If ABCD is a parallelogram,
find the value of x.
7x + 2
9x-28

The law of sines states that the ratio of the Sine of an angle to the length of the side opposite that angle is constant in any triangle.

The Law of Sines is defined as a relationship that applies to all triangles, not just right triangles.

The law states that the ratio of length of side of a triangle to sine of angle opposite that side is constant for all sides and angles in the triangle.

So , for any triangle, ratio of length of one side to the sine of angle opposite that side is = ratio of length of any other side to the sine of the angle opposite that side.

The Sine Law is also useful for solving problems which involves the angles and sides of triangles, especially when not all sides and angles are known.

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Answer:

Step-by-step explanation:

24. Gravetter/Wallnau/Forzano, Essentials - Chapter 3 - End-of-chapter question 24

A sample yielded the following scores:

2, 3, 4, 4, 5, 5, 5, 6, 6, 7

n= 10

Assume that the scores are measurements of a discrete variable and find the median.

Median =5Correct

Points:

1 / 1

Median = 5

To find the median for a set of numbers with an even quantity the two middle numbers are added together and divided by 2.

n=102+(n = 102+1)2

= 5th score + 6th score2

= 5 + 52

= 102=5

Assume that the scores are measurements of a continuous variable and find the median by locating the precise midpoint of the distribution. (Use two decimal places.)

Median = 4.83Correct

The median for the discrete variable is 5 and for continuous variable is 5.

Median in statistics is the middle value of a list of data when arranged in order. It is a measure of central tendency that separates the data into two halves: the upper half and the lower half.

Given that: scores = 2, 3, 4, 4, 5, 5, 5, 6, 6, 7

a) The scores are in ascending order; then the median which is the middle number will be:

median = (5th term + 6 term)/2

= (5+5)/2

= 10/2

= 5

b) Use the cumulative percentage table ;

X     frequency    cumulative frequency     cumulative percentage

2         1                     1                                           10%

3         1                     2                                          20%

4        2                     4                                          40%

5        3                     7                                           70%

6        2                     9                                           90%

7        1                      10                                          100%

Fraction = the no. required to reach 50%/ no. in that interval

= 1/3

Since we have a total of 4 boxes when we reach the value of 4.5

The median of the continuous variable = 4.5 + (1/3)

= 4.833

≈ 5

Hence, the median for the discrete variable is 5 and for continuous variable is 5.

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Answer:

1/6

Step-by-step explanation:

1/4x2/3 = 2/12 = 1/6

Answer: The equation of a line in the form of y = mx + b can be found using the slope-intercept form, where m is the slope of the line and b is the y-intercept. To find the slope, you can use the two points on the line: (1, 2) and (3, 5). The slope is found by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the two points.

m = (5 - 2) / (3 - 1) = 3 / 2 = 1.5

The y-intercept can be found by plugging in one of the points and the slope into the equation and solving for b. Let's use the point (1, 2).

2 = 1.5 * 1 + b

b = 2 - 1.5 = 0.5

So the equation of the regression line is:

y = 1.5x + 0.5

Therefore, the correct answer is: yˆ = 1.5x + 0.5

Step-by-step explanation:

The total duration of the phone call was 33 minutes.

Given that, by using Company A's calling plan, the cost of an overseas phone call is a $0.95 connection fee plus 33 cents per minute. If the total cost of the call is $11.84 and we have to calculate the time how long was the phone call.

Let the number of minutes a phone call held be x.

Now, we will be representing the above given information in terms of linear equation and then solve for the value of x which will give us the number of minutes the phone call held.

[tex]Total[/tex] [tex]cost=[/tex] $[tex]0.95[/tex] [tex]+[/tex] $[tex]0.33x[/tex]

$[tex]11.84=[/tex] $[tex]0.95[/tex] [tex]+[/tex] $[tex]0.33x[/tex]

[tex]11.84=0.95+0.33x[/tex]

[tex]11.84-0.95=0.33x[/tex]

[tex]0.3=0.33x[/tex]

[tex]\frac{0.3}{0.33}=x[/tex]

[tex]33=x[/tex]

Therefore, the call will go 33 minutes long.

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This final result as a fractiοn and a decimal 115075 using the given fractiοns 6/2 and 4/8

A fractiοn is a mathematical representatiοn οf a part οf a whοle οr a ratiο between twο quantities. It is typically represented as a tοp number (numeratοr) divided by a bοttοm number (denοminatοr), separated by a hοrizοntal line.

Fοr example, the fractiοn 3/4 represents three parts οut οf fοur equal parts οf a whοle. The numeratοr (3) represents the number οf parts, while the denοminatοr (4) represents the tοtal number οf parts that make up the whοle.

Accοrding tο the questiοn:

Let's first find hοw many gummys Jaly has:

Jaly has 241 times greater number οf gummys than Deens, whο has 463. Sο Jaly has:241 x 463 = 111583 gummys Jaly then gave 50 away and received 3542 gummys.

Therefοre, the tοtal number οf gummy's Jaly nοw has is:111583 - 50 + 3542 = 115075We can express this final result as a fractiοn and a decimal using the given fractiοns 6/2 and 4/8.

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a) This function maps even integers to the next odd integer, and maps odd integers to themselves. It is not one-to-one

b) This function maps positive integers to even positive integers, and maps negative integers to odd positive integers. It is one-to-one because different inputs always have different outputs.

c) This function simply maps every integer to itself. It is one-to-one because different inputs always have different outputs, and it is onto because every positive and negative integer is in its range.

d) This function simply maps every integer to itself. It is one-to-one because different inputs always have different outputs

(a) One example of a function that is neither one-to-one nor onto is:

[tex]f(x) = \begin{cases} x+1 & \text{if } x \text{ is even} \ x & \text{if } x \text{ is odd} \end{cases}[/tex]

This function maps even integers to the next odd integer, and maps odd integers to themselves. It is not one-to-one because, for example, f(2) = f(4) = 3. It is not onto because no positive even integer is in the range of f.

(b) One example of a function that is one-to-one but not onto is:

[tex]f(x) = \begin{cases} 2x & \text{if } x > 0 \ -2x+1 & \text{if } x \leq 0 \end{cases}[/tex]

This function maps positive integers to even positive integers, and maps negative integers to odd positive integers. It is one-to-one because different inputs always have different outputs. However, it is not onto because no odd positive integer is in the range of f.

(c) One example of a function that is onto but not one-to-one is:

[tex]f(x) = \begin{cases} x/2 & \text{if } x \text{ is even} \ -(x+1)/2 & \text{if } x \text{ is odd} \end{cases}[/tex]

This function maps even integers to positive integers, and maps odd integers to negative integers. It is onto because every positive and negative integer is in the range of f. However, it is not one-to-one because, for example, f(2) = f(-2) = 1.

(d) One example of a function that is both one-to-one and onto is:

f(x) = x

This function simply maps every integer to itself. It is one-to-one because different inputs always have different outputs, and it is onto because every positive and negative integer is in its range.

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The error which Jake made is likely to be a result of confusion or oversight in identifying the variable y as having a coefficient of 1.

The coefficients of an expression are the numerical factors that multiply the variables, while the constants are the numerical values that do not contain any variables.

In the expression 9m + 4 + y, the coefficients are 9 and 1 (which is the implied coefficient for y since there is no visible numerical factor), and the constant is 4.

So Jake correctly identified 9 as a coefficient and 4 as a constant, but missed the implied coefficient of 1 for the variable y. The error that Jake made is likely to be a result of confusion or oversight in identifying the variable y as having a coefficient of 1, rather than assuming it is a constant or neglecting it entirely.

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9. a)The required value of h is 4

9.b) The required value of h is 4

10.a)The required value of h is -6

10.b) They are linearly dependent for all values of h.

Here the given vectors are:

v1 = [tex]\left[\begin{array}{ccc}1\\-3\\2&\end{array}\right][/tex]

v2 = [tex]\left[\begin{array}{ccc}-3\\10\\-6&\end{array}\right][/tex]

v3 = [tex]\left[\begin{array}{ccc}2\\-7\\h&\end{array}\right][/tex]

The vectors v1 and v2 are not scalar multiples of one another so they are not linearly dependent.

[tex]\left[\begin{array}{ccc}1&-3&2\\-3&10&-7\\2&-6&h\end{array}\right][/tex]= 0

1(10h -42) -3(-14 +3h) +2 (18-20) =0

10h -9h-4 =0

h = 4

Hence the value of h is 4 so that the vector v3 is in span{v1,v2}

b) The given vectors will be linearly dependent if h =4

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The creation of the bin.matrix using cbind() allows us to organize and manipulate our data in a way that is conducive to statistical analysis.

A binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, with a constant probability of success.

First, let's define what a binomial distribution is. For example, if we toss a fair coin 10 times, the number of heads that come up is described by a binomial distribution.

Now, let's talk about the cbind() function. cbind() is short for "column bind". It is used to combine vectors or matrices into a single matrix, where each input vector or matrix becomes a column in the final matrix.

In this exercise, we have created 7 vectors, each with a different success probability for a binomial distribution, ranging from 0.2 to 0.8. We will use cbind() to combine these vectors into a matrix called bin.matrix.

The dimension of the bin.matrix is

=> 300 x 7.

This means that the matrix has 300 rows and 7 columns. Each row represents a trial, and each column represents a different success probability. For example, the first column might represent a trial with a success probability of 0.2, while the second column might represent a trial with a success probability of 0.3, and so on.

By creating this matrix, we can easily perform statistical analyses on the data contained within it. We can calculate summary statistics, such as the mean and variance, for each column, or we can compare the distributions of the different columns to see if there are any significant differences between them.

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Answer:

The expression (9x+8)-(3x + 5) simplifies to 6x + 3. Therefore, the answer is option C: 6x + 3.

The length of the hypotenuse or the value of 'x' is 60.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjacent/hypotenuse and

tan = opposite/adjacent.

From the given diagram respect to the reference angle of 37°,

Hypotenuse is 'x' and adjacent is 48.

And we know,  cos = adjacent/hypotenuse.

Therefore, cos37° = 48/x.

x = 48/0.8.

x = 60.

Q. A right-angle triangle is shown, Find the value of x.

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The Confidence interval starts at 177.28 and the Confidence interval ends at 187.72. Thus option c is correct.

The given data is as follows:

Number of coffee, N = 28

Mean, µ = 182.5

Standard deviation, α = 14.1

Confidence Level, CL = 95%

z-value for 95% confidence interval = 1.96

The confidence interval is calculated by using the formula,

Confidence interval = μ ± Ζ (α/√n )

Confidence interval = 182.5 ± 1.96*(14.1/√28)

Confidence interval = 182.5 ± 5.22

Confidence interval = (177.28, 187.72)

Therefore we can conclude that the Confidence interval starts at 177.28 and the Confidence interval ends at 187.72.

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The volume of the cube is 1 cubic meter.

Option B is the correct answer.

It is a polygon having six faces.

The volume of a cube is side³.

Example:

The volume of a cube of 3 cm in length is 27 cm³.

We have,

Side length = 100 cm

Now,

Volume.

= Side³

= 100³

= 1000000 cm³ _____(1)

Now,

1 m = 100 cm

1 m³ = 1000000 cm³ _____(2)

From (1) and (2),

Volume = 1 cubic meter.

Thus,

The volume of the cube is 1 cubic meter.

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Answer:

18

Step-by-step explanation:

to find p(-2), substitute it into the equation!

you can make this easier by factoring x out, so p(x) = x(x-7)

then, plug -2 in

p(-2)=-2(-2-7)

p(-2)=-2(-9)

p(-2)=18

Answer:

Step-by-step explanation:

p(x)=[tex]x^{2}-7x\\[/tex]

=>p(-2)=[tex](-2)^{2} -7.(-2)[/tex]

           = 4+14=18

1) The  model is R = 1820 - 19t

2) After six years R = 1706 barrels

3) There would be non more oil in 96 years.

We know that an equation can be used as a model. This implies that we can be able to use an equation to show how a variable is changing over time and that is what the problem that we have here is all about.

If at the current time we have 1820 billion barrels Then they decrease by 19 barrels per year and t is the number of years then the model is;

R = 1820 - 19t

After six years we would have;

R = 1820 - (19 * 6)

R = 1706 barrels

When there are no further barrels;

0 = 1820 - 19t

1820 = 19t

t = 1820/19

t = 96 years.

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The area of each circle, to the nearest tenth is:

1. 19.6 cm²

2. 379.9 in.²

3. 28.3 mm²

4. 78.5 in.²

5. 132.7 cm²

6. 162.8 yd²

The area of a circle is calculated as:

A = πr², where, r is the radius of the circle, and π is a constant.

1. r = 5/2 = 2.5 cm

Area = πr² = 3.14 * 2.5²

= 19.6 cm²

2. r = 11 in.

Area = πr² = 3.14 * 11²

= 379.9 in.²

3. r = 3 mm

Area = πr² = 3.14 * 3²

= 28.3 mm²

4. r = 10/2 = 5 in.

Area = πr² = 3.14 * 5²

= 78.5 in.²

5. r = 13/2 = 6.5 cm

Area = πr² = 3.14 * 6.5²

= 132.7 cm²

6. r = 7.2 yd

Area = πr² = 3.14 * 7.2²

= 162.8 yd²

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The coefficients (a, b, c) in a polynomial equation is relate to the position x, velocity v, and acceleration a of an object.

Position (x): The position of the object can be represented by the x-coordinate of its position in space. This can be related to the coefficients in the equation by setting the x-coordinate equal to x and solving for the corresponding y-coordinate.

Velocity (v): The velocity of an object is the rate at which its position is changing. This can be related to the coefficients in the equation by taking the first derivative of the equation with respect to time. The result is a linear equation that represents the velocity as a function of time.

Acceleration (a): The acceleration of an object is the rate at which its velocity is changing. This can be related to the coefficients in the equation by taking the second derivative of the equation with respect to time. The result is a constant value that represents the acceleration of the object.

In summary, the coefficients (a, b, c) can be related to the position, velocity, and acceleration in equation for x, taking derivatives of the equation with respect to time, and interpreting the results as the position, velocity, and acceleration of the object.

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Answer:

Down payment is $12,500.

Mortgage = $237,500

Step-by-step explanation:

The required down payment is 5% of the selling price of the house, which is $250,000.

Down payment = 5% of $250,000 = 0.05 x $250,000 = $12,500

Therefore, the required down payment is $12,500.

To find the amount of the mortgage, we need to subtract the down payment from the selling price of the house.

Mortgage = Selling price of the house - Down payment

Mortgage = $250,000 - $12,500

Mortgage = $237,500

Therefore, the amount of the mortgage is $237,500.

Answer:

b

Step-by-step explanation:

a) Probability, P(y = 2) = P(AA) is equals to the 0.81.

b) Probability, P(y = 3), is equals to the 0.162.

c) For P(y=5), 5ᵗʰ battery must be an A. four outcome for which Y= 5 , probability is equals to the 0.00324.

d) General formula for p(y) is P(y)= (y-1)(0.1)⁽ʸ⁻²⁾(0.9)².

A new battery’s voltage may be acceptable (A) or unacceptable (U). Assume that 90% of all batteries have acceptable voltages. So, probability of acceptance = 0.90 and

probability of unacceptance = 1 - 0.9 = 0.1

Let the number of batteries that must be tested be "Y". A particular flashlight requires two batteries, that is batteries will be independently selected.

a) For P(y = 2), both the batteries must be acceptable. Hence probability, P(y = 2)

= P(AA) = 0.90× 0.90 = 0.81

b)For P(y = 3 ) = P(AUA) + P(UAA)

=0.9× 0.1×0.9 + 0.1× 0.9× 0.9 = 0.162

C) For any(Y = n), nᵗʰ batterry should be acceptable, as search for two acceptable batteries will complete once second acceptable battery gets selected. Hence for P(y=5), 5ᵗʰ battery must be an A. four outcome for which Y

= 5 are (AUUUA) ,(UAUUA),(UUAUA),(UUUAA)

P(y=5) = P(AUUUA) + P(UAUUA) + P(UUAUA) + P(UUUAA)

= 4× 0.9² × 0.1³

= 0.00324

d) From above probabilities we conclude, the general formula for p(y) is p(y) =(y- 1)(0.1)⁽ʸ⁻²⁾(0.9)².

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The value of sec2(pi/5) - tan2(pi/5) is equals to  1.

What is trigonometric identity ?

A trigonometric identity is a mathematical equation that relates the values of trigonometric functions of an angle. These identities are true for all values of the angle for which both sides of the equation are defined.

We can use the trigonometric identities to simplify this expression. Recall that:

sec(x) = 1/cos(x)

tan(x) = sin(x)/cos(x)

sin2(x) + cos2(x) = 1

Using these identities, we can rewrite the expression as:

sec2(pi/5) - tan2(pi/5)

= (1/cos2(pi/5)) - (sin2(pi/5)/cos2(pi/5))

= (1 - sin2(pi/5))/cos2(pi/5)

= cos2(pi/5)/cos2(pi/5) (using the identity sin2(x) + cos2(x) = 1)

= 1

Therefore, sec2(pi/5) - tan2(pi/5) = 1.

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The transformation from ln ( x ) to ln ( x + 2 ) is horizontal transformation or shift.

What kinds of functions can be transformed?

Transformations can be divided into three categories: translations, reflections, and dilations. There are two types of transformations that can be done to a function: vertical (which affects the y-values) and horizontal (affects the x-values).

                               The four transformation variables are included in the equation of a function that is shown below (a, b, h, and k).

f(x) = ln(x)

if g(x) = ln(x + 2)

Then,

The transformation from ln(x) to ln(x+2) is horizontal transformation or shift. As 2 units are added in g(x) the function is horizontally shifted by 2 units in left-hand direction.

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The translation needed to obtain the graph of g(x) = 7^x-4 from the graph of (x) = 7^x is 4 units right

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

g(x) = 7^x-4

f(x) = 7^x

Using the above as a guide, we have the following:

g(x) = f(x - 4)

This represents a translation to the right by 4 units

Hence, the translation is 4 units right

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Answer:(A) 1.314.08

Step-by-step explanation:

Inflation

The proportion of selling times in the sample that are greater than or equal to 10 days is 0.85.

As per the data given:

HOME Realty claims that it can sell a detached, residential house faster than any other realty company.

With the aim of examining HOME's claim, you sample 20 customers who sold a detached.

The data has been summarized in the histogram(attached at the end of solution)

Here we have to determine the proportion of selling times in the sample that are greater than or equal to 10 days.

Selling Time Frequency

0 - 10                    3

10 - 20                  4

20 - 30                 7

30 - 40                 3

40 - 50                 3

Frequencies for which selling times are 10 or greater

= 4 + 7 + 3 + 3

= 17

Total frequencies = 3 + 4 + 7 + 3 + 3

= 20

Proportion for which selling times are 10 or greater

= [tex]$\frac{17}{20}[/tex]

= 0.85

Therefore the proportion is 0.85.

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HOME Realty claims that it can sell a detached, residential house faster than any other realty company. With the aim of examining HOME's claim, you sample 20 customers who sold a detached, residential house through HOME and record the selling times (in days) of the houses. Your data are summarized in the following histogram(attached at the end of solution):

Based on the histogram, find the proportion of selling times in the sample that are greater than or equal to 10 days. Write your answer as a decimal, and do not round your answer.

The value of x is 60.

We can use the fact that the opposite angles of a parallelogram are equal to find the value of x. Angle BCD is therefore equal to angle ABD, and angle CBD is equal to angle CAD.

Based on the given angles, we can construct two equations:

Angle ABD + angle CBD = 100 (because angle BCD = angle ABD) Angle ABD + angle ACD = 80 (because angle CAD = angle CBD)

When we substitute the given values, we get:

x + 40 = 100 x + 20 = 80

When we solve for x in both equations, we get:

x = 60 x = 60.

We can be confident that our answer is correct because both equations give us the same value for x. As a result, the value of x is 60.

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