Help please answer the number 3 only thanyou
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The completed two-column table that we can  use to prove the congruence of ∠BAD and ∠DCB indicates that the missing proof in step 6 of the table is substitution.

Therefore correct option is option B

Congruent angles are described as angles that have the same measurement.

The two-column table is shown below;

 Statements                                                           Reasons

1. ABCD is a parallelogram with diagonal                Given

2. ║ and ║                                                       Definition of a parallelogram

3. ∠2≅∠3, ∠1≅∠4                                              Alt. int. ∠s are ≅

4. m∠2 = m∠3 and m∠1 = m∠4                         Measures of ≅ ∠s are =

5. m∠1 + m∠2 = m∠4 + m∠2                              Addition prop. of equality

6. m∠1 + m∠2 = m∠4 + m∠3                              Substitution

7. m∠1 + m∠2 = m∠BAD                                     Angle addition property

m∠3 + m∠4 = m∠DCB

8. m∠BAD = m∠DCB                                          Substitution

9. ∠BAD ≅ ∠DCB                                              Angles are congruent if   their measures are the same    

Therefore, the missing reason in the partial proof is therefore substitution.

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The correct statements are given as follows:

The time it will take for them to complete the puzzle is obtained using the together rate, which is the sum of each separate rates.

The rates are given as follows:

The together rate is:

1/x.

In which x is the time needed to complete the puzzle.

Hence the equation is:

1/7 + 1/5 = 1/x.

The time is then obtained as follows:

1/x = (5 + 7)/35

x = 35/12

x = 2.9 hours.

The party part is incomplete, hence:

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To solve the inequality 2/3k - 6 < 24, we can start by adding 6 to both sides of the inequality:

2/3k - 6 + 6 < 24 + 6

Simplifying the left side gives:

2/3k < 30

To isolate k, we can multiply both sides by 3/2:

2/3k * 3/2 < 30 * 3/2

Simplifying the left side gives:

k < 45

Therefore, the inequality 2/3k - 6 < 24 expressed in its simplest form is k < 45.

The number used in the blanks to satisfy the inequality is 1/2.

i.e

1/2 x 12 < 12

6 < 12

We have,

___ x 12 < 12

Now,

To fill in the blank we substitute the following.

- 2/2

- 3/2

- 1/2

Substitute each option in the blanks and see which satisfies the inequality.

Now,

2/2 x 12 < 12

1 x 12 < 12

This is not true.

3/2 x 12 < 12

3 x 6 < 12

18 < 12

This is not true.

1/2 x 12 < 12

6 < 12

This is true.

Thus,

The number used in the blanks to satisfy the inequality is 1/2.

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If the table does not represent a function, the value of "a" may be: A. -4; D. 2; and F. 5. [Note, no calculation is needed, just apply the criteria that makes a table a function].

A table that represents a function will have each x-value assigned to only one y-values, in order words, on the x-values column, there will be no repeating x-value.

Looking at the table given with the options, we see that:

if a = -4, we will have a repeating x-value, the same with 2 and 5.

However, if we have a represented as 0, 1, and 3, there would be no repeating x-value. Therefore, for the table not to be a function, a may be equal to:

A. -4; D. 2; and F. 5

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The inverse matrix used to decrypt the message is given as follows:

[tex]\left[\begin{array}{cc}-5&-9\\-1&2&\end{array}\right][/tex]

To obtain the inverse matrix, we must have the original matrix side by side with the identity matrix, as follows:

[tex]\left[\begin{array}{cc}2&9\\1&5&\end{array}\right] \left[\begin{array}{cc}1&0\\0&1&\end{array}\right][/tex]

Then we must do row operations on the right matrix so we end with the identity matrix on the right and the inverse matrix on the right.

First we divide the first line by 2, hence:

[tex]\left[\begin{array}{cc}1&4.5\\1&5&\end{array}\right] \left[\begin{array}{cc}0.5&0\\0&1&\end{array}\right][/tex]

Then we want the element a row 2 column 1 to be of zero, hence:

R2 -> R2 - R1

[tex]\left[\begin{array}{cc}1&4.5\\0&0.5&\end{array}\right] \left[\begin{array}{cc}0.5&0\\-0.5&1&\end{array}\right][/tex]

Then we want the diagonal element of the second row to be of 1, hence we multiply by 2, thus:

[tex]\left[\begin{array}{cc}1&4.5\\0&1&\end{array}\right] \left[\begin{array}{cc}0.5&0\\-1&2&\end{array}\right][/tex]

Finally, we want the element of 4.5 to be of zero, hence:

R1 -> R1 - 4.5R2

Then:

[tex]\left[\begin{array}{cc}1&0\\0&1&\end{array}\right] \left[\begin{array}{cc}-5&-9\\-1&2&\end{array}\right][/tex]

The inverse matrix is of:

[tex]\left[\begin{array}{cc}-5&-9\\-1&2&\end{array}\right][/tex]

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Answer:

Step-by-step explana

To fill in the table, we can use the following formula:

Account value at end of year = (Initial investment + amount borrowed) x (1 + interest rate) x (1 + mutual fund return rate)

Let's first calculate the amount borrowed based on the margin level:

50% margin level: $1,000 x 50% = $500 borrowed

75% margin level: $1,000 x 75% = $750 borrowed

100% margin level: $1,000 x 100% = $1,000 borrowed

Now, let's use the formula to fill in the table:

Margin level Mutual fund return Account value in stellar market Account value in fair market Account value in terrible market

50% 40% $1,500 $1,050 $525

50% 5% $1,100 $1,027.50 $717.45

50% -30% $700 $665 $465

75% 40% $1,750 $1,225 $612.50

75% 5% $1,312.50 $1,221.88 $853.63

75% -30% $875 $831.25 $581.88

100% 40% $2,000 $1,400 $700

100% 5% $1,500 $1,400 $980

100% -30% $1,000 $950 $665

Note that the account value in each market scenario is lower than the initial investment plus the amount borrowed. This is because Ike has to pay back the borrowed amount with interest at the end of the year. The interest rate is 10%, so the account value has to be higher than the initial investment plus the amount borrowed by at least 10% in order to make a profit.tion:

The value of the side x is 1. 23

To determine the value, we have that the properties of a square are;

From the information given, we have that;

Hypotenuse side = √3

Opposite side = x

Angle = 45 degrees

Using the sine identity, we have that;

sin θ = opposite/hypotenuse

substitute the values, we get;

sin 45 = x/√3

cross multiply the values, we have;

x = 0. 7071× 1. 7321

x = 1. 23

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Answer:

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

Standard form for the equation of a circle is:

Using the given endpoints of the diameter find the center, which is the midpoint:

The radius is half the distance between endpoints:

Substitute values into equation:

Answer:

Step-by-step explanation:

To find the area of the shaded region, we need to first find the x-coordinates of the points where the two functions intersect. We can set f(x) = g(x) and solve for x:

x^4 - 12x^3 + 48x^2 = 44x + 105

x^4 - 12x^3 + 48x^2 - 44x - 105 = 0

We can use a numerical method, such as the Newton-Raphson method, to approximate the roots of this equation. Using a graphing calculator or computer algebra system, we can find that the roots are approximately:

x = -1.932, x = 0.695, x = 4.149

Note that the root x = -1.932 is outside the given interval [3, 4], so we can ignore it.

The shaded region is bounded by the x-axis, the line y = 340, and the graphs of f(x) and g(x) between x = 3 and x = 4. To find the area of this region, we can integrate the difference between the two functions over this interval:

A = ∫3^4 [g(x) - f(x)] dx

A = ∫3^4 [44x + 105 - (x^4 - 12x^3 + 48x^2)] dx

A = ∫3^4 [-x^4 + 12x^3 - 48x^2 + 44x + 105] dx

We can integrate term by term using the power rule:

A = [-x^5/5 + 3x^4 - 16x^3 + 22x^2 + 105x]3^4

A = [-1024/5 + 192 - 192 + 22 + 105] - [-81/5 + 108 - 192 + 66 + 105]

A = 347.2

Therefore, the area of the shaded region is approximately 347.2 square units.

A. The margin of error for a 99% confidence interval is $$2,320.75.

B. The confidence interval for the mean starting salary of college graduates who have taken a statistics course is CI = $42,462.25 to $47,103.75

PART A.

The margin of error (ME) is determined using the formula:

ME= z ∗ σ/√n

where:

z is the z-score for the desired confidence level

σ is the population standard deviation

n is the sample size

For a 99% confidence level, the z-score is 2.576. The population standard deviation is $10,272, and the sample size is 130.

Substituting these values into the formula, we have:

ME =  2.576 ∗ 10272/√130

ME = $2,320.75

PART B

The confidence interval (CI) is determined using the formula:

CI = [tex]\bar{x}[/tex] ± ME

where:

[tex]\bar{x}[/tex] is the sample mean

ME is the margin of error

The sample mean is $44,783, and the margin of error is $2,320.75.

Substituting the values into the formula, we get:

CI= 44783 ± 2320.75

CI = $42,462.25 to $47,103.75

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The probability that a male student is taller than 74 inches is 0.3085.

We are given that

σ = 4 inches.

We are also told that 95% of the heights are between 62 inches and 78 inches, which means that 2.5% of the heights are below 62 inches and 2.5% of the heights are above 78 inches.

Using a standard normal distribution table, we can find the z-scores corresponding to these percentages:

The z-score corresponding to the 2.5% below 62 inches is -1.96.

The z-score corresponding to the 2.5% above 78 inches is 1.96.

For the lower limit:

-1.96 = (62 - μ) / 4

For the upper limit:

1.96 = (78 - μ) / 4

Solving for μ in both equations, we get:

μ = 70.08 for the lower limit

μ = 73.92 for the upper limit

Now, the average of these two estimates:

μ ≈ (70.08 + 73.92) / 2 ≈ 72 inches.

To approximate the probability that a male student is taller than 74 inches, we can standardize the height value using the z-score formula:

z = (x - μ) / σ

z = (74 - 72) / 4 = 0.5

As, the probability that a standard normal random variable is greater than 0.5, which is 0.3085.

Therefore, the probability that a male student is taller than 74 inches is 0.3085.

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[tex]\tan(44^o )=\cfrac{\stackrel{opposite}{29}}{\underset{adjacent}{x}} \implies x=\cfrac{29}{\tan(44^o)}\implies x\approx 30.03[/tex]

Make sure your calculator is in Degree mode.

The perimeter of the irregular shape is 40 cm.

We know that a polygon is defined as a closed figure made up of three or more line segments connected end to end.

Given that the parameters as :

10 cm

15 cm

7 cm

6 cm

2 cm

Perimeter  ; the sum of length of the sides used to made the given figure..

Let Perimeter  = p

Perimeter P = 10 + 15 + 7 + 6 + 2

= 40 cm

The answer will be 40 cm.

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The  center and variation of the  data set is determined by calculating  the mean and standard deviation.

The time spent volunteering is centered around 7 hours

The values differ from the average by about 4 hours.

A data set is described as a collection of data which corresponds to one or more database tables, where every column of a table represents a particular variable, and each row corresponds to a given record of the data set in question for tabular data sets.

The mean is found as:

Mean = (6 + 5 + 7 + 8 + 9) / 5 = 7 hours

The Range = maximum value - minimum value

Range = 9 - 5 = 4 hours.

The Deviations are  (-1, -2, 0, 1, 2)

Standard deviation = √ [((-1)² + (-2)² + 0² + 1² + 2²) / 5]

Standard deviation = √ [(1 + 4 + 0 + 1 + 4) / 5]

Standard deviation = √2

Standard deviation = 1.4 hours

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The approximate percentage of daily phone calls numbering between 33 and 39 is about 68%.

The empirical rule states that for a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations of the mean, and approximately 99.7% falls within three standard deviations of the mean.

In this case, the mean is 36 and the standard deviation is 3.

To find the percentage of daily phone calls numbering between 33 and 39, we need to first calculate the number of standard deviations that separate these values from the mean:

For 33: (33 - 36) / 3 = -1

For 39: (39 - 36) / 3 = 1.

So, we are looking for the percentage of data that falls between -1 and 1 standard deviations from the mean.

According to the empirical rule, this interval contains approximately 68% of the data.

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The approximate area to the left of z= 2​ is 0.978

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

The left of z= 2​

The area to the left of z is calculated by calculating the probability that the z-score is less than 2

In other words, this is represented as

Area = (z < 2)

This can then be calculated using a statistical calculator or a table of z-scores,

Using a statistical calculator, we have the area to be

Area =  0.97725

When this value is approximated, we have the approximated area to ve

Area =  0.978

Hence, the area is 0.978

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Hello

2/7 = 2x5/7x5 = 10/35

10/35 > 6/35

=> 2/7 > 6/35

The reduced row echelon form of the matrix is given as follows:

[tex]\left[\begin{array}{cccc}-1&0&0&8\\0&1&0&-2\\0&0&1&-6\end{array}\right][/tex]

The matrix in the context of this problem is defined as follows:

[tex]\left[\begin{array}{cccc}-1&5&-3&6\\0&3&6&-42\\0&-6&-1&18\end{array}\right][/tex]

First we want a value of 1 at line 1, column 1, hence we multiply the first line by -1, that is:

R1 -> -R1.

Hence:

[tex]\left[\begin{array}{cccc}1&-5&3&-6\\0&3&6&-42\\0&-6&-1&18\end{array}\right][/tex]

Then we want a value of 1 at line 2 column 2, thus:

R2 -> R2/3.

Hence:

[tex]\left[\begin{array}{cccc}1&-5&3&-6\\0&1&2&-14\\0&-6&-1&18\end{array}\right][/tex]

Then we want a value of 0 at line 3, column 2, hence:

L3 -> L3 + 6L2

[tex]\left[\begin{array}{cccc}1&-5&3&-6\\0&1&2&-14\\0&0&11&-66\end{array}\right][/tex]

Then the solution to the system of equations is given as follows:

Hence the row echelon form of the matrix is given as follows:

[tex]\left[\begin{array}{cccc}-1&0&0&8\\0&1&0&-2\\0&0&1&-6\end{array}\right][/tex]

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Answer:

Step-by-step explanation:

A) $50.40

B) $50.68

Answer:

D={x|x≥2}, R={y|y≥0}.

Step-by-step explanation:

The side length x=6.63.

By using Pythagoras' theorem on right angle triangle,

"The square of the hypotenuse side is equal to the sum of squares of the other two sides". (Pythagoras' theorem)

(12)^2=(10)^2+(x)^2

(x)^2=144-100

(x)^2=44

The side length is x=6.333.

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The concentration will be 0.5 mg/L at time t =39.86 hours

To determine when the concentration will be 0.5 mg/L, we need to solve the equation:

c(t) = 0.5

20t/(t²+4) = 0.5

Multiplying both sides by (t²+4), we get:

20t = 0.5(t²+4)

Simplifying, we get:

20t = 0.5t² + 2

0.5t² - 20t + 2 = 0

Solving this quadratic equation using the quadratic formula, we get:

[tex]2\left(10+3\sqrt{11}\right)[/tex]

2(10+3(3.31))

2(10+9.93)

39.86

So the concentration will be 0.5 mg/L at t =39.86 hours

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The value of x in the circle is 4√5

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

The circle

The value of x in the circle can be calculated using the following pythagoras theorem

x² = (24/2)² - (16/2)²

When the quotients are evaluated, we have

x² = 12² - 8²

When the exponents are evaluated, we have

x² = 144 - 64

When the difference are evaluated, we have

x² = 80

When the exponents are evaluated, we have

x = √80

Simplify

x = 4√5

Hence, the value of x is 4√5

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Since the P-value is less than the level of significance (0.0128 < 0.05), we reject the null hypothesis and conclude that there is sufficient evidence to suggest that Gentle Ben has an overall average glucose level higher than 85.

The level of significance is α = 0.05.

The test statistic is:

z = (x - μ) / (σ / √n)

where x is the sample mean,

μ is the population mean,

σ is the population standard deviation, and

n is the sample size.

Plugging in the given values, we get:

z = (93.5 - 85) / (12.5 / √8) ≈ 2.24

Using a standard normal distribution table or calculator, we find that the P-value is approximately 0.0128.

Since the P-value is less than the level of significance (0.0128 < 0.05), we reject the null hypothesis and conclude that there is sufficient evidence to suggest that Gentle Ben has an overall average glucose level higher than 85.

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It is an exercise where the calculation of the circumference of a circle is made from its radius, it is a very common mathematical operation. The circumference is the distance a point on the edge of a circle moves around its center, and the radius is the distance from the center of the circle to its edge.

Circumference = 2πr

Where "r" is the radius of the circle and "π" is a mathematical constant approximately equal to 3.14. Therefore, the circumference of the circle is obtained by multiplying "π" twice by the value of the radius "r".

It is important to remember that the radius and circumference of a circle are related in a directly proportional way: as the radius increases, so does the circumference, and vice versa.

Therefore we apply the formula C =2πr. What we must do is substitute the radius and the value of pi in the formula and solve, then

C =2πr

C = 2 × 3.14 × 19 km

C = 119.32 km

The circumference of the circle can change, varying the value that we give to pi.