area of square = (10 cm)^2

Area of square = 100 cm^2

Hence, the area of square is 100 square centimeter.

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The simplified form of the expression 12c + 8k - 8 - 6c + 6, combining the like term is 6c + 8k - 2.

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations like subtraction and addition.

To simplify an expression means rewriting the same algebraic expression with no like terms or to write an equivalent expression which contains no similar terms.

Therefore, let's simplify the expression with no like terms.

12c + 8k - 8 - 6c + 6

combine the like terms

12c - 6c + 8k - 8 + 6

Therefore, the simplified expression is 6c + 8k - 2

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Step-by-step explanation:

So you have 5/8 and you want the equivalent fraction to have a denominator of 40. You put 5/8=X/40 and find for x.

First, multiply both sides by 40

5/8*40=x

Express 5/8 * 40 as a single fraction.

5*40/8=x

Multiply 5 40 to get 200.

200/8=x

Divide 200 by 8 to get 25.

25=x

Swap sides so that all variable terms are on the left-hand side.

x=25

Solutions of x²-3x + 7 = 0 is 3 + √19/2 and 3 - √19/2.

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable. The phrase "quadratic" in mathematics refers to something that has to do with squares, the squaring operation, terms of the second degree, or equations or formulas that contain such terms. Latin's word for square is quadratus.

Given

Equation

x²-3x + 7 = 0

Using quadratic formula,

x = -b±√b² - 4ac/2a

x = -(-3) ± √((-3)² - 4×1×7/2×1

x = 3/2± √19 1/2i

x = 3 + √19/2 and 3 - √19/2

Solutions of x²-3x + 7 = 0 is 3 + √19/2 and 3 - √19/2.

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Thus after assuming the degrees of freedom equals 18 so the t-critical value will be =2.306

Degree of freedom {df}=18

We have to calculate the t-value such that 0.05 of the area under the curve is to the right of t

It means that, [tex]$\mathrm{P}(\mathrm{T} > \mathrm{t})=0.05$[/tex]

As we know, t distribution provides the cumulative probability

As the value of the total area under the t distribution will 1

So, we can write it as:

[tex]$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-\mathrm{P}(\mathrm{T} > \mathrm{t})$$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-0.05$$=0.95$[/tex]

Now, using excel, we can easily calculate the t-critical value as follows

=T. INV ( Probability, DF)

Where Probability is the area and DF is the degree of freedom,

Now we will enter these values in excel:

=T. INV (0.95,18)

t-critical value can also be found using t table

Look up for df = 18, in very first column

Now look up for 0.05 in one tail row

Now intersect both of them to get the t-critical value

We will get it as: 2.306

So t-critical value will be =2.306

[tex]$\mathrm{P}(\mathrm{T} > 2.306)=0.05$[/tex]

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The number of minutes that will be used for commercials will be 20 minutes.

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.

If the radio program plays 40 minutes of music.

Suppose the radio program is of one hour which is 60 minutes. Then the number of minutes will be used for commercials will be given as,

⇒ 60 - 40

⇒ 20 minutes

The number of minutes that will be utilized for plugs will be 20 minutes.

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The value of 'x' in the expression 20/x = 2 is 10.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, A numerical expression in the form of fraction 20/x = 2.

Now, To make 'x' in the numerator we'll move it to the other side which is,

2x = 20.

x = 20/2.

x = 10

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All solutions of the following system of linear inequalities are given-

B (6, 2), C (9, 9), D (8, 2)

For the stated question,

Therefore, the solutions of the following system of linear inequalities are-

B (6, 2), C (9, 9), D (8, 2).

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It is to be noted that the boat traveled a distance of 8.39 miles South, and 12.44 miles west. This is solved using trigonometric ratios principles.

Using the trigonometric ratio involving the right triangle, we can answer how far the boat moved northward and westward, or the vertical and horizontal components of the displacement vector.

Solving for the horizontal component Vₓ, we'll be using the ratio of the sine function with regard to angle 34°

Thus,

Sin 34° = Vₓ/ 15

Vₓ = 15 * (Sin 34°)

= 15 * 0.55919290

Vₓ  = 8.39 miles.

Solving for the vertical component of, V[tex]_{y}[/tex] we'll be using the ratio of Cosine Function with respect to the angle 34°

Cos 34° = V[tex]_{y}[/tex] / 15

V[tex]_{y}[/tex] = 15 * Cos 34°

V[tex]_{y}[/tex]= 15 * 0.82903757255

V[tex]_{y}[/tex] = 12.44 miles.

Thus, the boat traveled a distance of 8.39 miles South, and 12.44 miles west.

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a) The group of points labeled X are the non-outlier scores, while point Y is an outlier score.

b) The association between the variables is positive.

There are two possible classifications for the associations between variables, as follows:

For this problem, the variables are given as follows:

As the number of assignments submitted increases, the test scores also increases, hence there is a positive relationship between these two variables.

The point Y is an outlier, as the student got a considerably worse grade than expected, meaning that combined with his low score on the assignments, the student may have considerable difficulties in the subject.

The graph is given by the image shown at the end of the answer.

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The corresponding trigonometric ratios are -6/√61,  5/√61, -6/5, -5/6,  √61/5, -√61/6

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant  (sec) are the six trigonometric ratios. A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle.

First of all we need to find the distance between the point (5,-6) and origin (0,0)

Distance (r) = √(5-0)²+(-6-0)²

= √25+36

= √61

Now, P(5,-6) is compared with (x,y)

Now, sin Ф = y/r = -6/√61

cos Ф = x/r = 5/√61

tan Ф = y/x = -6/5

cot Ф = 1/tan Ф = -5/6

sec Ф = 1/cos Ф = √61/5

cosec Ф = 1/sin Ф = -√61/6

The corresponding trigonometric ratios are -6/√61,  5/√61, -6/5, -5/6,  √61/5, -√61/6

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Answer:

show the whole question

Step-by-step explanation:

The binary representation of each of these hexadecimal numbers is given as follows:

a) 80E = 100000001110

b) 135AB = 00010011010110101011

c) ABBA = 1010101110111010

d) DEFACED = 1101111011111010110011101101

To convert a number from hexadecimal to binary, each hexadecimal character is converted to it's respective four bit binary code, given as follows:

Then, for example:

80E hexadecimal = 100000001110.

As:

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The cost of the carpentering of the floor at the rate 12 rupees per square meter is 60 rupees.

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.

We have the room as a cuboid.

And its length is 6 meters and height is 3 meters.

The volume of the cuboid = length x height x width

90 = 6 x 3 x width

width = 90 / 18

width = 5 meter.

To find the cost of carpentering the floor, the rate of Rs. 12 per square meter.:

12 x width = 12 x 5 = 60 rupees.

Therefore, at the rate of 12 rupees per square meter, the cost of the carpentering of the floor is 60 rupees.

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Answer:

3

Step-by-step explanation:

on edge

Answer:

  x = 3

Step-by-step explanation:

You want the root of the polynomial equation x(x -2)(x +3) = 18.

A graph of the equation in the form x(x -2)(x +3) -18 = 0 is attached. The solution is the x-intercept. It shows the only real root is x = 3.

There are many ways the polynomial can give rise to a system of equations. The basic idea is to write two expressions that are supposed to be equal to each other. The graphing calculator can show the value(s) of x that make them equal.

Dividing both sides of the given polynomial by (x -2)(x +3) gives the equation ...

  x = 18/((x -2)(x +3))

This can be graphed as two equations:

  y = x

  y = 18/((x -2)(x +3))

This is shown in the second attachment. It tells us the root is x=3. (Both sides of the "x=" equation have the value 3 at x=3.)

__

Additional comment

Here, you are asked to use a system of equations. A graphing calculator can usually find the solution more easily when the equation is written in the form f(x) = 0. Often x-intercepts are easier to identify than points where graphs cross each other.

A prompt is one to three sentences that pose a problem or a query that you must address in an essay.

In the given question we have to prompt the user to enter four numbers, each corresponding to a person's weight in pounds and store all weights in a list and output the list.

(1) weights = [float(input('Enter weight 1: \n')),

float(input('Enter weight 2: \n')),

float(input('Enter weight 3: \n')),

float(input('Enter weight 4: \n'))]

print("Weights:", weights)

(2) weights = [float(input('Enter weight 1:\n')),

float(input('Enter weight 2:\n')),

float(input('Enter weight 3:\n')),

float(input('Enter weight 4:\n'))]

print("Weights:", weights)

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The right question is given below: