Solve the equation 9x²y² - 12xy + 4 = 0, expressing y in terms of x.

Note that the right triangle's area is 750 units². Here is how to get this.

A right triangle or right-angled triangle, or more technically an orthogonal triangle, formerly known as a rectangle triangle, is a triangle with one right angle, i.e. two perpendicular sides.

Trigonometry is founded on the relationship between the sides and other angles of a right triangle.

So since this triangle is a multiple of a 5-12-13 triangle

Its sides are    25 - 60 - 65( summing this will give 150.)

Its area is  (1/2) * product of the legs  =  (1/2)(25)(60)  =  750 units²

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The reasonable way to test this one is to identify the validity of the hypothesis can be tested.

The hypothesis suggests that when an electric current passes through a wire, it generates a magnetic field. If this magnetic field is strong enough, it could magnetize a non-magnetic nail that is placed nearby. To test this hypothesis, an experiment can be conducted as follows:

A non-magnetic nail, a battery, a wire, and a switch.

Connect the wire to the battery and switch in series. The other end of the wire should be wrapped around the nail multiple times. Once the apparatus is set up, turn on the switch to pass an electric current through the wire.

Before running the current through the wire, test the nail for its magnetic properties by holding it close to some iron filings or other small magnetic objects. If it does not attract any of these objects, then it is non-magnetic.

Turn on the switch and run the electric current through the wire wrapped around the nail for a few minutes.

After running the current through the wire, test the nail again for its magnetic properties. Hold it close to the iron filings or other small magnetic objects and observe if it attracts them.

Compare the results obtained before and after running the current through the wire. If the nail exhibits magnetic properties after running the current, then the hypothesis that passing an electric current through a wire can magnetize a non-magnetic nail can be considered valid.

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Julio can complete one math problem in 10/3 = 3.33 minutes.

Therefore, he can complete all 14 math problems in 14 x 3.33 = 46.62 minutes.

So, it took Julio approximately 46.62 minutes to complete his math homework.

To solve this problem, we need to use the concept of rate and time. We are given that Julio can complete 3 math problems in 10 minutes, which means his rate of work is 3/10 = 0.3 math problems per minute. We need to find out how long it would take him to complete 14 math problems, which is simply a matter of multiplying the number of problems by his rate of work. So, 14 x 0.3 = 4.2 math problems per minute.

However, we need to convert this to time, so we take the reciprocal of 0.3 to get 3.33 minutes per math problem. Finally, we multiply this by the total number of problems (14) to get the total time it took Julio to complete his homework, which is approximately 46.62 minutes.

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The solution to the equation −18 − 6k = 6(1 + 3k) in terms of k is k = -3/4.

A statement that affirms the equivalence of two expressions joined by the equals symbol "=" is known as an equation.

Your steps are correct, and here's the solution to the equation:

−18 − 6k = 6(1 + 3k)

To solve for k, we first use the distributive property to remove the parentheses:

−18 − 6k = 6 + 18k

Then, we simplify the equation by combining like terms:

−18 − 6k + 6k = 6 + 18k + 6k

-18 = 24k

Finally, we isolate k by dividing both sides by 24:

-18/24 = 24k/24

-3/4 = k

Therefore, the solution to the equation −18 − 6k = 6(1 + 3k) in terms of k is k = -3/4.

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The complete question is:

Solve for the value of k in the equation:

-18 - 6k = 6(1 + 3k)

where k is an unknown constant.

The answer is option A. increasing the sample size.

The central limit theorem (CLT) is a statistical theory that explains the behavior of sample means when drawn from a population with any distribution, as long as the sample size is large enough. The CLT states that as the sample size increases, the sampling distribution of the means approaches a normal distribution, regardless of the shape of the original population distribution.

One implication of the CLT is that increasing the sample size makes the sampling distribution more precise and reliable, as the standard error of the mean decreases with larger samples. However, the CLT does not necessarily imply that increasing the sample size decreases the dispersion (or variability) of the sampling distribution itself.

The dispersion of the sampling distribution is determined by the variability of the original population and the sample size, but it does not change with sample size alone. For example, if the original population has a large standard deviation, the sampling distribution of the means will also have a large standard deviation, even with a large sample size. However, as the sample size increases, the means will be more tightly clustered around the population mean, which means that the precision of our estimate of the population mean increases.

Therefore, the answer is option A. increasing the sample size.

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The length and the width of the rectangle are 86m and 86m respectively

The maximum area of a rectangle with a given perimeter, we need to use the fact that the perimeter of a rectangle is the sum of all four sides, or twice the length plus twice the width.

Let L be the length and W be the width of the rectangle, then we have:

Perimeter = 2L + 2W = 344 meters

We want to find the length and width that maximize the area of the rectangle, given this perimeter.

The area of a rectangle is given by the formula:

Area = Length x Width = L x W

To maximize the area, we can use the fact that the area is a quadratic function of one of the variables (either L or W) and that it has a maximum at the vertex of the parabola.

To find the vertex of the parabola, we can use the formula:

Vertex = (-b/2a, f(-b/2a))

where a, b, and c are the coefficients of the quadratic function f(x) = ax^2 + bx + c.

In this case, the area function is:

f(L) = L(172 - L)

where 172 is half the perimeter (since 2L + 2W = 344, we have L + W = 172, so W = 172 - L).

To find the vertex of this parabola, we need to find the value of L that maximizes the area. We can do this by taking the derivative of f(L) with respect to L, setting it equal to zero, and solving for L:

f'(L) = 172 - 2L = 0

L = 86 meters

This gives us the length of the rectangle that maximizes the area. To find the width, we can substitute L = 86 into the equation for the perimeter:

2L + 2W = 344

2(86) + 2W = 344

W = 86 meters

Therefore, the length and width of the rectangle that has the given perimeter and a maximum area are 86 meters and 86 meters, respectively.

The Perimeter of Rectangle could be considered as one of the important formulae of the rectangle. It is the total distance covered by the rectangle around its outside. you will come across many geometric shapes and sizes, which have an area, perimeter and even volume. You will also learn the formulas for all those parameters. Some of the examples of different shapes are circle, square, polygon, quadrilateral, etc. In this article, you will study the key feature of the rectangle

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[tex]ANSWER \\ (( \frac{1}{3} ) {}^{4} ) {}^{ \frac{1}{2} } \\ [/tex]

simplify the expression

[tex]( \frac{1}{3} ) {}^{ \frac{4}{1} \times } {}^{ \frac{1}{2} } \\ ( \frac{1}{3} ) {}^{ \frac{4}{2} } \\ ( \frac{1}{3} ) {}^{2} \\ = \frac{1}{9} [/tex]

~hope it helps~

have a nice day (✿^‿^)

First, we need to calculate what's inside the parentheses of the exponent.

1/3^4 = 1/81

Now, we can simplify the exponent:

(1/81)^1/2 = 1/9

Therefore, (1/3^4)^1/2 = 1/9. <⁠(⁠￣⁠︶⁠￣⁠)⁠>

A z-score of -1.32 indicates that Tim's score on the test is below average, but not extremely unusual or unexpected.

If Tim's calculated z-score for his test score of 72 is -1.32, it means that his score is 1.32 standard deviations below the mean of the distribution.

A z-score represents the number of standard deviations that a data point is away from the mean of the data set.

A negative z-score means that the data point is below the mean, while a positive z-score means that the data point is above the mean.

To calculate Tim's score, we can use the formula:

z = (x - μ) / σ

where:

z = the z-score

x = the test score

μ = the mean of the distribution

σ = the standard deviation of the distribution

Substituting the given values, we get:

-1.32 = (72 - μ) / σ

To solve for μ, we need to rearrange the equation as:

μ = 72 - (-1.32) × σ

This means that if Tim's z-score is -1.32 and his test score is 72, then the mean score.

The distribution is 1.32 standard deviations above his score.

The mean score using the standard deviation of the distribution, but we would need additional information such as the standard deviation value.

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The distance between (x, y) and the focus is given by:

d = √((x - 3)² + (y + 1)²)

And the distance between (x, y) and the directrix is given by:

d' = |y + 2|

To find the focus and directrix of the parabola, we need to first determine its equation. Since we are given two points on the parabola, we can use them to write the general form of its equation, which is y = ax² + bx + c, where a, b, and c are constants.

Using the given points (-2, -5) and (6, -1), we can form two equations as follows:

-5 = 4a - 2b + c

-1 = 36a + 6b + c

Solving these equations simultaneously, we get a = 1/4, b = -3/2, and c = -7/4. Therefore, the equation of the parabola is y = (1/4)x² - (3/2)x - (7/4).

The equation of the axis of symmetry is x = -b/2a, which in this case is x = 3. Therefore, the vertex of the parabola is (3, -2).

The distance between the vertex and the focus is given by |1/(4a)|, which in this case is 1. Therefore, the focus of the parabola is (3, -1).

d = √((x - 2)² + (y + 4)²) = √((x - 3)² + 1²)

Squaring both sides of the equation and simplifying, we get:

(x - 2)² + (y + 4)² = (x - 3)² + 1

Expanding and rearranging the terms, we get the equation of the directrix as:

3x - 4y - 2 = 0

Now that we have the focus and directrix of the parabola, we can find the distances from any point on the parabola to them. Let (x, y) be a point on the parabola. Then, the distance between (x, y) and the focus is given by:

d = √((x - 3)² + (y + 1)²)

And the distance between (x, y) and the directrix is given by:

d' = |y + 2|

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The line of code needed below to complete the factorial recursion method is: return x * fact(x-1);

This will recursively call the fact method with x-1 as the parameter until x reaches 1, and then it will start multiplying all the values from x down to 1 to get the factorial value.

To complete the factorial recursion method using the terms you provided, you can add the following line of code:

```java
public int fact(int x) {
   if (x <= 1) {
       return 1;
   }
   return x * fact(x - 1);
}
```

This code checks if x is less than or equal to 1, and if so, returns 1. Otherwise, it returns x multiplied by the factorial of x-1, allowing for the proper recursive calculation of the factorial.

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Based on the given side lengths of 3cm, 7cm, and 7.4cm, the triangle is a(n) scalene triangle. In a scalene triangle, all sides have different lengths.

Triangles are described in terms of their sides and angles in geometry. A closed planar three-sided polygon shape with three sides and three angles is known as a triangle. The lengths of the sides of a scalene triangle vary. They are not equal, and the angles have three measurements. However, it still has a 180° angle sum, just like all triangles.

A scalene triangle is a triangle with three different side lengths and three different angle measurements. The total of all internal angles, however, is always equal to 180 degrees. As a result, it satisfies the triangle's condition of angle sum.

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Answer:

  r√2

Step-by-step explanation:

You want to know the distance from the center of a marble of radius r to the corner of an L-shaped track in which it rolls.

The center of the marble can only come within r of the track edges, so the distance to the corner will be the hypotenuse of a right triangle with legs r. That distance is r√2.

The center of the marble is r√2 from the corner of the track.

__

Additional comment

You can see in the second attachment that the distance to the corner of the track will depend on where the marble is rolling in the track. It might only be r away from the corner.

<95141404393>

The length of BD is 8.

We can use the property that medians of a triangle divide each other in a 2:1 ratio.

Let BD be x. Then, using this property, we can write:

CE = 2ED

FA= 2FD

BE = 2 x ED

Since EB = 12, we can substitute 12 for EB and solve for ED:

12 = 2 x DE

DE = 6

Now, the length of DB is

= 12/3 + 12/3

= 4 + 4

= 8

Therefore, the length of DB is 8.

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Answer:

1 kilogram = 2.204623 pounds

$17/kilogram = $17/2.204623 pounds

= $7.71/pound

The spring constant of the spring is determined as 5,444.4 N/m.

The maximum acceleration of the object in simple harmonic motion is given by:

a = ω²A

where;

The spring constant k is given as;

ω = √(k/m)

ω²m = k

ω² = k/m

a = ω²A

a = (k/m ) A

Where;

k/m = a/A

k = m (a/A)

k = 25 x 9.8 / 0.045

k = 5,444.4 N/m

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A) The probability of a z-score of 0.5909 or higher is 0.0808.

B) The probability of a three-year return of 10% or less is 0.3413.

C) A return of at least 18.91% would put a domestic stock fund in the top 15% for the three-year period.

(a) The probability that an individual large-cap domestic stock fund had a three-year return of at least 17% is 0.0808.

To calculate this probability, we can use the z-score formula:

z = (x - μ) / σ

Where:

x = 17%

μ = 14.4%

σ = 4.4%

z = (17% - 14.4%) / 4.4% = 0.5909

Using a standard normal distribution table or calculator, we can find that the probability of a z-score of 0.5909 or higher is 0.0808.

(b) The probability that an individual large-cap domestic stock fund had a three-year return of 10% or less is 0.1151.

Using the same formula and substituting x = 10%, we get:

z = (10% - 14.4%) / 4.4% = -1.0000

The probability of a z-score of -1.0000 or lower is 0.1587. However, we want the probability of a return of 10% or less, so we need to subtract this probability from 0.5 (since the normal distribution is symmetric around 0) and round to four decimal places:

P(z ≤ -1.0000) = 0.1587

P(z ≥ 1.0000) = 0.1587

P(z ≤ -1.0000) + P(z ≥ 1.0000) = 0.3174

1 - 0.3174 = 0.6826

0.6826 / 2 = 0.3413

So, the probability of a three-year return of 10% or less is 0.3413.

(c) To be in the top 15% of large-cap domestic stock funds for the three-year period, a fund's return would need to be at least 18.91%.

To find this value, we need to find the z-score that corresponds to the top 15% of the distribution, which is 1.0364 (found using a standard normal distribution table or calculator). Then, we can use the z-score formula to solve for x:

1.0364 = (x - 14.4%) / 4.4%

x - 14.4% = 1.0364 * 4.4%

x = 18.91%

Therefore, a return of at least 18.91% would put a domestic stock fund in the top 15% for the three-year period.

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The equation of the circle is given as follows:

x² + y² = 2704.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The center is the position of the transmitter site, hence it is at the origin.

As stated in the problem, the radius of the circle is given as follows:

r = 52 miles.

Hence the equation of the circle is given as follows:

x² + y² = 52²

x² + y² = 2704.

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Answer: 121/209= 57.89% rounded

Step-by-step explanation:

total golf balls are 209

add red +  yellow balls = 121

121/209= 57.89% rounded

Answer:

Step-by-step explanation:

To check conditions for the use of the ANOVA F-test, the ratio of the largest sample variance to the smallest sample variance is useful.

To check conditions for the use of the ANOVA F-test, we need to examine histograms of the homework hours for all four samples (never attend, attend infrequently, attend frequently, and attend very frequently).

Assuming that the conditions are met for the use of the ANOVA F-test, the data do not support the alternative hypothesis that there is a relationship between church attendance and hours spent on homework each week. The p-value of 0.245 is greater than the typical significance level of 0.05, indicating that there is not enough evidence to reject the null hypothesis that there is no relationship between church attendance and hours spent on homework each week.

(L3) You are dealing with a(n) circumcenter perpendicular segment intersects the side of a triangle at the midpoint.

If a perpendicular segment intersects the side of a triangle at the midpoint, then you are dealing with a circumcenter. The circumcenter is the point of intersection of the three perpendicular bisectors of the sides of a triangle. It is equidistant from the three vertices of the triangle, and it is the center of the circle that passes through all three vertices of the triangle. The circumcenter is an important point of a triangle, and it has several geometric properties that can be used to solve various problems in geometry. For example, the distance between the circumcenter and any vertex of the triangle is the same, and this distance is called the circumradius of the triangle.

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If a and b are integers and c is an irrational number it will produce an irrational number .

Here a is an integer and b is an integer and c is an irrational number

So taking number accordingly

Let us take an example and take a = 5 , b = - 6 , c = √3

New number produces = a × b × c

Putting all the value in the equation we get,

New number produces = 5 × ( - 6 ) × √3

New number produces = 30√3

The new number produced 30√3 is an irrational number.

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The given problem involves the calculation of the ratio of varyi eyi for each of the cases in the previous problem, where there is a relationship between the mean and variance.

The ratio of varyi eyi represents the variance of the data points relative to their mean. To calculate this ratio, we need to find the variance and mean of the given data set. The variance represents the spread of data points around the mean. If the variance is high, then the data points are spread out widely, indicating a large deviation from the mean.

On the other hand, if the variance is low, the data points are clustered closely around the mean, indicating a small deviation from the mean. After calculating the variance and mean, we can find the ratio of varyi eyi for each case. The case with the greatest variance relative to the mean will have the highest ratio of varyi eyi.

This ratio is an important measure of the variability of the data set. In conclusion, to solve the given problem, we need to calculate the ratio of varyi eyi for each case and compare them to find the case with the highest ratio. This will help us understand the variable of the data set and how it relates to the mean.

To analyze this, let's first define the terms:

1. Mean: The average of a set of data points, calculated by summing all data points and dividing by the total number of points.

2. Variance: A measure of how spread out a set of data points is, calculated by averaging the squared differences between each point and the mean.

3. Ratio: A comparison between two quantities, expressed as a fraction.

Once you have calculated the ratio of variance to mean for each case, compare the values to determine which case has the greatest variance relative to the mean. The case with the highest ratio value will have the greatest variance relative to the mean.

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The value of cos⁻¹(−0.53) is approximately equals to  -1.012 radians (rounded to 3 decimal places).

Use the inverse cosine function on a calculator to find the value of cos⁻¹(−0.53),

Evaluate it to at least 3 decimal places, use the following steps,

cos⁻¹(−0.53) = x

⇒cos(x) = −0.53

Use the identity cos²(x) + sin²(x) = 1 to solve for sin(x),

⇒sin²(x) = 1 − cos²(x)

⇒sin²(x) = 1 − (−0.53)²

⇒sin²(x) = 0.7191

⇒ sin(x) ≈ ±0.8479

Both a positive and negative value for sin(x),

since sine is positive in both the first and second quadrants.

To determine which value of sin(x) is correct,

The range of values for the inverse cosine function.

The range of cos⁻¹(x) is [0, π], or [0°, 180°],

⇒ The output of the inverse cosine function is always a non-negative angle in the first or second quadrant.

Since sin(x) is negative in the second quadrant, eliminate the positive value for sin(x).

⇒ sin(x) = −0.8479

Now use the inverse sine function to find x,

⇒sin⁻¹(−0.8479) = x

⇒x ≈  -1.012radians

Therefore, cos⁻¹(−0.53) ≈  -1.012 radians (rounded to 3 decimal places).

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The above question is incomplete, the complete question is:

Use your calculator to evaluate cos⁻¹( − 0. 53 ) to at least 3 decimal places. Give the answer in radians

Step-by-step explanation:

It goes up and to the right ....it has a positive slope

find two convenient points   ( -3,1) and  (0,2)

 slope, m = (y1-y2) / ( x1-x2) =  (1-2) / ( -3 -0) =  1/3

Answer:

1/3

Step-by-step explanation:

The slope of a line is the [tex]\frac{rise}{run}[/tex].  Rise being how many units you go up and down, and run being how many units you go left and right.

Given a chart, we can just count how many units we go up/down and left/right, but if we were given 2 points and no chart, we would use the formula:

[tex]\frac{y2-y1}{x2-x1}[/tex]

For this example, we have a chart, so let's choose 2 solid points: (-3,1) and (0,2).

We can see that from the first point (-3,1) to get to the second point (0,2), we need to go up 1 unit.

We can also see that from going up 1 unit, we need to go right 3 units.

We can rewrite this in the formula for slope:

1/3

This means that our slope is 1/3.

Check it

To check this, we can use our slope point formula:

[tex]\frac{y2-y1}{x2-x1}[/tex]

Given the 2 points, (-3,1), and (0,2)....

[tex]\frac{2-1}{0+3}\\ =\frac{1}{3}[/tex]

Hope this helps! :)

The value of the test statistic is 1.177.

What is test statistic?

A test statistic is a numerical summary of sample data that is used in hypothesis testing. It is used to assess the strength of evidence against a null hypothesis by comparing the observed data to what would be expected if the null hypothesis were true.

To find the value of the test statistic, we need to use the formula:

test statistic = (sample statistic - hypothesized parameter) / (standard error of the sample statistic)

In this case, the hypothesized parameter is the standard deviation of pulse rates of adult males, which is stated to be more than 12 bpm. So, we have:

hypothesized parameter: σ > 12 bpm

sample size: n = 141

sample standard deviation: s = 13.4 bpm

To calculate the standard error of the sample standard deviation, we use the formula:

standard error of s = σ / √n

Since we don't know the value of σ, we will use the sample standard deviation s as an estimate for it:

standard error of s = s / √n = 13.4 / √141 = 1.126

Now, we can plug in the values into the formula for the test statistic:

test statistic = (s - σ) / (standard error of s)

= (13.4 - 12) / 1.126

= 1.177

Therefore, the value of the test statistic is 1.177.

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, the probability of one person randomly picking a cherry popsicle and another person selecting a grape popsicle from the box is 1/15.

The probability of one person randomly picking a cherry popsicle is 4/16 (since there are 4 cherry popsicles out of a total of 16 popsicles in the box), and the probability of another person selecting a grape popsicle from the remaining popsicles is 4/15 (since there are only 4 grape popsicles left out of 15 popsicles after one cherry popsicle has been selected).

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, the probability of one person randomly picking a cherry popsicle is 4/16 because there are 4 cherry popsicles in the box out of a total of 16 popsicles. After one cherry popsicle has been selected, there are only 15 popsicles left in the box, of which 4 are grape popsicles. Therefore, the probability of another person selecting a grape popsicle from the remaining popsicles is 4/15.

To find the overall probability of both events happening (one person picking a cherry popsicle and another person picking a grape popsicle), we multiply the two probabilities together:

(4/16) x (4/15) = 1/15

Therefore, the probability of one person randomly picking a cherry popsicle and another person selecting a grape popsicle from the box is 1/15.

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Answer:

9/10 or 0.9

Step-by-step explanation:

Slope of a line passing through two points (x1, y1) and (x2, y2) is given by
Slope m = rise/run

where
rise = y2 - y1
run = x2 - x1

Given points (- 6, - 5) and (4, 4),

rise = 4 - (-5) = 4 + 5 = 9

run = 4 - ( - 6) = 4 + 6 = 10

Slope = rise/run = 9/10 or 0.9

a) For a one-tail test with Zx = 1.46 and a = 0.10, the area in the tail to the right of 1.46 is 0.0735. Since this is greater than 0.10, we fail to reject the null hypothesis.

b) For a one-tail test with Zx = -2.48 and a = 0.01, the area in the tail to the left of -2.48 is 0.0066. Since this is less than 0.01, we reject the null hypothesis.

c) For a two-tail test with Zx = -1.92 and a = 0.01, the area in each tail is 0.025. The total area in the tails is 0.050. Since this is greater than 0.01, we fail to reject the null hypothesis.

d) For a two-tail test with Zx = 2.76 and a = 0.02, the area in each tail is 0.01. The total area in the tails is 0.02. Since this is less than 0.02, we reject the null hypothesis.

Followings are the answers of 9.3 :

a) Since the test is for the alternative hypothesis that ? > 50, and the sample mean is 52, which is greater than 50, we reject the null hypothesis.

b) The test statistic is Z = (52 - 50) / (12 / sqrt(36)) = 1.5. The area in the tail to the right of 1.5 is 0.0668. Therefore, the p-value for the test is 0.0668.

Followings are the answers of 9.4 :

a) Since the test is for the alternative hypothesis that ? < 120, and the sample mean is 111, which is less than 120, we reject the null hypothesis.

b) The test statistic is Z = (111 - 120) / (26 / sqrt(40)) = -2.3038. The area in the tail to the left of -2.3038 is 0.0104. Therefore, the p-value for the test is 0.0104.

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The numeral 201 (base three) is equivalent to 19 in base 10.

To understand how to convert the numeral 201 (base three) to base 10, it is helpful to first understand what these two number systems represent.

Base 3 (ternary) is a positional number system that uses three digits: 0, 1, and 2. Each digit represents a different power of 3, with the rightmost digit representing [tex]3^0[/tex], the next digit to the left representing [tex]3^1[/tex], and so on. Therefore, the numeral 201 (base three) can be interpreted as:

[tex]2 * 3^2 + 0 * 3^1 + 1 * 3^0[/tex]

To convert this numeral to base 10 (decimal), we simply evaluate this expression:

[tex]2 * 3^2 = 18[/tex]

[tex]0 * 3^1 = 0[/tex]

[tex]1 * 3^0 = 1[/tex]

Adding these values together, we get:

18 + 0 + 1 = 19

Therefore, the numeral 201 (base three) is equivalent to 19 in base 10.

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