3.13 what substitution system results when we use a 1 * 25 playfair matrix?

Answer:

             The x intercept:    (1.5, 0)

The slope intercept form:   y = 2x - 3

                      The slope:    m = 2

Step-by-step explanation:

x intercept means y=0

4x - 2y = 6

4x - 2·0 = 6

4x = 6

x = 1.5

The slope intercept form is:  y = mx + b

4x - 2y = 6            {subtract 4x from both sides}

- 2y = - 4x + 6       {dividing both sides by (-2)}

y = 2x - 3            ← slope intercept form

Slope is the number by x, in slope intercept form of line's equation

Answer:

yes

Step-by-step explanation:

Answer:

It's true for values of m = ±9

Explanation:

for m = -9 :

\( {( {}^{ - } 9)}^{2} = 81\)

For m = +9 :

\(( {}^{ + } 9) {}^{2} = 81\)

hence m is -9 and +9

The most appropriate choice for permutation and combination will be given by

Number of sequences obtained by drawing three balls = 8000

Number of sequences obtained by drawing four balls = 16000

What is permutation and combination?

When there is a case of ordering, the number of arrangements that can be made in a set is called permutation

When there is no case of ordering, the number of arrangements that can be made in a set is called combination.

Here,

For three balls

Total number of balls = 20

Number of balls drawn = 3

This problem is same as the problem for drawing of r balls from n balls with replacement

So number of choices for first place = 20

Number of choices for second place = 20

Number of choices for third place = 20

Total number of sequences obtained = \(20 \times 20 \times 20\)

                                                              = 8000

For four balls

So number of choices for first place = 20

Number of choices for second place = 20

Number of choices for third place = 20

Number of choices for fourth place = 20

Total number of sequences obtained = \(20 \times 20 \times 20 \times 20\)

                                                              = 16000

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Answer:

yes you plug the numbers in

Answer:

The person in the at-risk population is much more likely to actually have the disease

Step-by-step explanation:

The probability of a randomly selected doctor having the disease is 1 in 1,000 (P(I)=0.0001).

The probability that a doctor is infected with SARS, given that they tested positive is:

\(P(I|+)=\frac{P(I)*0.99}{P(I)*0.99+(1-P(I))*0.01}\\P(I|+)=\frac{0.0001*0.99}{0.0001*0.99+(1-0.0001)*0.01}\\P(I|+)=9.9*10^{-3}\)

The probability of a randomly selected person from the at-risk population having the disease is 20 in 100 (P(I)=0.20).

The probability that a person in the at-risk population is infected with SARS, given that they tested positive is:

\(P(I|+)=\frac{P(I)*0.99}{P(I)*0.99+(1-P(I))*0.01}\\P(I|+)=\frac{0.2*0.99}{0.2*0.99+(1-0.2)*0.01}\\P(I|+)=0.962\)

Therefore, the person in the at-risk population is much more likely to actually have the disease

Answer:

1/8

Step-by-step explanation:

5/4   divided by   10/1   is the same as  

    5/4   times  1/10

       5/4 *  1/10 =  5/40    = 1/8

Answer: 1/8

Step-by-step explanation:

\(\displaystyle\\\frac{\frac{5}{4} }{10} =\\\\\frac{5}{4}:10=\\\\\frac{5}{4} *\frac{1}{10}=\\\\ \frac{5*1}{4*10}=\\\\\frac{5}{4*5*2} =\\\\\frac{1}{4*2}=\\\\\frac{1}{8}\)

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 4.8\%\to \frac{4.8}{100}\dotfill &0.048\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &10 \end{cases} \\\\\\ A=2000\left(1+\frac{0.048}{12}\right)^{12\cdot 10}\implies A=2000(1.004)^{120}\implies A\approx 3229.06\)

Answer:

15x^2−14xy−8y^2−x−y

Step-by-step explanation:

Combine like units.

Answer:

hope it helped

have a good day

The value of x such that the hcf is 26 and the l.c.m is 1092 is 156

The numbers are given as:

182 and x

The HCF and LCM are given as:

HCF = 26

LCM = 1092

As a general rule;

The product of LCM and HCF of x and y equals the product of x and y

So, we have:

182 * x = 26 * 1092

Divide both sides by 182

x = 156

Hence, the value of x is 156

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True. The central limit theorem states that if the sample size n is large enough (usually considered to be at least 30), then the sampling distribution of the mean will be approximately normal, regardless of the shape of the population distribution.

The sampling distribution of the mean can be approximated by the normal distribution if the sample size (n) is at least 30. This statement is based on the Central Limit Theorem, which states that the sampling distribution of the mean of a random sample drawn from any population will approach a normal distribution as the sample size increases, regardless of the shape of the population distribution. A sample size of 30 is often considered the threshold for approximating a normal distribution in such cases.

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Answer:

$ 144

Step-by-step explanation:

Cost Price = CP = $ 120

Profit % = 20%

\(Selling\ price = \dfrac{100+Profit}{100}*CP\\\\\\\)

                     \(=\dfrac{120}{100}*120\)

                     = 12 * 12

                     = $ 144

An irrational number could not be written as a fraction.

We need to clasify the following numbers in rational or irrational:

The average speed is 9 km / 3 hours = 3 km/hr.

The average velocity is 9 km / 3 hours = 3 km/hr

a) The average speed of the man for the whole journey can be calculated as the total distance divided by the total time.

The total distance

7 km + 2 km = 9 km

The total time

2 hours + 1 hour = 3 hours.

the average speed

9 km / 3 hours = 3 km/hr.

b) The average velocity of the man for the whole journey is the displacement divided by the total time. since the direction did not change this is same as speed hence

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The linear equation 4 · x + 5 will be greater than 4 and less than 175 for 42 integers.

Herein we must find what integers are within the interval of a simultaneous linear inequality, whose definition is shown below:

4 < 4 · x + 5 < 175        

Which is equivalent to the following two inequalities:

4 · x + 5 > 4                     (2)

4 · x + 5 < 175                  (3)

By (2):

4 · x + 5 > 4

4 · x > - 1

x > - 1 / 4

x > - 1

By (3):

4 · x + 5 < 175

4 · x < 170

x < 170 / 4

x < 85 / 2

x < 42.5

x < 43

Then, the number of integers within the simultaneous inequality is:

n = 1 + (42 - 1)

n = 42

The linear equation 4 · x + 5 will be greater than 4 and less than 175 for 42 integers.

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If a test of hypothesis has a Type I error probability (alpha) of 0.01, it means that if the null hypothesis is true, you reject it 1% of the time. This is known as a false positive or Type I error.

It is important to control Type I error probability because it can lead to incorrect conclusions and wasted resources. The level of significance (alpha) is typically set before conducting the test and is often set at 0.05 or 0.01. This means that if the p-value (the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true) is less than alpha, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis. Answering this question required understanding of probability and hypothesis testing, and it is important to ensure that Type I error probability is appropriately controlled in statistical analyses.

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(a) Null hypothesis: The variable Female is not significant in the regression equation relating Sales to the six predictor variables.

Alternative hypothesis: The variable Female is significant in the regression equation relating Sales to the six predictor variables.

Test used: F-test

Conclusion: At a 5% level of significance, the F-statistic is less than the critical value. Therefore, we fail to reject the null hypothesis and conclude that the variable Female is not significant in the regression equation.

(b) Null hypothesis: The variables Female and HS are not significant in the regression equation relating Sales to the six predictor variables.

Alternative hypothesis: The variables Female and HS are significant in the regression equation relating Sales to the six predictor variables.

Test used: F-test

Conclusion: At a 5% level of significance, the F-statistic is greater than the critical value. Therefore, we reject the null hypothesis and conclude that the variables Female and HS are significant in the regression equation.

(c) The 95% confidence interval for the true regression coefficient of the variable Income can be computed using the t-distribution. The formula for the confidence interval is:

b1 ± t*(s / sqrt(SSx))

where b1 is the estimate of the regression coefficient, t is the t-value from the t-distribution with n-2 degrees of freedom and a 95% confidence level, s is the estimated standard error of the regression coefficient, and SSx is the sum of squares for the predictor variable.

Assuming that the assumptions for linear regression are met, we can use the output from the regression analysis to find the values needed for the formula. Let b1 be the estimate of the regression coefficient for Income, t be the t-value with 48 degrees of freedom and a 95% confidence level, s be the estimated standard error of the regression coefficient for Income, and SSx be the sum of squares for Income. Then the confidence interval for the true regression coefficient of the variable Income is:

b1 ± t*(s / sqrt(SSx))

(d) The percentage of the variation in Sales that can be accounted for when Income is removed from the regression equation can be found by comparing the sum of squares for the reduced model (without Income) to the total sum of squares for the full model (with all predictor variables). Let SSR1 be the sum of squares for the reduced model and SST be the total sum of squares for the full model. Then the percentage of variation in Sales that can be accounted for when Income is removed is:

(SSR1 / SST) * 100%

(e) The percentage of the variation in Sales that can be accounted for by the three variables Price, Age, and Income can be found by comparing the sum of squares for the full model with all six predictor variables to the sum of squares for the reduced model with only Price, Age, and Income as predictor variables. Let SSRf be the sum of squares for the full model and SSRr be the sum of squares for the reduced model. Then the percentage of variation in Sales that can be accounted for by the three variables is:

[(SSRr - SSRf) / SST] * 100%

(f) The percentage of the variation in Sales that can be accounted for by the variable Income when Sales is regressed on only Income can be found by comparing the sum of squares for the reduced model with only Income as a predictor variable to the total sum of squares for the full model with all predictor variables. Let SSRr be the sum of squares for the reduced model and SST be the total sum of squares for the full model. Then the percentage of variation in Sales that can be accounted for by Income is:

(SSRr / SST) * 100%

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Answer:

2,598,960

Step-by-step explanation:

Answer:

The  2598960 cards can be dealt from a standard deck of 52

cards if 5-card selected.

What is permutation and combination?

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

We have a standard deck of 52 cards.

5 cards selected.

Total combination:

= C(52, 5)

= 2598960

Thus, the  2598960 cards can be dealt from a standard deck of 52

cards if 5-card selected.

Answer:

75 and 115

Step-by-step explanation:

50+25=75

83+32=115

Answer:

1) Angle ABD = Angle ABC + CBD.

Angle ABD = \(50+25=75\)°

2) Angle WYX = Angle WYZ + ZYX

Angle WYX = \(32+83=115\)°

Answer:

it's acually 107,800

Answer:

30,000 yes this is correct

Step-by-step explanation:

The table has a greater rate of change.

The rates of change are equal.

In the given problem, we have a table showing the relationship between x and y values. By comparing the change in y with the change in x, we can determine the rate of change. Looking at the table, we observe that for every increase of 1 in x, there is a corresponding increase of 1 in y. Therefore, the rate of change for this table is 1.

The slopes are equal.

The equation has a greater slope.

In problem 2, we are given a linear equation in the form y = mx + b, where m represents the slope. The given equation is y = 2x + 7, which means the slope is 2. To compare the rates of change, we compare the slopes. If the slopes are equal, the rates of change are equal. In this case, the slopes are equal to 2, so the rates of change are the same.

The function rule has a greater slope.

The slopes are equal.

In problem 3, we are told that as x increases by 1, y increases by 3. This information gives us the rate of change between x and y. The slope of a function represents the rate of change, and in this case, the slope is 3. Comparing the slopes, we find that they are equal, as both have a value of 3. Therefore, the rates of change are the same.

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Answer:

Female: 93/328

Adult: 103/328

Baby: 61/328

Step-by-step explanation:

71 + 93 + 103 + 61 = 328

Male: 71/328

Female: 93/328

Adult: 103/328

Baby: 61/328

The answer to this Question is 13.31

What is mean?

Mean is simply defined as sum of observations divided by number of observations

Solution:

As in this Question at every value of height , frequency is different but for particular value of height frequency is fixed

Hence we will use integration here

Let us denote height by h and frequency by f

mean =    \(\frac{\int\limits^a_b {f} \, dh}{\int\limits^a_b \, dx }\)

here numerator is simply the area under curve that we can find and that comes out to be 1065 sq units

and denominator is just b - a where b = 200 and a = 120

hence denominator is 80

on putting values we get 1065/80

mean = 13.31

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It means the probability of a random permutation of n numbers gets sorted after 1 pass of bubble sort is n!

According to the statement

we have to find the probability of random permutation of the N numbers.

So, according to the definition of A random permutation is a random ordering of a set of objects, that is, a permutation-valued random variable.

In this we order of select the objects randomly.

So, Let There are n−1 comparisons, so 2n−1 possible sequences of actions - swap or don't swap.

To find the permutations, start with 1,2,3,4,5 and undo a sequence.

For example, if let n=5, there are 24=16 out of 5!

which is 5! =120 that end after one round of bubble sort.

So, It means the probability of a random permutation of n numbers gets sorted after 1 pass of bubble sort is n!

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The book is opened to pages 11 and 12.

How to get the product of the page

x * (x + 1) = 132

Expanding the equation, we get:

x² + x = 132

To solve for x, we need to rewrite the equation as a quadratic equation:

x²+ x - 132 = 0

Now, we can factor the quadratic equation:

(x - 11)(x + 12) = 0

This equation has two solutions for x:

x = 11

x = -12

Since page numbers cannot be negative, we discard the second solution. Thus, the left-hand page number is 11, and the right-hand page number is 11 + 1 = 12.

So, the book is opened to pages 11 and 12.

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obtain the solution using the long division method

Each banana Split costs $6 and each hot fudge sundae costs $2.

Let b be the cost of one banana split and h be the cost of one hot fudge sundae. We can set up a system of two equations with two variables based on the given information:

6b + 5h = 46    (equation 1)

2b + 5h = 22    (equation 2)

We can solve for one variable in terms of the other in one of the equations and substitute that expression into the other equation to solve for the remaining variable. For example, we can solve equation 2 for b in terms of h:

2b + 5h = 22

2b = 22 - 5h

b = (22 - 5h)/2

We can substitute this expression for b into equation 1 and solve for h:

6b + 5h = 46

6[(22 - 5h)/2] + 5h = 46

66 - 15h + 5h = 46

-10h = -20

h = 2

Now that we know the cost of one hot fudge sundae is $2, we can substitute this value into either equation to solve for the cost of one banana split:

6b + 5(2) = 46

6b + 10 = 46

6b = 36

b = 6

Therefore, each banana split costs $6 and each hot fudge sundae costs $2.

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Any two points can be at most 1 unit far from each other. As, any two points can lie at maximum distance from each other when they both lie on the boundary of the triangle.

Given, an equilateral triangle of side length 1 unit.

Five points are inside the triangle.

we have to show that there are 2 points at distance of at most 1 unit.

As, Five points lie inside the triangle.

So, any two points can lie at maximum distance from each other when they both lie on the boundary of the triangle.

As, it is given that the side length of the triangle is 1 unit so, the two points can be at most 1 unit far from each other.

Hence, it is shown that any two points can be at most 1 unit far from each other. As, any two points can lie at maximum distance from each other when they both lie on the boundary of the triangle.

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Using Arithmetic Progression, the largest of these integers is 63 for the sum of some consecutive positive integers is 1000.

We can use algebra to solve this problem. Let's call the first integer "x". Then, the next consecutive integer will be "x + 1", the one after that will be "x + 2", and so on. If we add up "n" consecutive integers starting with "x", we get the formula:

x + (x + 1) + (x + 2) + ... + (x + n-1) = 1000

Simplifying this equation, we get:

nx + (1 + 2 + ... + n-1) = 1000

nx + (n-1)(n/2) = 1000

Solving for "n" using the quadratic formula, we get:

n = (-1 ± √801)/2

Since we're dealing with positive integers, we know that "n" must be a positive integer. Therefore, we can ignore the negative solution, and we get:

n = (√801 - 1)/2 ≈ 28.1

This means that we're dealing with 28 consecutive positive integers that add up to 1000. To find the largest of these integers, we just need to add 27 to "x", which gives us:

x + 27 = 1000/28 + 27 ≈ 62.7

Therefore, the largest integer is approximately 63.

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