Part IV – Applications of Chi Square Test
Q15) Retention is measured on a 5-point scale (5 categories).
Test whether responses to retention variable is independent of
gender. Use significance level

The other two sides of the triangle will be 8 cm.

Let's call the length of each of the other two sides "x".

Since the triangle is isosceles, it has two sides of equal length. Therefore, the perimeter of the triangle can be expressed as:

perimeter = 6 + x + x

Simplifying this equation, we get:

perimeter = 2x + 6

We know that the perimeter is 22 cm, so we can set up an equation and solve for x:

22 = 2x + 6

Subtracting 6 from both sides, we get:

16 = 2x

Dividing both sides by 2, we get:

x = 8

So the other two sides could both be 8 cm long in order to make an isosceles triangle with a perimeter of 22 cm.

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Answer:

8 cm

Step-by-step explanation:

Let's call the length of each of the other two sides x. Since the triangle is isosceles, it has two sides of equal length. Therefore, the perimeter of the triangle can be expressed as 6 + x + x Simplifying this equation, we get 2x + 6 We know that the perimeter is 22 cm so we can set up an equation and solve for x. 22 = 2x + 6 Subtracting 6 from both sides, we get  16 = 2x Dividing both sides by 2, we get x=8

Answer:

Step-by-step explanation:

(a) and (b) see diagram

(c) you can see from the graph, the purple line hits the parabola twice which is y=6   or k=6

(d)  Solving simultaneously can mean to set equal

6x - x² = k                        >subtract k from both sides

6x - x² - k = 0                  >put in standard form

- x² + 6x - k = 0               >divide both sides by a -1

x² - 6x + k = 0

(e) The new equation is the same as the original equation just flipped (see image)

(f)  The discriminant is the part of the quadratic equation that is under the root. (not sure if they wanted the discriminant of new equation or orginal.  I chose new)

discriminant formula = b² - 4ac

equation:   x² - 6x + 6 = 0            a = 1      b=-6    c = 6

discriminant = b² - 4ac

discriminant= (-6)² - 4(1)(6)

discriminant = 36-24

discriminant = 12

Because the discriminant is positive, if you put it back in to the quadratic equation, you will get 2 real solutions.

Answer:

chips 1.50 cents hot dogs 2 dollars

Step-by-step explanation:

Hot do is 2 dollars because the same chips were put but 1 extra dog is 2 dollard and you divide from there and get 1.50 for chips

so with what do u need help?

Answer:

4

Step-by-step explanation:

d = -12

a2 = 100

We know the formula for the terms of an arithmetic sequence is

an = a1+d(n-1)

We can find the first term

100 = a1-12(2-1)

100 = a1-12(1)

Add 12 to each side

112 = a1

The first term is 112

Using the formula with n=10

a10 = 112-12(10-1)

a10 = 112 -12(9)

     = 112-108

     = 4

Answer:

5) distributive property

7) Transitive property

8) Associative property

Step-by-step explanation:

Answer:

4 cups

Step-by-step explanation:

(   20   /  5       ) ×  1  = 4

cups     total      lemon

            ratio       juice

                           ratio

Answer:

12/6 simplified to lowest terms is 2/1.

Step-by-step explanation:

Divide both the numerator and denominator by the HCF

12 ÷ 6

6 ÷ 6

Reduced fraction:

12/6 simplified to lowest terms is 2/1.

Answer: 2:1

Step-by-step explanation:

12:6

Both left and right can be divided by 6, like a fraction, reduce.

= 2:1

The answer is:

In slope-intercept form

Y=1/5x+5 1/4

1. The predicted trade for each pair using the gravity model is as follows:

  - Pair 1 (US-UK): Approximately $312.56 billion

  - Pair 2 (US-CAN): $700 billion

  - Pair 3 (US-MEX): $840 billion

  - Pair 4 (Vietnam-Thailand): $7.056 billion

Now, let's move on to the next questions.

2. The trade between the US and Mexico is predicted to be 20% higher than the trade between the US and Canada.

This is primarily due to the difference in GDP between Mexico and Canada. Despite the distance between the US and both countries being the same, Mexico's higher GDP leads to a higher predicted trade volume according to the gravity model. The gravity model suggests that larger economies tend to trade more with each other, all else being equal.

Now, let's move on to the third question.

3. For the trade between Vietnam and Thailand to double (i.e., increase by 100%), Vietnam's GDP would need to grow by approximately 100%.

  To increase its trade with Vietnam by $5 billion, Thailand's GDP would need to grow by approximately 70.86%.

  If both Vietnam and Thailand's GDPs fell by 5% in 2022 due to a resurgent pandemic, their trade would decrease by approximately 9.75%.

Answer:

1.5gallons

Step-by-step explanation:

Here,

no. of bottles(a) : 12

no. of cups (b) :a*2

=12*2

=24

Now,

No. of gallons. :24/16

:1.5gallons

.·.A cartoon contains 1.5 gallons of lemon tea.

When the consumption schedule lies below the 45-degree reference line, it means that at every level of income, people are consuming less than their income.

The consumption schedule represents the relationship between income and consumption in an economy, while the 45-degree reference line represents the line where income and consumption are equal.

In this scenario, saving occurs because people are not spending all of their income. The difference between their income and consumption is their savings. Thus, the amount of saving in the economy will increase as the consumption schedule moves further below the 45-degree reference line.

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When the consumption schedule lies below the 45-degree reference line, saving what does it means?

Mrs. Rosenblatt's class has an average grade of 87. After realizing she left out Joe's score of 65, the new mean will be lower than 87.

Explanation:

To find the new mean, we need to calculate the sum of all the grades in the class, including Joe's score of 65, and divide it by the total number of students in the class. Let's assume there are n students in the class.

The sum of all the grades in the class, including Joe's score, will be (87 * n) + 65, since the average grade before Joe's score was added was 87. Therefore, the new mean will be:

[(87 * n) + 65] / (n + 1)

Expanding this expression, we get:

(87n + 65) / (n + 1)

Simplifying this expression, we get:

(87n / (n + 1)) + (65 / (n + 1))

Since n is a positive integer, the value of (87n / (n + 1)) will be slightly less than 87. Therefore, the new mean will be slightly less than 87, reflecting the lower score added to the class average.

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Using the hsd test qcrit = 3.65  

HSD testis used to check differences among sample way for significance. The Tukey's HSD assessments all pairwise variations at the same time as controlling the probability of making one or greater type I errors.

A Tukey-Kramer test lets us check the null speculation of no distinction between the population approach for all pairs of businesses. The Tukey-Kramer check (also known as a Tukey sincere importance test, or Tukey HSD), is carried out in R inside the function.

solution

given;

   using HSD test, the degree of freedom = 16

                                                         and α=0. 05

                                                         groups = 3

                         Hence,                    Qcrit = 3.65    {using HSD table}

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b) A bar graph is a horizontal or vertical representation of the frequency or relative frequency of the categories. The height of each rectangle represents the frequency category's frequency or relative frequency.

A C. A Pareto chart is a bar graph whose bars are drawn in decreasing order of frequency or relative frequency t of each rectangle represents the category's frequency or relative frequency

A bar graph is used to represent data that is categorical or numerical. It is typically used to compare different categories of data, such as sales figures for different products or the number of students in different grades in a school.

The data is typically represented in a horizontal or vertical bar chart, with the length of each bar representing the quantity of the data. The categories are usually arranged from highest to lowest in a bar graph.

A Pareto chart is a specific type of bar graph. It is used to show the distribution of data into different categories and the relative importance or frequency of each category.

The categories are typically arranged in order of importance, with the most important or frequent category first and the least important or frequent category last. The bars in a Pareto chart are usually drawn in descending order, with the highest category on the left.

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Complete question:

What is a bar graph? What is a Pareto chart? What is a bar graph? O A. A bar graph is a circular graph that uses bars to divide it into segments corresponding to each category The segments are proportional to the frequency of its category O B. A bar graph is a horizontal or vertical representation of the frequency or relative trequency of the categories. The height of each rectangle represents the of the frequency category's frequency or relative frequency o c. A bar graph represents the frequencies of values either from left to-right or right-to-left. The different segments of the bar are used to indicate the different frequencies of each category What is a Pareto chart O A. A Pareto chart is a combination of a pie chart and a bar graph O B. A Pareto chart is a display of two data sets side ty side where the heigh O C. A Pareto chart is a bar graph whose bars are drawn in decreasing order of trequency or relative trequency t of each rectangle represents the category's frequency or relative frequency

The side lengths of the triangle APC are a = 11.4 m, p = 13.2 m and c = 18.1 m

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

Triangle CAP:

c = 18.1 m, a = 11.4 m and p = 13.2 m

For the triangle APC, we have the following vertices

a, p and c

These are the same vertices in the triangle CAP

This means that

The side lengths of the triangle APC the same as the side lengths of the triangle CAP

And these side lengths are: are a = 11.4 m, p = 13.2 m and c = 18.1 m

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The number of decimal places should be one more than the least accurate measurement, and the number of significant figures can be determined by counting the digits in the number, excluding the decimal point.

Rounding a number is important when providing an answer to a calculation or question. The number of decimal places and significant figures the answer should be rounded to depends on the accuracy of the answer that is required.

To calculate the number of decimal places and significant figures the answer should be rounded to, the general rule is to round to one more decimal place than the least accurate measurement. For example, if the least accurate measurement used in the calculation is rounded to two decimal places, the answer should be rounded to three decimal places.

The significant figures of the rounded answer can be determined by counting the number of digits in the number, excluding the decimal point. For example, the number 6,782 would have four significant figures, as there are four digits in the number.

In conclusion, the number of decimal places and significant figures the answer should be rounded to depends on the accuracy of the answer that is required. The number of decimal places should be one more than the least accurate measurement, and the number of significant figures can be determined by counting the digits in the number, excluding the decimal point.

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The solutions of linear equations are x = t and y = (3 - 5t)/2 for infinitely many solutions when k = 10.

The value of k for which the system of linear equations has infinitely many solutions, we need to find the condition under which the equations are dependent. Here are the equations:
1) 5x + 2y = 3
2) kx + 4y = 6
3) 20x + 8y = 12
First, let's express equation 1 in terms of y and make it match the form of equation 2:
y = (3 - 5x)/2
Now, substitute this expression into equation 2:
kx + 4((3 - 5x)/2) = 6
Simplify:
kx + 6 - 10x = 6
Now, let's express equation 3 in terms of y:
y = (12 - 20x)/8
Simplify:
y = (3 - 5x)/2
This is the same as the expression we found for equation 1, so the system is dependent.

To find the value of k, we'll set the simplified versions of equations 1 and 2 equal to each other:
kx - 10x = 0
Factor out x:
x(k - 10) = 0
For infinitely many solutions, k must be equal to 10. So, the system of equations becomes:
1) 5x + 2y = 3
2) 10x + 4y = 6
Now we can solve for the solutions in terms of the parameter t:
For this equation to be true, we must have k = 10. So, substituting k = 10 in the original equations, we have: 5x + 2y = 3 10x + 4y = 6 Dividing the second equation by 2, we get: 5x + 2y = 3

We can see that the two equations are identical, which means that any values of x and y that satisfy one equation will automatically satisfy the other equation. Therefore, the solutions to the system are given by: x = t y = (3-5t)/2 where t is any real number.
x = t
y = (3 - 5x)/2
y = (3 - 5t)/2
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The half life obtained to the nearest tenth is 5.0 days.

The half life is the time taken for only half of the initial amount of the radioactive substance to remain. We know that we have to use the formula;

N=N0e^-kt

N = amount present at time t

No = Amount initially present

k = The constant

t = The half life

We now have that;

HALF LIFE = O.693/k

We have to recall that the term k is the decay constant for the process as shown.

Half life = O.693/0.1394

Half life = 5.0 days

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Answer:

210 days

Step-by-step explanation:

The way to solve this problem is to take the LCM (Least Common Multiple) of 30 and 42. Since the prime factorization of 30 is 2*3*5 and the prime factorization of 42 is 2*3*7, the LCM will be 2*3*5*7 which is 210.

Hope this helps :)

When we subtract 3 from 22, the simplified answer is 19. The subtraction operation involves removing or deducting one value from another, resulting in the difference between the two quantities.

To subtract 3 from 22, we can perform the subtraction operation as follows:

22

3

19

We align the numbers vertically and subtract each corresponding place value from right to left. In this case, subtracting 3 from 2 requires borrowing or regrouping. However, since 2 is greater than 3, we can directly subtract 3 from 2 and write the difference, which is 1, in the one's place.

Therefore, the simplified answer is 19.

The subtraction process involves taking away or removing a certain quantity from another. In this case, we subtracted 3 from 22, resulting in a difference of 19. The process of simplifying the answer is simply expressing the result in its most concise and reduced form.

By subtracting 3 from 22, we removed 3 units from the original value of 22, leaving us with 19. This can be visualized as taking away three objects from a group of 22 objects, resulting in a remaining count of 19.

In summary, when we subtract 3 from 22, the simplified answer is 19. The subtraction operation involves removing or deducting one value from another, resulting in the difference between the two quantities.

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Answer:

Step-by-step explanation:

3 a) 6

3 b) 12

3 c) 12

4 a) 4/5

4 b) 10/9

4 c) 17/15

Answer:

The solution to the recurrence relation is given by an = 2^(n+1) - 1.

Step-by-step explanation:

(a) To solve the recurrence relation an = an-2 + 4, with initial conditions a1 = 3 and a2 = 5, we'll consider two cases: one for when n is even and one for when n is odd.

For n even:

Substituting n = 2k (where k is a positive integer) into the recurrence relation, we get:

a2k = a2k-2 + 4

Now let's write out a few terms to observe the pattern:

a2 = a0 + 4

a4 = a2 + 4

a6 = a4 + 4

...

We notice that a2k = a0 + 4k for even values of k.

Using the initial condition a2 = 5, we can find a0:

a2 = a0 + 4(1)

5 = a0 + 4

a0 = 1

Therefore, for even values of n, the solution is given by an = 1 + 4k.

For n odd:

Substituting n = 2k + 1 (where k is a non-negative integer) into the recurrence relation, we get:

a2k+1 = a2k-1 + 4

Again, let's write out a few terms to observe the pattern:

a3 = a1 + 4

a5 = a3 + 4

a7 = a5 + 4

...

We see that a2k+1 = a1 + 4k for odd values of k.

Using the initial condition a1 = 3, we find:

a3 = a1 + 4(1)

a3 = 3 + 4

a3 = 7

Therefore, for odd values of n, the solution is given by an = 3 + 4k.

(b) To solve the recurrence relation an = 2an-1 + 1, with initial condition a1 = 1, we'll find a general expression for an.

Let's write out a few terms to observe the pattern:

a2 = 2a1 + 1

a3 = 2a2 + 1

a4 = 2a3 + 1

...

We can see that each term is one more than twice the previous term.

By substituting repeatedly, we can express an in terms of a1:

an = 2(2(2(...2(a1) + 1)...)) + 1

= 2^n * a1 + (2^n - 1)

Using the initial condition a1 = 1, we have:

an = 2^n * 1 + (2^n - 1)

= 2^n + 2^n - 1

= 2 * 2^n - 1

Therefore, the solution to the recurrence relation is given by an = 2^(n+1) - 1.

Answer:

The length of the curtain is 10.625 feet

Step-by-step explanation:

The length of the curtain to cover one side of the room depends on the shape of the room

Given a room shape of a square, we have;

Perimeter = 4 × Side length of the room

Length of the curtain = Side length of the room

Therefore;

Perimeter = 4 × Length of the curtain

42.5 feet = 4 × Length of the curtain

Length of the curtain = (42.5 feet)/4 = 10.625 feet

The length of the curtain = 10.625 feet.

Answer:

Present Value = \(X [\frac{1}{(1 + 0.12)^{1} } + \frac{1}{(1 + 0.12)^{2} } + \frac{1}{(1 + 0.12)^{3} } + \frac{1}{(1 + 0.12)^{4} } + \frac{1}{(1 + 0.12)^{5} } ]\)

Step-by-step explanation:

To find - If discount rate is 12%, the present value of Rs X received at the end of each year for the next five years is equal to .... ?

Solution -

We know that, formula for finding the Present vale is given by

Present value = Future value / (1 + r)ⁿ

where r is the rate of interest

and n is Number of periods

Now,

Here in the question, we have

r = 12% = 12/100 = 0.12

n = 5

Also, Given that, we have received Rs X at the end of each year

So,

Present Value = \(\frac{X}{(1 + 0.12)^{1} } + \frac{X}{(1 + 0.12)^{2} } + \frac{X}{(1 + 0.12)^{3} } + \frac{X}{(1 + 0.12)^{4} } + \frac{X}{(1 + 0.12)^{5} }\)

                        = \(X [\frac{1}{(1 + 0.12)^{1} } + \frac{1}{(1 + 0.12)^{2} } + \frac{1}{(1 + 0.12)^{3} } + \frac{1}{(1 + 0.12)^{4} } + \frac{1}{(1 + 0.12)^{5} } ]\)

⇒Present Value = \(X [\frac{1}{(1 + 0.12)^{1} } + \frac{1}{(1 + 0.12)^{2} } + \frac{1}{(1 + 0.12)^{3} } + \frac{1}{(1 + 0.12)^{4} } + \frac{1}{(1 + 0.12)^{5} } ]\)

Answer:

large

Step-by-step explanation:

Answer:

A. Large

Step-by-step explanation:

Answer:

23/55

Step-by-step explanation:

Assuming you want this simplified,

23/55