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We can prove the formula given in the question as a theorem using the truth table method.

A Truth Table is referred to as a logic table that can be used to perform logic functions with some formulas. The logic functions that can be performed include Boolean algebra.

Let A, B, and C represent propositions. We construct a truth table as follows:

A B C (A → (B − C)) (B → (A → C))

T T T T T

T T F T F

T F T T T

T F F T T

F T T T T

F T F T T

F F T T T

F F F T T

From the truth table, we can see that the formula holds for all possible truth values of A, B, and C. Therefore, the formula is a theorem.

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Answer: x = 1, y = -1

Step-by-step explanation:

      To solve this system by elimination, we will set it up so both of the y, or x, variables have opposite coefficients.

3x - 5y = 8

2x+ 3y = -1

3(3x - 5y = 8)

5(2x+ 3y = -1)

9x - 15y = 24

10x + 15y = -5

      The 15y and -15y cancel each other out, so we're left with 9x + 10x on the left side and 24 - 5 on the right side of the equation.

19x = 19

x = 19/19

x = 1

      Now, we will plug this back into one of the equations to solve for y.

3x - 5y = 8

3(1) - 5y = 8

3 - 5y = 8

-5y = 5

y = -1

Answer:1/4 (I think)

Preferred shares = 0.40/25.00 = 1.60%    

Common shares = 0.07/17.50 = 0.40%

What is stock  market?

The phrase "stock market" describes a number of marketplaces where shares of publicly traded firms can be purchased and sold. Such financial transactions take place on official exchanges and in over-the-counter (OTC) markets that adhere to a predetermined set of rules.

Year Total         Preference   Common   Dividend per

             dividend     dividend      dividend    common share

1       80000 80000 0 0.32 0.00

2       90000 90000 0 0.36 0.00

3       150000 130000 20000 0.52 0.04

4       150000 100000 50000 0.40 0.10

5       160000 100000 60000 0.40 0.12

6       180000 100000 80000 0.40 0.16

Note:       2.40 0.42

Preference dividend per year = 250000*$20*2%=  100000  

Preference dividend for the 3rd year includes arrear dividend of $20000 for the 1st year

and $10000 for the second year, in addition to the $100000 dividend of that year.

Average annual dividend per share:      

Preferred shares = 2.40/6 = $0.40      

Common shares = 0.42/6 = $0.07      

Average annual percentage return:      

Preferred shares = 0.40/25.00 = 1.60%    

Common shares = 0.07/17.50 = 0.40%

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The arithmetic mean of a and b in the expression  1/a + 1/b = 1/c is 2c.

Arithmetic mean or average can be obtained by adding all the given values and then dividing the total sum by the number of values.

Given, An expression of the form 1/a + 1/b = 1/c.

We know average of two numbers is sum of those numbers divided by 2.

So,  {(1/a) + (a/b)}/2 = 1/c.

Now to keep the equality we also have to divide the RHS by 2.

Therefore,   {(1/a) + (a/b)}/2 = (1/c)/2.

{(1/a) + (a/b)}/2 = (1/c)×((1/2).

{(1/a) + (a/b)}/2 = 1/2c.

So, The arithmetic mean of 1/a + 1/b is 1/2c.

Now taking the reciprocal of 1/a and 1/b which is a and b the arithmetic mean is

2c.

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answer: Mean:5

median:4

range: 9

mode: 2

Step-by-step explanation:

The true statements are as follows

This is a chi-square test for association

The null and alternative hypothesis is

The null hypothesis is that here is no association between state and sporting preference.

The alternative hypothesis is that there is an association between state and sporting preference.

as given in the question

a survey was conducted with large group of teenagers from

6 different states.

let the portion of teenagers who selected the sports most preferred as (p)

(p1) as the the teenagers that for state 1

(p2) as for the teenagers that for state 2

(p3) as for the teenagers that for state 3

(p4) as for the teenagers that for state 4

(p5) as for the teenagers that for state 5

(p6) as for the teenagers that for stage 6

the formula of chi-square test is

[tex]\chi^2=\sum\frac{(O_i-E_i)^2}{E_i}[/tex]

where

[tex]O_i[/tex] is the observed value

[tex]E_i[/tex] is the expected value

[tex]\chi^2[/tex] is chi squared value

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Note:

The full question is

A survey was conducted with a large group of teenagers from 6 different states and it asked them for their favorite sport out of a large list of sports. The study aims to look at whether a teenager's state of residence is associated with their sporting preferences.

Assume that p is the proportion of teenagers who selected the sport most preferred in their state of residence, such that p1 is that for State 1 , p2 is that for State 2 and so on.

Select from the following all statements that are true as well as the hypothesis that corresponds to this study:

[tex]This\ is\ a\ chi-square test for association.& \mathrm{H}_0: \mathrm{p}_1 \neq \mathrm{p}_2 \neq \ldots \neq \mathrm{p}_6 \\& \mathrm{H}_{\mathrm{a}}: \mathrm{p}_1 \neq \mathrm{p}_2 \neq \ldots \neq \mathrm{p}_6 \\& \mathrm{H}_0: \mathrm{p}_1=\mathrm{p}_2=\ldots=\mathrm{p}_6$\mathrm{H}_0$ : There is no association between state and sporting preference. $\mathrm{H}_{\mathrm{a}}$ : There is an association between state and sporting preference. This is a one-way ANOVA test for equality of means.[/tex]

[tex]$\mathrm{H}_0$ : There is an association between state and sporting preference.$\mathrm{H}_{\mathrm{a}}: \mathrm{p}_1=\mathrm{p}_2=\ldots=\mathrm{p}_6$$\mathrm{H}_{\mathrm{a}}$ : There is no association between state and sporting preference.[/tex]

The total monthly rent for these three stores is $8,786.25.

What is total ?

Total refers to an entire or complete amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16.

The outcome of adding two or more numbers or phrases is known as the sum in mathematics. The sum is a method of bringing things together as a result. To put it another way, adding two or more numbers together results in a new result or total.

The monthly cost for a square foot of rental space in each city is as follows:

   Place            Monthly Cost for a Square Foot

Los Angeles                      $5.75

San Francisco                    $6.95

   Seattle                           $4.25

It is also provided that the store in Los Angeles will be 580 square feet, the store in San Francisco will be 500 square feet, and the store in Seattle will be 465 square feet.

Compute the total monthly rent for these three stores as follows:

Total Monthly Rent = Monthly Cost for a Square Foot × Area

                 = (5.75 * 580) +(6.95 * 500) +(4.25 * 465)

                 = 3335 + 3475 + 1976.25

                 = 8786.25

Thus, the total monthly rent for these three stores is $8,786.25.

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The exponential representation is a decreasing function

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

y = 200(0.75)x

Rewrite properly

So, we have the following representation

y = 200(0.75)ˣ

An exponential function is represented as

y = abˣ

Where

b = rate

This means that

b = 0.75

Since b is less than 1, then the function is a decreasing function

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The region inside the unit circle centered at the origin is 1. positive 2. positive 3. positive 4. positive 5. negative

Without calculation we need to state if the each of the integrals below are positive, negative, or zero. let d be the region inside the unit circle centered at the origin

xeˣ is positive for positive , and negative for negative , but the exponential factor makes the positive part dominating, so that the integral over D is positive overall.

The integrals over B and T are identical by symmetry, and both are equal to half the value of the integral over D, so they are both positive as well.

The integral over L is negative because it takes strictly non-positive values of x .

Similarly, the integral over R is positive because it considers non-negative values of x.

Therefore, the region inside the unit circle centered at the origin is 1. positive 2. positive 3. positive 4. positive 5. negative

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The value of the missing angle of the triangle is; x = 31°

Alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.

Now, from the diagram, we can tell that ∠GAB is congruent to ∠CBA by alternate angles theorem.

Thus, ∠GAB = 28°

Similarly, sum of angles on a straight line = 180°. Thus;

∠EDA = 180 - (4x + x)

∠EDA = 180 - 5x

Also, sum of angles in a triangle is 180 degrees. Thus;

∠CAB = 180 - (90 + 28)

∠CAB = 62°

Thus;

62 + 3x + 180 - 5x = 180

62 - 2x = 0

2x = 62

x = 62/2

x = 31°

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f 57 and 63 are the 90% confidence limits for the population mean, then [60, 60] might be the 97% confidence limit.

A population is a discrete collection of things having observable traits, such humans or animals, for the purpose of analysis and data collection. It is made up of a comparable collection of species that live in a specific area and have the ability to interbreed.

The average calculated from the whole population, distribution, or group is known as the population mean. It is calculated by dividing the total number of population variables by the sum of all population variables. The population mean can be found here as. Observations in the population are added together to form X.

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CSC 23° can be written as sec 67° in as its cofunction.  

A branch of mathematics called trigonometry in geometry focuses on the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to angles and sides.

The six trigonometric ratios are sin, cos, tan, cot, cosec, and sec.

From Trigonometrical Ratios of (90° - θ)

=> sin (90° - θ) = cos θ

=> cos (90° - θ) = sin θ

=> tan (90° - θ) = cot θ

=> csc (90° - θ) = sec θ

=> sec (90° - θ) = csc θ

=> cot (90° - θ) = tan θ

Here we have CSC 23°

Here we need to write csc 23° into its cofunction

From Trigonometrical Ratios of (90° - θ)

csc (90° - θ) = sec θ

23° can be taken as (90 - 67)°  

=>  csc 23° = csc (90 - 67)° = sec 67°    

Therefore,

CSC 23° can be written as sec 67° in as its cofunction.

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x = number of small boxes

y = number of large boxes

well, we know a total of 20 boxes, large and small were shipped, that means that whatever "x" and "y" may be, we know that x + y = 20.

so the volume of one small box is 8 ft³, so sticking to ft³, we can say that the volume of 1 box is 8(1) ft³, and the volume of 2 boxes will then be 8(2) and three is 8(3) ft³ and the volume of "x" boxes will then just be 8(x) ft³.

now, we can say the same thing about large boxes, volume of 1 is 21(1) ft³, for two is 21(2) ft³, for three 21(3) ft³, and for "y" boxes that'll just be 21(y) ft³.

that said, well hell their volume combined must be 8x + 21y, and we happen to know that's 264 ft³, namely 8x + 21y = 264.

[tex]\begin{cases} x+y=20\\\\ 8x+21y=264 \end{cases}\hspace{5em}\stackrel{\textit{using the 1st equation}}{x+y=20\implies }y=20-x \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{8x+21(\underset{y}{20-x})=264}\implies 8x+420-21x=264 \\\\\\ 8x+420=264+21x\implies 8x+156=21x\implies 156=13x \\\\\\ \cfrac{156}{13}=x\implies \boxed{12=x}\hspace{13em}\stackrel{20~~ - ~~12}{\boxed{y=8}}[/tex]

Answer:

(−3, 2); 2 < y < ∞

Step-by-step explanation:

It's either (−3, 2); 2 < y < ∞ or (−3, 2); −∞ ≤ y < ∞ but I'm pretty sure its (−3, 2); 2 < y < ∞

Answer:

[tex]\dfrac{x\sqrt{4-x^2}}{4-x^2}[/tex]

Step-by-step explanation:

Given:

[tex]\tan \left(\sin^{-1}\left(\dfrac{x}{2}\right)\right)[/tex]

[tex]\boxed{\begin{minipage}{5cm}\underline{Trigonometric Identity}\\\\$\tan(\arcsin(x))=\dfrac{x}{\sqrt{1-x^2}}$\\ \end{minipage}}[/tex]

Use the tan(arcsin(x)) trigonometric identity and replace x for (x/2):

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\sqrt{1-\left(\dfrac{x}{2}\right)^2}}[/tex]

Simplify the denominator:

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\sqrt{1-\dfrac{x^2}{4}}}[/tex]

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\sqrt{\dfrac{4-x^2}{4}}}[/tex]

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\dfrac{\sqrt{4-x^2}}{\sqrt{4}}}}[/tex]

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\dfrac{\sqrt{4-x^2}}{2}}}[/tex]

[tex]\textsf{Apply the fraction rule}: \quad \dfrac{\frac{a}{c}}{\frac{b}{c}}=\dfrac{a}{b}[/tex]

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{x}{\sqrt{4-x^2}}[/tex]

Multiply the numerator and denominator by the denominator to eliminate the radical from the denominator:

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{x}{\sqrt{4-x^2}} \cdot \dfrac{\sqrt{4-x^2}}{\sqrt{4-x^2}}[/tex]

Simplify:

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{x\sqrt{4-x^2}}{4-x^2}[/tex]

∠4=∠6 because each pair of alternate interior angles is equal ( The two column proof is attached ).

Every two-column proof has exactly two columns. One column represents our statements or conclusions and the other lists our reasons. In other words, the left-hand side represents our “if-then” statements, and the right-hand side explains why we know what we know.

We can clearly observe here that ∠1=∠5 , ∠2=6, ∠3=∠7, ∠4=∠8 as Corresponding angles are equal.

∠4 + ∠3 = 180°……..(1) PQ is the straight line

∠6 + ∠7 = 180°……..(2) t is the straight line

therefore from the two equations we get

∠4 =∠6

Hence, ∠4  ≅∠6 ( The two column proof is attached )

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The construction that the figure represents is perpendicular bisector

A perpendicular bisector is a line that cuts through the intersection of two other line segments at a right angle.

So, a perpendicular bisector always splits a line segment through its middle, as we can see. By definition, the word "bisect" denotes an even or uniform division.

Perpendicular Bisector Properties for AB in the figure

It cuts AB in half, or into two equal halves.

It is perpendicular to AB or at right angles to it.

The distance between each point along the perpendicular bisector from points A and B is equal.

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Answer:

  A, B, C

Step-by-step explanation:

You want to find the dimensions, perimeter, and area of a foundation such that the length is 6 feet more than twice the width, and the area is 1046 more that the value of the perimeter.

We can let x and y represent the length and width, respectively. Then the given relations translate to the equation ...

  A = LW . . . . . . . area formula

  P = 2(L +W) . . . . perimeter formula

  y = 2x +6 . . . . . relation between dimensions

  xy = 2(x +y) +1046 . . . . . relation between perimeter and area

Using the first equation to substitute for y, we have ...

  x(2x +6) = 2(x +(2x +6)) +1046

  2x² +6x = 6x +1058 . . . . . . . . . . . . eliminate parentheses

  x² = 529 . . . . . . . . . . . . . subtract 6x and divide by 2

  x = √529 = 23 . . . . . . . . . width; matches B

  y = 2(23) +6 = 52 . . . . length

  area = (23)(52) = 1196 . . . area; matches A

  perimeter = 2(23 +52) = 2(75) = 150 . . . . matches C

The area is 1196 square feet. (A)

The width is 23 feet. (B)

The perimeter is 150 feet. (C)

The Greatest Common Divisor (GCD) of 85 and 51 is 17.

The greatest common factor that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor is another name for it (HCF).

Explanation

Step 1: Divide 85 by 51. The quotient is 1 and the remainder is 34.

Step 2: Divide 51 by 34. The quotient is 1 and the remainder is 17.

Step 3: Divide 34 by 17. The quotient is 2 and the remainder is 0.

Step 4: Since the remainder is 0, the Greatest Common Divisor (GCD) of 85 and 51 is 17.

The GCD of 85 and 51 is 17.

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Answer:

That looks correct to me!

Answer:

g = 18(1/3)

Step-by-step explanation:

The sub is made of 18 sections of 1/3, so it is 18(1/3) feet long (or 6ft when simplified)

Amount of money needed to carry to the sari sari store is 59.

a) According to question

Amount of eggs to buy = 3

Rate of eggs = 8

Total amount for eggs = 3x8=24

Amount of  hotdogs to buy = 2

Rate of hotdogs = 10

Total amount to pay for hotdogs = 2x10=20

Amount of  bread to buy = 3

Rate of bread = 5

Total amount to pay for bread=3x5=15

So money needed to take to the sari sari store=24+20+15=59

b) Polynomial is 4x²+2x-3

1) x=1

  4(1)²+2(1)-3

  4+2-3

  3

2) x=2

 4(2)²+2(2)-3

 4(4)+4-3

 16+4-3

 17

3) x=3

 4(3)²+2(3)-3

 4(9)+6-3

 36+6-3

 39

4) x=5

 4(5)²+2(5)-3

 4(25)+10-3

 100+10-3

 107

5) x=6

 4(6)²+2(6)-3

 4(36)+12-3

 144+12-3

 153

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The value of the estimated standard error is 1.

The set of d (differneces) scroes: 4, 8, 4 ,4

Consider,

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

Mean of the D-score is [tex]$$\begin{aligned}\bar{d} & =\frac{1}{n} \sum d_i \end$[/tex]

[tex]=\frac{1}{4}[/tex](4+8+4+4)

=5

Standard deviation of D-score is given by [tex]$$\begin{aligned}\hat{\sigma} & =\sqrt{\frac{1}{n-1} \sum_{i=1}^n\left(d_i-\bar{d}\right)^2} \\& =\sqrt{\frac{1}{4-1}\left\{(4-5)^2+(8-5)^2+(4-5)^2+(4-5)^2\right\}} \end[/tex]

The value of the estimated standard error for the following set D scores is

[tex]$$\begin{aligned}\widehat{\mathrm{SE}(d)} & =\frac{\hat{\sigma}}{\sqrt{n}} \\& =\frac{2}{\sqrt{4}}\end{aligned}$$[/tex]

[tex]=\frac{2}{2}=1[/tex]

Therefore, the value of the estimated standard error for the following set of d scroes is 1.

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On solving the provided question we can say that - mean of x mean of y

27.37136 30.73706

In statistical inference studies, an alternative hypothesis is a statement. This is represented by Ha or H1, which conflicts with the null hypothesis. It only serves as a zero replacement. The claims that researchers are investigating in hypothesis testing are alternative theories.

[tex]t = -11.067, \\df = 2301.5, \\p-value < 2.2e-16[/tex]

alternative hypothesis: true difference in means is less than 0

95 percent confidence interval:

[tex]-Inf -2.865266[/tex]

sample estimates:

mean of x mean of y

27.37136 30.73706

Conclusion:-

Here   p-value = 2.2e-16 < 0.05(Level of significance)

Therefore we reject  at 5% Loss

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Answer:

8x + y > 4

y > -8x + 4

Answer:

y - 8 = 2 (x - 6)

Step-by-step explanation:

The point-slope equation is ...

y - y1  = m ( x - x1 )

In the coordinate (6,8)

x = 6 and y = 8

m = 2

Plug in values to find the point-slope form

y - 8 = 2 (x - 6)

We are done!

a) The distribution of X is a discrete geometric distribution with pmf p(x) = (5/36)(1/6)^(x-1).b) The theoretical mean (mu) of X is 6.c) The theoretical variance of X is 35.d) The expected value of Y is 6 and the variance of Y is 3.875.

The distribution of X is a discrete geometric distribution, which means that the probability of X taking on any particular value is given by the formula p(x) = (5/36)(1/6)^(x-1). The theoretical mean (mu) of X is 6, which means that on average it should take 6 trials to obtain a sum of 7. The theoretical variance of X is 35, which means that there is a considerable amount of variability in the number of trials needed to obtain a sum of 7. If we consider the random variable Y, the average number of trials needed to roll a sum of 7 based on 25 trials, then the expected value of Y is 6 and the variance of Y is 3.875. This indicates that the average number of trials needed to obtain a sum of 7 is 6 and that the variability decreases as more trials are taken.

a) p(x) = (5/36)(1/6)^(x-1)

b) theoretical mean (mu) of X mu = 6

c) Var(X) = (5/36)*∑x=1∞(1/6)^(x-1)^2 - mu^2

       = (5/36)*(1-1/36^2) - 6^2

       = 35

d) The expected value of Y , E(Y) = 6

Var(Y) = Var(X/6)

       = Var(X)/6^2

       = 35/6^2

       = 3.875

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