What is the solution 8x-3(2x-4)=3(x-6)

Answer:

θ

can be in the first quadrant

0

≤

θ

≤

90

or the fourth quadrant

270

≤

θ

≤

360

If

θ

is in the first quadrant,

then

sin

θ

=

5

13

cos

θ

=

12

13

tan

θ

=

5

12

Therefore,

sin

2

θ

=

2

sin

θ

cos

θ

=

2

×

5

13

×

12

13

=

120

169

cos

2

θ

=

cos

2

θ

−

sin

2

θ

=

(

12

13

)

2

−

(

5

13

)

2

=

144

169

−

25

169

=

119

169

If

θ

is in the fourth quadrant,

then

sin

θ

=

−

5

13

cos

θ

=

12

13

tan

θ

=

−

5

12

Therefore,

sin

2

θ

=

2

sin

θ

cos

θ

=

2

×

−

5

13

×

12

13

=

−

120

169

cos

2

θ

=

cos

2

θ

−

sin

2

θ

=

(

12

13

)

2

−

(

−

5

13

)

2

=

144

169

−

25

169

=

119

169

Answer:

A. 1/6

B. 1

Step-by-step explanation:

A. 9/j x j/54= 9/54 = 1/6

B. 6k/8m : 3k/4m = 6k/8m : 4m / 3k = 2/2 =1

Answer:

a. 3/2

b. 1

Step-by-step explanation:

A. To simplify the expression, we can cancel out the common factor of j:

9/j * j/54 = (9/1 * 1/6) = 3/2

Therefore, 9/j * j/54 simplifies to 3/2.

B. To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction. That is,

(a/b) ÷ (c/d) = (a/b) x (d/c)

Using this rule, we can simplify the given expression as follows:

6k/8m ÷ 3k/4m = (6k/8m) x (4m/3k)

             = (6/8) x (4/3)  

             = 2/2

             = 1

56.78% of the penguins in the population have a weight between 13.0 kg and 16.5 kg, according to the usual distribution.

Given,

The mean of the population, μ = 15.1 kg

Standard deviation, σ = 2.2 kg

We have to find the percent of the penguins from the population have a weight between 13. 0 kg and 16. 5 kg;

Here,

z score = x - μ / σ

The ratio of the p-value of Z when X = 16.5 minus the p-value of Z when X = 13 indicates the percentage of penguins in the population whose weight is between 13.0 kg and 16.5 kg.

x = 16.5

z score = x - μ / σ

z = (16.5 - 15.1) / 2.2  = 0.64

Z = 0.64 has a p-value of 0.7389.

x = 13

z score = x - μ / σ

z = (13 - 15.1) / 2.2 = -0.95

Z = -0.95 has a p-value of 0.1711.

0.7389 - 0.1711 = 0.5678.

0.5678 = 56.78% of the penguins from the population have a weight between 13.0 kg and 16.5 kg.

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The nth term rule for the given arithmetic sequence 5, 7, 9, 11 is Tn = 2n + 3.

The given sequence, 5, 7, 9, 11, is an arithmetic sequence where each term increases by 2.

In this sequence, we observe that each term is obtained by adding 2 to the previous term.

The first term, 5, can be represented as 5 + (0 × 2), the second term, 7, as 5 + (1 × 2), the third term, 9, as 5 + (2 × 2), and so on.

From this pattern, we can deduce that the nth term of the sequence can be expressed as:

Tn = 5 + (n - 1) × 2

Tn = 5 + 2n - 2

Tn = 2n+ 3

In this expression, n represents the term number, and Tn represents the corresponding term in the sequence.

Therefore, the nth term rule for the given sequence 5, 7, 9, 11 is Tn = 2n + 3.

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Answer:

Angle a=45, Angle b=45

Step-by-step explanation:

The angles are complementary angles which means they both add up to 90 degrees.  And if angles a and b are equal then its 90/2 which is 45.

Answer: 65

Step-by-step explanation:
1 + 64 = 65

The MLE of μ is the sample mean of the data, which is calculated by taking the sum of the values and dividing by the sample size μ = (x₁ + x₂ + ... + xₙ)/n.

The maximum likelihood estimation (MLE) is a method of estimating the parameters of a statistical model given a set of data. It involves maximizing a likelihood function, which is a function of the model's parameters that defines the probability of obtaining the data that was actually observed.

The sample mean is the average of a set of sample data, calculated by adding all the values together and dividing by the number of values in the sample.

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The probability that Ahmad chooses a big sticker or a star from the packet can be calculated by considering the total number of big stickers and stars in the packet and dividing it by the total number of stickers.

To determine the probability, we need to find the number of big stickers and stars in the packet. There are 8 big stars and 7 big rockets, which gives us a total of 8 + 7 = 15 big stickers. Additionally, there are 3 small stars and 13 small rockets, resulting in a total of 3 + 13 = 16 small stickers.

Now, to calculate the probability that Ahmad chooses a big sticker or a star, we need to consider the total number of stickers in the packet. The packet contains 15 big stickers and 16 small stickers, so the total number of stickers is 15 + 16 = 31.

Therefore, the probability that Ahmad chooses a big sticker or a star is (15 + 16) / 31 = 31 / 31 = 1.

This means that Ahmad is guaranteed to choose either a big sticker or a star from the packet, as the probability is equal to 1.

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Answer:

1/3

Step-by-step explanation:

We can calculate the slope using 2 points: (3,0) and (0,-1).

\(\frac{y_2-y_1}{x_2-x_1}=\frac{0- -1}{3-0}\)=

\(\frac{1}{3}\)

Answer:

\(3n^2+3n-6=54\)

Step-by-step explanation:

Total Area=54 square inches. Area=length*width.

Because the length is \([3(n-1)]\), and the width is \((n+2)\), you can plug that into the equation for area. In this case, because the total area is 54, we can plug that in for area.

\([3(n-1)](n+2)=54\)

Distribute through the parenthesis in \(3(n-1)\).

\((3n-3)(n+2)=54\)

Then, multiply \(3n-3\) and \(n+2\) using whatever method you prefer. I used FOIL, which stands for First, Outer, Inner, Last. You multiply the first terms together, the outer terms together, the inner terms together, and the last terms together.  

\(3n^2+6n-3n-6=54\)

Simplify.

\(3n^2+3n-6=54\)

The value of x is 5.

The value of y is 40°.

It is a two dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

A composite figure that has three triangles.

Two equilateral triangles.

One isosceles triangle.

We see that,

Both equilateral triangles have the same sides and the same angles.

5x - 1 = 24

5x = 24 + 1

5x = 25

x = 5

We see that,

Let the opposite angle of 6y° = m

6y° + 60 + 60 + m = 360

6y + 120 = 360

6y = 360 - 120

6y = 240

y = 40°

Thus,

x = 5 and y = 40°

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To construct a 4x2 matrix D such that AD=I2, we can use the following matrix: D = [0 0 1 0; 0 0 0 1]. It is not possible for CA to be equal to 4 or 14 for any 4x2 matrix C.

Constructing a matrix D such that AD=I2

Let A = -1 be a 1x1 matrix. We want to construct a 4x2 matrix D such that their product AD is equal to the 2x2 identity matrix I2. We can use the following matrix for D:

D = [0 0 1 0; 0 0 0 1; 1 0 0 0; 0 1 0 0]

To verify that AD=I2, we can compute the matrix product:

AD = [-1 0 0 0; 0 -1 0 0] [0 0 1 0; 0 0 0 1; 1 0 0 0; 0 1 0 0]

= [0 0 -1 0; 0 0 0 -1]

= -I2

Note that D only uses 1 and 0 as entries.

Now, it is not possible for CA to be equal to 4 or 14 for any 4x2 matrix C. To see why, we can use the definition of matrix multiplication. Let C be a general 4x2 matrix:

C = [c11 c12; c21 c22; c31 c32; c41 c42]

Then, we can compute CA as:

CA = [-1 0; 0 -1] [c11 c12; c21 c22; c31 c32; c41 c42]

= [-c11 -c12; -c21 -c22; -c31 -c32; -c41 -c42]

Since CA is a 4x2 matrix and 4 is a scalar, it is not possible for CA to be equal to 4. Similarly, since the entries of C are only 0 or 1, it is not possible for CA to be equal to 14.

Therefore, there is no matrix C that satisfies the equations CA=4 or CA=14.

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Answer:

x=-1,\:y=4

Step-by-step explanation:

Answer:

x = 1

y = -2

Step-by-step explanation:

3y + 7 = x

5x + 4y = -3

Let's use substitution method, plug in the top equation x into the bottom one

5(3y + 7) + 4y = -3

15y + 35 + 4y = -3

19y + 35 = -3

Subtract 35 from both sides

19y + 35 = -3

     - 35    - 35

19y = -38

Divide both sides by 19

19y/19 = -38/19

y = -2

Plug in the new y into one of the original equations, I'll use the top one

3(-2) + 7 = x

-6 + 7 = x

x = 1

The given class boundaries are reasonable and provide a clear and informative summary of the savings account balances at the bank.

In statistics, a frequency distribution is a way of organizing data into intervals, or classes, and counting the number of observations that fall within each interval. The purpose of constructing a frequency distribution is to summarize large amounts of data and identify patterns and trends in the data.

When constructing a frequency distribution for savings account balances at a bank, it is important to choose appropriate class boundaries that are meaningful and representative of the data.

The class boundaries given in the question are $0.00-$5,000, $5,000-$10,000, $10,000-$15,000, and $15,000-$20,000, with the minimum balance of $5.00 and the maximum balance of $18,700.

These class boundaries are reasonable and appropriate for representing the savings account balances at the bank. The first class includes balances from $0.00 to $5,000, which is the minimum balance that the bank allows. The remaining classes are each $5,000 in width, which provides a consistent and easy-to-follow pattern.

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Complete question is:

In constructing a frequency distribution for the savings account balances for customers at a bank, the following class boundaries might be acceptable if the minimum balance is $5.00 and the maximum balance is $18,700:

$0.00-$5,000

$5,000-10,000

$10,000-$15,000

$15,000-$20,000

Are these class boundaries reasonable.

Answer:

  x = 117

Step-by-step explanation:

The sum of the interior angles of a pentagon is 180°(5 -2) = 540°. This means ...

  x +59 +138 +140 +86 = 540

  x +423 = 540 . . . simplify

  x = 117 . . . . . . . . subtract 117

Answer:

a=6

Step-by-step explanation:

-6(2+a)=-48

-12-6a=-48

-6a=-36

a=6

Using off-colored language in speech is almost always a bad choice for the following reasons: it models inappropriate language in public, sets the speaker apart from other public speakers, and can be seen as disrespectful towards the audience.

However, one exception to this is that it cannot be known in advance to what extent the use of rude epithets might undermine the speaker's credibility with audience members. Using off-colored language in public speech is generally discouraged because it models inappropriate language and behavior. When we speak in public, we serve as models for how people ought to speak in public settings. By using foul language, we contribute to a culture of disrespectful and offensive communication, which is not conducive to maintaining a professional or respectful environment. Furthermore, the use of off-colored language can make a speaker stand out in a negative way. Public speakers often aim to be memorable for their ideas, expertise, and ability to engage the audience, rather than for their use of inappropriate language. By resorting to offensive language, a speaker risks being remembered primarily for their choice of words rather than the substance of their message. In addition, many people view the use of foul language as a sign of disrespect towards the audience. Such language can alienate listeners and create a sense of discomfort or offense. Public speaking is about establishing a connection with the audience, and using offensive language undermines this connection by conveying a lack of respect for the audience's sensibilities. However, there is one exception to the negative consequences of off-colored language in speech. It is difficult to predict in advance the extent to which the use of rude epithets might undermine a speaker's credibility with audience members. While it is generally advisable to avoid offensive language, there may be situations or specific audiences where the use of certain language is deemed acceptable or even expected. Nonetheless, it is crucial to exercise caution and consider the potential risks before deviating from appropriate and respectful speech.

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Answer: $0.14 per fluid ounce.

Step-by-step explanation: $4.48 divided by 32 = $0.14

Given table shows the counts of respondents of a survey that asked 1000 adults about their employment status and whether they owned stocks:

Employment Status Owning Stocks Not Owning Stocks Employed 400 300

Unemployed 50 250 Retired 150 100We have to complete the following parts:

a) How many of the respondents are unemployed or do not own any stocks?

b) If a respondent is chosen at random, what is the probability that the respondent owns stocks?

c) If a respondent is chosen at random, what is the probability that the respondent is retired and does not own stocks?d) If a respondent is chosen at random, what is the probability that the respondent is employed or retired?

e) If a respondent is chosen at random, what is the probability that the respondent is employed, given that the respondent does not own stocks?

Solution:

a) The total number of respondents who are unemployed or do not own any stocks is 50 + 250 + 100 = 400.

b) Probability that a respondent owns stocks = Number of respondents owning stocks / Total number of respondents= (400 + 50 + 150) / 1000= 0.6

c) Probability that a respondent is retired and does not own stocks= Number of retired respondents not owning stocks / Total number of respondents= 100 / 1000= 0.1

d) Probability that a respondent is employed or retired= (Number of employed respondents / Total number of respondents) + (Number of retired respondents / Total number of respondents)= (400 / 1000) + (150 / 1000)= 0.55

e) Probability that a respondent is employed, given that the respondent does not own stocks= (Number of employed respondents not owning stocks / Total number of respondents not owning stocks)= 300 / 350= 0.86

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Answer:

Step-by-step explanation:

The manager is not correct in her calculation.

Step-by-step explanation:

There are 244 males and n females who entered the mall as the manager at the shopping mall counts.

If 25% of all males are children, then the number of male children are .

Again, the 25% of all female are children, then the number of female chilfren are .

Therefore, the total number of children will be (60 + 0.25n).

But the manager gives the number of children to be 0.25n + 61 who entered the mall.

So, the manager is not correct in that calculation. (Answer)

Answer:  \(\frac{1}{\sqrt{2}}\) which is the same as \(\frac{\sqrt{2}}{2}\)

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

Explanation:

Let's make point J the center of both the octagon and the square.

Connect points E and F to this center to form triangle EFJ.

Angle FJE is 360/n = 360/8 = 45 degrees. We simply split the central angle 360 into 8 equal parts because we have a regular octagon.

Without loss of generality, let's make segment JE to be 1 unit long. This means JF is also 1 unit long. The distance from the center J to any corner point on the octagon is the same. We could scale this radial distance up or down, and still arrive at the same final answer. So it really doesn't matter what JE is.

Use the SAS triangular area formula to get the area of triangle EFG.

\(\text{area} = 0.5*\text{side1}*\text{side2}*\sin(\text{angle})\\\\\text{area} = 0.5*JF*JE*\sin(\text{angle FJE})\\\\\text{area} = 0.5*1*1*\sin(45^\circ})\\\\\text{area} = 0.5*\frac{\sqrt{2}}{2}\\\\\text{area} = \frac{\sqrt{2}}{4}\)

The area of triangle EFJ is exactly \(\frac{\sqrt{2}}{4}\) square units when we start off with JE = 1. We have 8 identical such triangles that form the entire octagon.

Multiply the previous area by 8 to find the area of the full octagon.

\(8*(\text{area of triangle}) = 8*\frac{\sqrt{2}}{4} = 2\sqrt{2}\)

Let \(n = 2\sqrt{2}\) represent the area of the octagon when JE = 1.

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

Now to compute the area of the square ACEG.

Like earlier, split the figure into identical four triangles.

Let's find the area of triangle GJE.

\(\text{area} = 0.5*\text{side1}*\text{side2}*\sin(\text{angle})\\\\\text{area} = 0.5*JG*JE*\sin(\text{angle GJE})\\\\\text{area} = 0.5*1*1*\sin(90^{\circ})\\\\\text{area} = 0.5\)

Keep in mind that the diagonals of any square are always perpendicular, which is why angle GJE is 90 degrees.

Four such identical triangles compose the square, so 4*0.5 = 2 square units is the area of the square when we let JE = 1. We'll use this square area later, so let m = 2.

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

The last step is to divide the values of m and n, which are the square and octagon areas in that order (when JE = 1).

\(\frac{m}{n} = \frac{2}{2\sqrt{2}}\\\\\frac{m}{n} = \frac{1}{\sqrt{2}}\\\\\frac{m}{n} = \frac{1*\sqrt{2}}{\sqrt{2}*\sqrt{2}}\\\\\frac{m}{n} = \frac{\sqrt{2}}{2}\\\\\)

Interestingly, this is exactly equal to the value of sin(45). That fraction is roughly equal to 0.707, meaning that the square's area is roughly 70.7% of the octagon's area.

The ratio of the area of ACEG and the area of ABCDEFGH will be √2/2.

The space occupied by any two-dimensional figure in a plane is called the area.The space occupied by the octagon in the two-dimensional plane will be the area of the octagon.

Let's make point J the center of both the octagon and the square. Connect points E and F to this center to form triangle EFJ. Angle FJE is 360/n = 360/8 = 45 degrees. We simply split the central angle 360 into 8 equal parts because we have a regular octagon.

Use the SAS triangular area formula to get the area of triangle EFG.

Area = 0.5 x JF x JE x sin(FJE)

Area = 0.5 x 1  x sin45

Area = 0.5 x ( √2 / 2 )

Area = √2 / 4

The area of triangle EFJ is exactly √2 / 4 square units when we start off with JE = 1. We have 8 identical triangles that form the entire octagon.

Multiply the previous area by 8 to find the area of the full octagon.

8 x area of triangle = 8 x ( √2 / 4 ) = 2√2

Let n = 2√2 represent the area of the octagon when JE = 1. Now to compute the area of the square ACEG.

Let's find the area of triangle GJE.

Area = 0.5 x JG x JE x Sin(GJE)

Area = 0.5 x 1 x 1 x sin(90)

Area = 0.5

Keep in mind that the diagonals of any square are always perpendicular, which is why angle GJE is 90 degrees.

The last step is to divide the values of m and n, which are the square and octagon areas in that order (when JE = 1).

m / n = 2 / 2√2

m / n = √2 / 2

Therefore, the ratio of the area of ACEG and the area of ABCDEFGH will be √2/2.

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Answer:

Step-by-step explanation:          

\(49x^2-42x+(\frac{42}{2})^2=49x^2-42x+(\frac{42}{2} )^2\)    (completing the square)  

  \(49x^2-42x+441=49x^2-42x+21^2\)

                              \(=(7x-21)^2\)

So    \(49x^2-42x+441=(7x-21)^2\)

Solution: The required constant is 441.

Remember:    Completing the square IN \(ax^2+bx+c\) involves adding  \((\frac{b}{2} )^2\)     to both sides of the equation. THIS KEEPS IT BALANCED AND ALLOWS US TO MAKE A PERFECT SQUARE.    

Answer:

D. 44

Step-by-step explanation:

180 - 68 = 112

m∠1 = 112

112 + 24 = 136

180 - 136 = 44

Answer:

15.53 sq inches, 15.71 inches

Step-by-step explanation:

(3 * 4) + (1.5^2 * pi)/2 = 12 + 3.53 = 15.53 sq inches

3 + 4 + 4 + (2pi * 1.5)/2 = 15.71 inches

The number line below shows the numbers 4, 6, 8, and 10.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.

We can represent these whole numbers using fractions by noting that any number can be written as a fraction with the denominator equal to 1. For example, 4 can be written as 4/1, 6 can be written as 6/1, 8 can be written as 8/1 and 10 can be written as 10/1.

In addition, fractions can be used to represent these numbers in a more complex way. For example, 4 can be written as 2/2, 6 can be written as 3/2, 8 can be written as 4/2, and 10 can be written as 5/2. This is because each number can be divided by 2 to get the fraction, and the denominator of the fraction will remain 1.

We can also represent these numbers as fractions with a denominator other than 1. For example, 4 can be written as 8/4, 6 can be written as 12/4, 8 can be written as 16/4, and 10 can be written as 20/4. This is because each number can be divided by 4 to get the fraction, and the denominator of the fraction will remain 1.

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We have to calculate the estimated standard error and means of the two samples before calculating  the test statistic for a two sample test of means with population variances equal but unknown.

In the given question, we have to explain steps that are necessary before you can calculate the test statistic for a two sample test of means with population variances equal but unknown.

The test statistic for a two-sample independent t-test is derived by dividing the difference between the means of the two samples by the estimated standard error, either pooled or unpooled. The total amount of variation in both groups is gauged by the anticipated standard error.

So we have to calculate the estimated standard error and means of the two samples before calculating  the test statistic for a two sample test of means with population variances equal but unknown.

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Recall the following information:

1) In a plane, two lines that are parallel exist on the same axis.

2) Hence, any line which is perpendicular to one of two parallel lines is also perpendicular to the other.

3) This concept is evident in the model of ladders, where each of the vertical lines is perpendicular to the parallel step lines(horizontal lines).

With this information, it can be said that if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

T

Answer:

They are same side interior angles. Angle A measures 55°.

Step-by-step explanation: