4. -64
Multiplicative inverse

In order to sort the given numbers [11, 20, 30, 22, 60, 6, 10, 31] using the Merge sort algorithm, we can divide the list into smaller sublists, recursively sort them, and then merge them back together in a sorted order.

Here's an example implementation of the Merge sort algorithm in Python:

def merge_sort(arr):

   if len(arr) <= 1:

       return arr

   mid = len(arr) // 2

   left = arr[:mid]

   right = arr[mid:]

   left = merge_sort(left)

   right = merge_sort(right)

   return merge(left, right)

def merge(left, right):

   result = []

   i = j = 0

   while i < len(left) and j < len(right):

       if left[i] <= right[j]:

           result.append(left[i])

           i += 1

       else:

           result.append(right[j])

           j += 1

   result.extend(left[i:])

   result.extend(right[j:])

   return result

numbers = [11, 20, 30, 22, 60, 6, 10, 31]

sorted_numbers = merge_sort(numbers)

print(sorted_numbers)

In this code, the merge_sort function implements the Merge sort algorithm. It recursively divides the input list into smaller sublists until each sublist contains only one element. Then, it merges these sorted sublists together using the merge function. The merge function compares the elements of the left and right sublists, merges them into a new sorted list, and returns it. Running the code will output the sorted numbers: [6, 10, 11, 20, 22, 30, 31, 60]. This demonstrates the application of the Merge sort algorithm to sort the given numbers in ascending order.

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(a) The hypothesis that the mean inside bearing diameter is 8.25 cm, cannot be concluded.

(b) The p-value for this test is almost 0 < 0.00006.

(c) A 95% two-sided confidence interval on the mean bearing diameter is 8.252 < μ < 8.255.

(a) We have to test the hypothesis that the mean inside bearing diameter is 8.25 cm.

Use a two-sided alternative method.

n = 15

σ = 0.002

α = 0.05

μ = 8.25 cm

Null hypothesis VS Alternative hypothesis

H0: μ = 8.25cm

H1: μ ≠ 8.25cm

Reject the H0 since

\(\left |Z_{0} \right | > {{Za/2}}\)

\(\left | Z_{0}\right |=[(x-\bar{x})/(\sigma/\sqrt{n})]\)

\(\left | Z_{0}\right |\) = (8.2535-8.25)/(0.002/√15)

\(\left | Z_{0}\right |\) = 6.78

\(\left | Z_{0}\right | > Z_{a/2}\)

We conclude that to reject H0: μ = 8.25cm

We cannot say that 8.25 cm is the average inner diameter.

b) Here, Z-Value = 6.78 is outside of the acceptable range for the table, hence P-value is almost 0 < 0.00006.

c) Bearing Diameter is 95% of the 2-sided Confidence interval mean bearing

= \(\bar{x}-1.96\left(\frac{0.002}{\sqrt{15}}\right) < \mu < \bar{x}+1.96\left(\frac{0.002}{\sqrt{15}}\right)\)

= \(8.2535-1.96\left(\frac{0.002}{\sqrt{15}}\right) < \mu < 8.2535+1.96\left(\frac{0.002}{\sqrt{15}}\right)\)

= 8.252 < μ < 8.255

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Answer:

60 degrees

Step-by-step explanation:

ACD and ACB are complementary angles. Find ACB=30 degrees. Subtract 30 from 90 degrees. ACD=60 degrees.

Answer:

ACD=60

BCA=30

BCD=90

90-30=60

Answer:

310000000

That’s the answer

ANSWER

• x = 1/3

• y = 2/3

• z = 1

EXPLANATION

There are many methods to solve a linear system of equations, but in this case we have to use the substitution method -which consists in clearing one variable as a function of the other/s and replace in another equation. For a system of three variables such as this one, we have to do this twice:

1° clear x from the first equation:

Replace x by this expression in the second equation:

Note that now we have two variables, y and z. Before the next step we have to rewrite the equation above so that we only have one y:

2° clear y from the equation above:

And replace y by this expression in the last equation. Note that the third equation also contains x, so we have to replace first x as a function of y like in the first step:

Rewrite it so we only se one y:

And now we replace y by the expression we found in the second step:

So now we have one equation with one variable. Let's solve for z:

We have that z = 1.

The next steps are to back replace and find the other variables. Remember that in the second step we had y as a function of z:

Replace z = 1 and solve:

y = 2/3

And finally, replace y = 2/3 in the expression of the first step, where we found x as a function of y:

and we got x = 1/3

Answer: 272 legs on the bus

Step-by-step explanation:

It says the women and cats are on the bus, but it does not say that the kittens are on the bus, so only the women and cat legs will be counted.

Each woman has 2 legs and each cat has 4 legs.

so: 8 x 2 = 16 human legs

     8 bags with 8 cats in each bag = 64 cats

     64 x 4 = 256 cat legs

      16 + 256 = 272 legs

Therefore 272 legs are on the bus.

-8/13 x 26/-3 = -208/-39 = 16/3.

16/3, D

Answer:

D. (16/3)

Step-by-step explanation:

 -8          26

-------  ×  -------  

  13          -3

Multiply the top and the bottom together.

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

-8 x 26 = -208

13 x -3 = -39

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

 -8          26        -208

-------  ×  -------  =  --------

  13          -3          -39

Simply the fraction

 -208   ÷  13           -16

------------           =  ----------

   -39  ÷   13             -3

Cancel out the negatives

-16          16

-------  =  -------

 -3            3

I hope this helps!

By solving the given Algebraic expression, the correct answer is Option (C) ,a = 2y and b = –.

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

There are different components of an algebraic expression. Let us have a look at the image given below in order to understand the concept of Variables, Constants, Terms, and Coefficients of any algebraic expression.

Assume that  8y2 - 12y + 4  has  terms with a=8y² , b=-12y, c=4

Now, to divide 8y2 - 12y + 4  by the monomial (single term) 4y,

The easy way is divide each term of the dividend by the monomial:

8y2 - 12y + 4  /4y

=(8y²-12y+4)/4y

=(8y²/4y)-(12y/4y)+(4/4y)

=2y-3+1/y

After performing the division we get that now a = 2y and  b = –3

We can conclude that the correct answer is a = 2y and b = –3

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Answer:

  x = 11

Step-by-step explanation:

If we assume that points A, B, and C are on the same line with B between A and C, then we have ...

  AB +BC = AC

  (4x +34) +(6x +6) = 150 . . . . use the given expressions

  10x +40 = 150 . . . . . . . . . . . . collect terms

  10x = 110 . . . . . . . . . . . . . . . .  subtract 40; next, divide by 10

  x = 11

Step-by-step explanation:

The line representing the equation 7x1 + 4x2 = 28 goes through the points (4,0) and (0,7).

To convert milligrams per liter (mg/L) to micrograms per fluid ounce (µg/fl oz), we can use the conversion factor of 29.5735.

This conversion factor takes into account the difference in volume between a liter and a fluid ounce.

1 fl oz = 29.5735 mL

1 L = 1000 mL

So, to convert from milligrams per liter to micrograms per fluid ounce, we divide by 29.5735 and multiply by 1000:

(mg/L) * 1000 / 29.5735 = (µg/fl oz)

Therefore, to convert a value x from milligrams per liter to micrograms per fluid ounce:

x (µg/fl oz) = x (mg/L) * 1000 / 29.5735

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Answer:

66

Step-by-step explanation:

Find the last side of the triangle using the Pythagorean theorem.

\(c^{2} = a^{2} + b^{2} \\20^{2} = 8^{2} + b^{2}\)

B=\(4\sqrt{21}\)

This makes b = 18.3

Now you can find the angle B = arcsin (opp/hyp)

B=arcsin \(\frac{4\sqrt{21} }{20}\)

B= 66.42

Answer:

22°

Step-by-step explanation:

Okay, to first find the missing side, you need to use a² +b² = c²

getting 21.54 for the hypotenuse. From there, you're going to divide the leg (8) that's opposite of the angle you're trying to find and divide it by the hypotenuse (21.54). Then on you're caluclator you should have a button that says "Sin-1". You're going to use that and plug in the answer you got from 8/21.54. This'll give you your answer!

(a) 5.2333.41−0.23 × 0.205

= (5.23) * (3.18 - 0.23) * (0.205)

= 8.48013

Rounded to the correct number of significant figures, the result is: 8.48

(b) 4.223-0.085.556×2.3

= (4.14) / (5.556) * (2.3)

= 1.759619378

= 1.76

Rounded to the correct number of significant figures, the result is: 1.76

5) To convert the melting point of tungsten from Fahrenheit to Celsius and Kelvin:

Melting point in Fahrenheit: 6192°F

To convert to Celsius:

°C = (°F - 32) * 5/9

°C = (6192 - 32) * 5/9

°C ≈ 3434.44°C

Rounded to the correct number of significant figures, the result is: 3434°C

To convert to Kelvin:

K = °C + 273.15

K = 3434.44 + 273.15

K ≈ 3707.59K

Rounded to the correct number of significant figures, the result is: 3708K

6) For the volume calculation of the aspirin tablet

Tablet weight: 250 mgTo find the volume, we use the formula:

Volume = Mass / Density

Volume = 250 mg / 1.40 g/cm³

Volume = 250 mg / 1.40 g/cm³ * (1 g / 1000 mg) * (1 cm³ / 1 mL)

Volume ≈ 178.571 cm³

Rounded to the correct number of significant figures, the result is: 179

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9514 1404 393

Answer:

  c, p

Step-by-step explanation:

When you remove the numbers and the math operations (multiplication, addition, subtraction), what is left are the variables. Here, the variables are c and p.

Answer:

m = -2

Step-by-step explanation:

The points I will be using are (-3, 6) and (0,0).

To find the slope, you sub these points into the slope formula - rise over run.

Answer:

The slope is -2

Step-by-step explanation:

to get from (0,0) to (-3,6) you rise 6 and go left 3. Then 6÷-3= -2.

Answer:

C

Hope that helps!

Step-by-step explanation:

The line integral of $2x^2 \mathrm{~d}y$ along the curve $C$ is equal to 486 according to the given information.

To calculate the line integral $\int_C 2x^2 \mathrm{~d}y$, we need to parameterize the curve $C$ and express $x$ and $y$ in terms of the parameter $t$. The given curve is defined as $\mathbf{r}(t) = \langle 3t-3, 3t \rangle$, where $0 \leq t \leq 4$.

Differentiating $\mathbf{r}(t)$ with respect to $t$, we have $\mathbf{r}'(t) = \langle 3, 3 \rangle$. Integrating $2x^2$ with respect to $y$ along the curve $C$ gives us:

$\int_C 2x^2 \mathrm{~d}y = \int_0^4 2(3t-3)^2 (3 \mathrm{~d}t) = 2 \int_0^4 (27t^2 - 54t + 27) \mathrm{~d}t$.

Evaluating the integral, we get $\int_C 2x^2 \mathrm{~d}y = [9t^3 - 27t^2 + 27t]_0^4 = 486$.

Therefore, the line integral $\int_C 2x^2 \mathrm{~d}y$ along the curve $C$ is equal to 486.

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The probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship is 69.75%.

Note that this is simple probability.

Hence probability of the 75% football starts selected randomly where the chance is 93% =

75% x 93%

= 69.75%

The chance that 25% of the five-star recruit will not select a university form one of the three best conferences is explained as follows:

Because only 75% stand the chance of being selected into the three ivy leagues, this means that 25% stand no chance.

Recall that the total population is 100%.

From the statement of problem given, it is clear that the events are mutually exclusive. Recall "Historically, five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to.

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You should pay $13,050 for the note to earn 4% annual simple interest and be worth $13,500 in 10 months.

To calculate the amount you should pay for a note to earn 4% annual simple interest and be worth $13,500 in 10 months, follow these steps:

1. Convert the annual interest rate to a monthly rate: 4% / 12 months = 0.3333% per month.

2. Convert the investment period from 10 months to a fraction of a year: 10 months / 12 months = 0.8333 years.

3. Calculate the total interest earned during the investment period: $13,500 x 0.04 x 0.8333 = $450.

4. Subtract the interest from the final value of the note to find the initial investment amount: $13,500 - $450 = $13,050.

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Answer:

False, 82 inches is not greater than 5 feet and 10 inches

Step-by-step explanation:

1 feet = 12 inches

5x12=60+10=70

82 is greater than 70.

The algebraic expression for the verbal expression 7 divided by the product of 9 and x is 7/9x.

Given verbal expression is 7 divided by the product of 9 and x.

Hence, the required algebraic expression for given verbal expression is 7/9x.

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Answer:

question 11 is d   and question 12 is g   hope it helps

Step-by-step explanation:

subtract 24.65from 75              

add both fractions

Answer:

m = 12

Step-by-step explanation:

\(-\frac{m}{3} =-4\\\)

→ Multiply both sides by 3

\({-m} =-12\\\)

→ Multiply both sides by -1

m = 12

Answer:

The equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2, where h, k, is the center and r is the radius.

So, in this case: the center is (-1, 5) and the radius is 2.

Let me know if this helps!

Answer:

13/99

Step-by-step explanation:

Answer: 13/99

Step-by-step explanation:

Answer:

it is A.

Step-by-step explanation:

The answer is not an equation, because for it to be an equation, an equal sign is required. Therefore it is an expression.

It is algebraic because there are variables involved. If there were only numbers, it would be numerical.

hope this helps!

Answer:

A. an algebraic expression

Step-by-step explanation:

It is algebraic because there is a variable involved, s. It is also an expression because there is no equal sign before or after the terms.

Answer:

x = -4 and y = 0

Step-by-step explanation:

We can solve the system of equations by substitution or elimination. Here, we will use the substitution method.

First, we will solve for y in the first equation:

y = -16 - 4x

Next, we will substitute this expression for y into the second equation:

2x - 3y = -8

2x - 3(-16 - 4x) = -8

2x + 48 + 12x = -8

14x = -56

x = -4

Now that we have found the value of x, we can substitute it back into the first equation to solve for y:

y = -16 - 4x

y = -16 - 4(-4)

y = -16 + 16

y = 0

Therefore, the solution to the system of equations is x = -4 and y = 0.

Answer:

(- 4, 0 )

Step-by-step explanation:

4x + y = - 16 → (1)

2x - 3y = - 8 → (2)

multiplying (1) by 3 and adding to (2) will eliminate y

12x + 3y = - 48 → (3)

add (2) and (3) term by term to eliminate y

(2x + 12x) + (- 3y + 3y) = - 8 - 48

14x + 0 = - 56

14x = - 56 ( divide both sides by 14 )

x = - 4

substitute x = - 4 into either of the 2 equations and solve for x

substituting into (1)

4(- 4) + y = - 16

- 16 + y = - 16 ( add 16 to both sides )

y = 0

solution is (- 4, 0 )

Answer:

2

Step-by-step explanation:

Mode means the number in an array that is the most common. The most common number (mode) in this array is 2, with 3 entries.