4. Fill in the blanks to complete the two-column proof.
Given: 22 23
Prove: 21 and 23 are supplementary.
Proof:
(in picture)

Answer:

12) complementary,   x=15

13) complementary, x = 35

x+ (x-20) = 90

x+x+20=90

2x=70

x=35

14) supplementary, x=31

2x+3x+25=180

5x=155

x=31

15) <1 = 130 degrees

 <2 = 50 degrees

<3 = 130 degrees

16) x=53

x+2x+21=180

3x=159

x=53

Answer:

1.28 Step-by-step explanation: got

The probability that the two smartest people will be in the same group is approximately 0.023 or 2.3%.

The probability of the two smartest people being in the same group can be calculated by considering the total number of possible ways the groups can be formed and the number of ways the two smartest people can be in the same group.

To find the total number of ways the groups can be formed, we can use the concept of combinations. In this case, we have 36 people in the class and we want to split them into 12 groups of 3. We can calculate the total number of ways the groups can be formed using the formula for combinations:

C(n, r) = n! / (r! * (n-r)!)

where n is the total number of people and r is the number of people in each group.

In our case, n = 36 and r = 3. Plugging these values into the formula, we get:

C(36, 3) = 36! / (3! * (36-3)!)

Simplifying this expression, we find that there are 7140 different ways to form the groups.

Now, let's calculate the number of ways the two smartest people can be in the same group. Since there are 12 groups and we want the two smartest people to be in the same group, we can treat them as a single unit. So, we need to calculate the number of ways to distribute the remaining 34 people into 11 groups of 3.

Using the same combination formula, we have:

C(34, 3) * C(11, 1) = (34! / (3! * (34-3)!) * (11! / (1! * (11-1)!))

Simplifying this expression, we find that there are 163,800 different ways to distribute the remaining people.

Now, to calculate the probability, we divide the number of ways the two smartest people can be in the same group by the total number of possible ways the groups can be formed:

Probability = (Number of ways the two smartest people in the same group) / (Total number of possible ways to form groups)

Probability = 163,800 / 7,140

Simplifying this expression, we find that the probability is approximately 0.023 or 2.3%.

Therefore, the probability that the two smartest people will be in the same group is approximately 0.023 or 2.3%.

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Answer:

Exact form: 36(3.14)

Step-by-step explanation:

6 x 6 x (3.14 or pie)

36(3.14)

Decimal form: 113.097 = 113.1

Answer: 28.3

Step-by-step explanation:

6/2 = 3(radius)

3*3*3.14 = 28.26

Round up for tenths place

28.3

Answer:

From largest to smallest: FG, FH, GH

Step-by-step explanation:

Given

\(FG = 6x + 7\)

\(GH = 8x - 5\)

\(FH = 10x - 11\)

\(Perimeter = 87\)

Required

Order the sides in descending order

First, we need to solve for x.

Perimeter of FGH is calculated as thus:

\(Perimeter = FG + GH + FH\)

Substitute values for FG, GH, FH and Perimeter

\(87 = 6x + 7 + 8x - 5 + 10x - 11\)

Collect Like Terms

\(87 - 7 + 5 + 11= 6x + 8x + 10x\)

\(96= 24x\)

Reorder

\(24x = 96\)

Divide through by 24

\(x = 96/24\)

\(x = 4\)

Substitute 4 for x in FG, GH and FH

\(FG = 6x + 7\)

\(FG = 6 * 4 + 7\)

\(FG = 24 + 7\)

\(FG =31\)

\(GH = 8x - 5\)

\(GH = 8 * 4 - 5\)

\(GH = 32 - 5\)

\(GH = 27\)

\(FH = 10x - 11\)

\(FH = 10*4 - 11\)

\(FH = 40 - 11\)

\(FH = 29\)

In order of arrangement in descending order, we have:

\(FG =31\)    \(FH = 29\)     \(GH = 27\)

The value of x is obtained as follows:

128º.

The measure of angle A is given as follows:

m < A = 132º.

For a parallelogram, the opposite angles are congruent, meaning that they have the same measure, hence the value of x is obtained as follows:

5x - 508 = x + 4.

4x = 512

x = 512/4

x = 128.

Then the measure of angle A is given as follows:

m < A = 5(128) - 508

m < A = 132º.

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Answer:

24 23/100

Step-by-step explanation:

I think this is the answer.

9514 1404 393

Answer:

  24 23/100

Step-by-step explanation:

"Twenty-three hundredths," or 23/100, is a fraction that cannot be reduced. The mixed number version is ...

  24 23/100

_____

Additional comment

You start with a denominator that corresponds to the place value of the least-significant digit. Here, that's hundredths, so the fraction you start with is some number of hundredths. Then you reduce the fraction if possible, by canceling all factors of 2 or 5 that you can.

Had it been 23.24, you would start with 23 24/100 and cancel a factor of 4 from numerator and denominator: 23 6/25.

The mean square errors for the three-month and four-month moving average forecasts shown below.

How closely a regression line resembles a set of data points is determined by the Mean Squared Error. It is a risk function that corresponds to the squared error loss's expected value. The average, more particularly the mean, of errors squared from data related to a function is used to determine mean square error.

Given:

According to the Given data we construct a table as

Month   Sales   3- month           4- month      3- month     4- month      

                         moving             moving         squared       squared

                        averages            averages      error           error

1             9.6      

2             9.2

3             9.3

4             9.2     9.367                                        0.111            

5             9.2     9.400                   9.450           0.160        0.123    

6             9.2     9.500                  9.500            0.010        0.140    

7             9.2     9.733                   9.625            0.001         0.006  

8             9.2     9.733                   9.725            0.751          0.776  

9             9.2     10.000                 9.950           0.010           0.002  

10            9.2     10.067                  9.975            0.218          0.141  

11             9.2     10.033                   9.950          0.401           0.322

12            9.2     9.633                   9.975             0.004          0.031

13                       9.567                 9.650    

                                                        MSE             0.185            0.176

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Answer:

s=6.2

Step-by-step explanation:

-3.1s=-19.22

divide -19.22 by -3.1 to get s

s=6.2

Answer:

c

Step-by-step explanation:

The greatest possible whole-number length of the unknown side among the option is 9 inches.

Obtuse triangle is a triangle that has one of it internal angle greater than 90 degrees.

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

If the sides of the triangles are x, y and z. Therefore,

x + y > z

x + z > y

y + z > x

Therefore, the greatest possible length among the option is 9.

Proof

12 + 14 > 9

12 + 9 > 14

14 + 9 > 12

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The correct statement is Most of the songs were between 3 minutes and 3.8 minutes long.

Based on the given information from the graph, we can determine the following:

The graph shows an upward trend from 2.8 to 3.4 on the horizontal axis.

Then, there is a downward trend from 3.4 to 4 on the horizontal axis.

From this, we can conclude that most of the songs played during the one-hour interval were between 3 minutes and 3.8 minutes long. This is because the upward trend indicates an increase in length from 2.8 to 3.4, and the subsequent downward trend suggests a decrease in length from 3.4 to 4.

Therefore, the correct statement is:

Most of the songs were between 3 minutes and 3.8 minutes long.

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Answer:

A

Step-by-step explanation:

Answer: 1.1

1.01 x 1.1 = 1.111

I hope this is good enough:

False. In statistical process control (SPC), the mean and the standard deviation serve different purposes and are not interchangeable.

The mean, often denoted as μ, represents the central tendency or average of a set of data points. It provides information about the typical or expected value of the process under consideration.

The mean is commonly used as a reference point in SPC to monitor and control the process performance. Control charts, which are a fundamental tool in SPC, typically plot the mean of the process data over time to detect any shifts or trends.

On the other hand, the standard deviation, often denoted as σ, is a measure of the dispersion or variability of the data points around the mean. It provides insights into the spread or consistency of the process. The standard deviation is not used as a substitute for the mean in SPC; rather, it is used to calculate control limits on control charts.

Control limits help identify when the process is exhibiting unusual variation that may indicate a special cause or a deviation from the desired performance.

In summary, the mean and the standard deviation are distinct statistical measures, each with its own role in SPC. They provide complementary information and should not be used interchangeably.

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The number that best represents the slope of the graphed line that is given is: -4.

The slope of a line is the ratio of the vertical distance to the horizontal distance across the line. It is calculated using the formula:

Slope (m) = rise/run = change in y / change in x = (y2 - y1)/(x2 - x1)

Given the two points on a coordinate plane as shown in the mage below, let:

(x1, y1) represent (0, 2)

(x2, y2) represent (0.5, 0)

Plug in the values

Slope (m) = change in y / change in x = (0 - 2) / (0.5 - 0)

Slope (m) = -2/0.5

Slope (m) = -4

Therefore, we can state that, the number that best represents the slope of the graphed line that is given is: -4.

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The actual answer is C.1/2

chust mee am a doktor

The most appropriate chart to see the correlation between car mileage and year the car was built for various car models would be a scatterplot chart.

In a scatterplot chart, each point represents a pair of values: one value on the x-axis (in this case, year the car was built) and another value on the y-axis (in this case, mileage). By plotting these pairs of values for each car model in the sample, we can visually examine the relationship between mileage and year built for each car model and determine if there is a correlation between the two variables.

A line chart is used to display data that changes over time, typically for a single variable. A heatmap chart is used to show the magnitude of values for different categories using different colors. Therefore, neither of these chart types would be appropriate to show the correlation between mileage and year built for various car models.

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Given:

Consider the given sequence is 9, 81, 729, 6561.

To find:

The common ratio.

Solution:

We have,

9, 81, 729, 6561

Here,

First term = 9

Second term = 81

Divide the second term by first term to get the common ratio.

\(r=\dfrac{81}{9}\)

\(r=9\)

Similarly,

\(\dfrac{81}{9}=\dfrac{729}{81}=\dfrac{6561}{729}=9=r\)

Therefore, the common ratio is 9.

The standard deviation for the dataset (4, 4, 4, 4, 4) is zero (0)

To find a data set with 5 values for which the standard deviation is zero,

⇒ (4, 4, 4, 4, 4)

For the above dataset;

Mean μ = 4

Number of samples n = 5

Standard deviation σ = \(\sqrt{\frac{sumof(xi - x)^2}{n} }\)

                                   = \(\sqrt{\frac{(4-4)^2+(4-4)^2+(4-4)^2+(4-4)^2+(4-4)^2}{5} }\)

                                   = 0

Therefore, for the dataset (4, 4, 4, 4, 4) the standard deviation is zero(0).

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The surface area of the larger cone is about 41.09 square inches.

To determine the surface area of the larger cone, we can set up a proportion based on the scale factor between the two cones. Let's call the scale factor "k".

From the given information, we know that the surface area of the smaller cone is 11.74 square inches and the surface area of the larger cone is unknown (let's call it "x" square inches).

Using the scale factor, we can write the proportion:

(11.74 / x) = (3.5 / 3.5)

Simplifying the proportion, we have:

11.74 = (x / 3.5)

To find the value of "x", we can cross-multiply:

x = 11.74 * 3.5

x ≈ 41.09

The surface area of the larger cone is approximately 41.09 square inches, rounded to the closest hundredth.

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Answer:

71°

Step-by-step explanation:

Given;

<A=27°

<B=82°

<T=?

We add all angles and subtract it from 180 since an interior angle adds up to 180

<A+<B+<T=180

27°+82°+<T=180

109°+<T=180

<T=180-109

<T=71°

Therefore angle T <T is equal to 71°degrees

Answer:

1.6

Step-by-step explanation:

an integer is defined as any positive or negative whole number.

1.6=16/10=8/5 . This is a fraction

0 is a whole number

8 is a whole number

-15 is a whole number

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Answer:

They are the same line. It means that they are overlapping line.

Answer:

Overlapping

Step-by-step explanation:

Divide every term of the second equation, it would be 2x + y = 6, which is the same as the first equation.

Answer:

v=pie r² ×h

v=3.14×2²×8

v= 100.48

Step-by-step explanation:

you are using diameter as the radius that is why exactly you are not getting it right! divide the diameter by 2 to get radius and use it with the formula

The measure of ∠4 = 44°.

We have two angles ∠3 and ∠4 which are complementary of each other.

We have to find the measure of ∠4.

Two angles are said to be complementary if their sum is equal to 90°.

Mathematically -   x + y = 90°

According to the question -

∠3 = 46°

∠4 = x (Let)

Now, ∠3 and ∠4 are Complementary angles. Therefore -

∠3 + ∠4 = 90°

∠4 = 90 - ∠3

∠4 = 44°

Therefore -

∠4 = 44°

Hence, the measure of ∠4 = 44°.

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6% of a length is 570m and the original length can be calculated by dividing 570m by 0.06, resulting in 9500m.

To calculate the original length given that 6% of it is 570m, we can use the following formula: Original length = (570 ÷ 0.06) Original length = 9500mTo solve this problem, firstly the percentage of 6% needs to be converted into a decimal by dividing 6 by 100. This will give us 0.06. Then, the original length is found by dividing the given value of 6% (570m) by the decimal equivalent (0.06). Therefore, the original length is 9500m. To summarise, 6% of a length is 570m and the original length can be calculated by dividing 570m by 0.06, resulting in 9500m.

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The best description of the passenger's linear and angular velocity while passing point A is option d) Linear Velocity Constant, Angular Velocity Constant.

When the passenger is at point A, which is the highest point of the ride, the seat exerts a normal force with a magnitude of 0.8F, where F represents the person's weight. This normal force provides the necessary centripetal force to keep the person moving in a circular path. At this point, the passenger's linear velocity remains constant, as there is no change in speed.

Since the passenger releases a small rock without hitting anything, there are no external torques acting on the system. Therefore, according to the law of conservation of angular momentum, the passenger's angular velocity remains constant as well. The angular velocity is determined by the rotational motion of the wheel and does not change as the passenger passes point A.

Therefore, the passenger's linear velocity is constant, and their angular velocity is also constant while passing point A, resulting in the most accurate description being d) Linear Velocity Constant, Angular Velocity Constant.

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The given equation 6x+2y=13 is a linear equation in two variables. In this equation, x and y are variables while 6 and 2 are their respective coefficients, and 13 is a constant term. The equation can be represented as a straight line on a graph. The slope of this line is -3, and it intersects the y-axis at the point (0, 13/2).

In this equation, if we substitute x=0, then y=13/2, and if we substitute y=0, then x=13/6. These are the two points that the line passes through the x and y-axis.

A linear equation is a polynomial equation that is of the first degree, meaning the variables in the equation are not raised to any powers other than one. This equation is in the standard form where the variables are in the first degree. 6x + 2y = 13 is the form of the given linear equation. x and y are the two variables, and 6 and 2 are their respective coefficients. The equation can be represented as a straight line on a graph. The slope-intercept form of this equation is y = -3x + 13/2. The equation is also in standard form.

When x = 0, the equation becomes 2y = 13. This means that the point of intersection is (0, 13/2) when y = 0, the equation becomes 6x = 13, and the point of intersection is (13/6, 0). The slope of the line is -3. When x increases by 1, y decreases by 3.

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Answer:

n=27 degrees

m=36 degrees

Step-by-step explanation:

So the inside triangle has two equal sides. To find these angles you would do the degrees of a triangle (180) minus the known value and then divided by two.

so it is: 180-126/2 which gives you 27 degrees.

this means the n value is 27.

to find m, you have to take away 90 degrees and the n value from 180.

so it is: 180-90-27 which gives you 63 degrees.

now you must take the smaller angle from 63 degrees to find m.

so it is: 63-27 which gives you 36

therefore...

n=27 degrees

m=36 degrees

Answer:

80°

Step-by-step explanation:

the triangles are symmetrical. therefore their angles will be equal.

interior angles of a triangle = 180°

180° - 30° - 70° = m<D

80° = m<D