12. Show that the argument form with premises (p ∧ t) → (r∨s), q→(u∧t), u→p, and ¬s and conclusion q → r is valid by first using Exercise 11 and then us- ing rules of inference from Table 1.11.Show that the argument form with premises p1,p2,...,pn and conclusion q → r is valid if the argument form with premises p1,p2,...,pn,q, and conclusion r is valid.

Answer:

D, because it just has 4 times more squares

Answer:

Step-by-step explanation:

You want to know the values of k that make the line 4y = k(x +4) either parallel or perpendicular to the line 12y = 9x +8.

The slopes of parallel lines are the same. When the equation of a line is written in "y =" form, the slope is the coefficient of x. Here, the two equations written in that form are ...

For parallel lines, we want to choose the value of k so that the slopes are equal:

  k/4 = 3/4

  k = 3 . . . . . . . . multiply by 4

The slopes of perpendicular lines have a product of -1. This means we want to choose k so that ...

  (k/4)(3/4) = -1 . . . . . the product of slopes k/r and 3/4 is -1

  k = -16/3 . . . . . . . . . multiply by 16/3

__

Additional comment

The attached graph shows the original line (dashed red) and the parallel and perpendicular lines with their respective values of k.

Answer:

Step-by-step explanation:

You want the value of the piecewise function for various values of x.

The first step in evaluating a piecewise function is determining which domain is applicable to the value of x you have. Then you use the corresponding function, evaluating it in the usual way.

For x = -5, the applicable domain is x < -3, so the function is ...

  h(-5) = -4(-5) -18 = 20 -18

  h(-5) = 2

For x = 0, the applicable domain is -3 ≤ x < 1, so the function is ...

  h(0) = 1

For x = 1 or 4, the applicable domain is x ≥ 1, so the function is ...

  h(1) = 1 +2 = 3

  h(4) = 4 +2 = 6

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The area covered by the pool and the cement walkway is 304  square feet. The width of the walkway would be 5 feet

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

Let x be represent the width of the walkway.

The pool measures 25 ft by 10ft . If the walkway must have a uniform width around the entire pool, then the total length of the pool and the walkway =  25+ x + x = 25 + 2x

The total width of the pool and the walkway = 10 + x + x = 10 + 2x

The area covered by the pool and the cement walkway is 304  square feet. This means that;

(25 + 2x)(10 + 2x) = 304

250 + 50x + 20x + 4x^2 = 304

4x^2 + 70x + 250 - 304 = 0

4x^2 + 70x - 54 = 0

x(x + 20) - 5(x + 20) = 0

(x - 5)(x + 20) = 0

x = 5 or x = - 20

Thus The width cannot be negative.

Therefore, the width of the walkway is 5 feet.

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The a) , c) & d) are convergent series and b) is divergent series.

a)

Given series,

\(\sum \limits^\infty_{n=1} (7+n(7))^{-7}\\ \\=\sum \limits^\infty_{n=1}7^{-7}+\sum \limits^\infty_{n=1}(7^nn)^{-7}\\\)

consider,

\(\sum \limits^\infty_{n=1}(7^nn)^{-7}=\sum \limits^\infty_{n=1}(n)^{-7}(7)^{-7}\\\\=\sum \limits^\infty_{n=1}(n)^{-7}(7)^{-7}\\\\=\sum \limits^\infty_{n=1}(n)^{-7}(\frac{1}{7})^{7}\)

comparing \(=\sum \limits^\infty_{n=1}(n)^kr^n\) we get,

\(k=-7\ and\ r=\frac{1}{7^7}=\frac{1}{823543}\)

here, \(|r|=|\frac{1}{7^7}|=1.2142*10^{-6}\) which is < 1

here |r| < 1,

Thus, the given series converges.

b)

Given series,

\(\sum \limits^\infty_{n=1} n^{\pi}(\frac{7^{2n}}{6^n+n^9})=\sum \limits^\infty_{n=1}n^kr^n\)clearly, k=π

To find r we need to use ratio test for \(a_n\)

\(a_n=\frac{7^{2n}}{6^n+n^9}\\\\L= \lim_{n \to \infty}|\frac{a_n+1}{a_n} |\\\\=\lim_{n \to \infty}|\frac{7^{2n+2}}{6^{n+1}+(n+1)^{9}}*\frac{6^{n}+(n)^{9}}{7^{2n}}|\\\\=\lim_{n \to \infty}|\frac{7^2(6^n+n^9)}{6{n+1}+(n+1)^9}|\\\\=\lim_{n \to \infty}|\frac{49(6^n+n^9)}{6^{n+1}+(n+1)^9}|\)

here \(r=\frac{49}{6}\) > 1

hence. the series diverges.

c)

Given series,

\(\sum \limits^\infty_{n=1}\frac{n^5+2}{n^6+7}\)

let \(u_n=\frac{n^5+2}{n^6+7}\)

take \(v_n=\frac{n^5}{n^6}=\frac{1}{n}\)

Now,

\(\lim_{n \to \infty} \frac{u_n}{v_n}= \lim_{n \to \infty}\frac{n^5+2}{n^6+2}*\frac{n}{1}\\=1\\Now,\\\\\sum v_n=\sum \frac{1}{n}\\\\=\sum (n)^{-1}(1)^n\\\\\)

comparing with \(\sum n^kr^n\) we get,

k=-1 and r=1

So, the series converges.

d)

Given series,

\(\sum \limits^\infty_{n=1} (\frac{2n^2+7n+7^{-3n}}{8^{n+2}+6n+7\sqrt{n}})^3\)

The dominant terms are \(2n^2\) and \(8^{n+2}\), the sum can be approximated as,

\(\sum \limits^ \infty_{n=1} (\frac{2n^2}{8^{2+n}})^3\\\\=\frac{2^3}{8^6}\sum \limits^ \infty_{n=1} n^6(\frac{1}{512})^n\)

comparing with \(\sum n^kr^n\) we get,k=6 and \(r=\frac{1}{512}\)

here also 0 < r <1,

Thus, the series converges.

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I believe it would 18 ounces of chips for 3 cups of flour. If you take half of 12 ounces then you get 6 ounces per cup of flour. Adding 6 ounces to the 12 would get us the total of the 18 ounces.

Answer:

1/4

Step-by-step explanation:

divide numerator and denominator by 3

This is not a syllogism. Hence option B is correct.

A logical structure for a formal argument that includes a major, minor, and conclusion.

This syllogism cannot be concluded without a given statement.

You'll need wrapping paper if you're going to wrap Holly's present. To get wrapping paper, you must visit a store.

Therefore, you will wrap Holly's present if you visit the store. This isn't a syllogism

Hence option B is correct.

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Answer:

This is not a syllogism

Step-by-step explanation:

I took the quiz. :)

Step-by-step explanation:

here,

principal (p)=£6000

Rate (R)=. 3.4%

time (t)=3 yrs

now,

total investment is compound amount i.e CA

here,

\(CA = p(1 + \frac{r}{100} ) ^{t} \)

=£6000(1+3.4/100)^3

=£6633.044

here he will get his total investment as £6633.044 in compound interest of 3.4%

a) There is not enough evidence to conclude that cars get significantly better fuel economy with premium gasoline.

In order to test the belief that premium gasoline provides better fuel economy, a study was conducted using 10 cars from a company fleet. Each car was randomly assigned either regular or premium gasoline, and the mileage for each tankful was recorded. The data was analyzed to determine if there is a significant difference in fuel economy between the two types of gasoline.

To evaluate this, a paired t-test can be used since the same cars were tested with both types of gasoline. The null hypothesis would be that there is no difference in fuel economy between regular and premium gasoline, while the alternative hypothesis would be that there is a significant difference.

The results of the study would be analyzed using the appropriate statistical test, such as a paired t-test, to determine the p-value. If the p-value is less than the chosen significance level (e.g., 0.05), then there would be evidence to reject the null hypothesis and conclude that there is a significant difference in fuel economy.

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The tree should be 22.5 feet tall in the mural.

To determine the height of the tree in the mural, we can set up a proportion based on the scale ratio between Devon's height and the height of the tree.

Let's denote the height of the tree in the mural as 'x'.

According to the given information:

Devon's actual height: 6 feet

Devon's height in the mural: 4.5 feet

Tree's actual height: 30 feet

Setting up the proportion:

(Devon's height in the mural) / (Devon's actual height) = (Tree's height in the mural) / (Tree's actual height)

Substituting the given values:

4.5 feet / 6 feet = x / 30 feet

To solve for 'x', we can cross-multiply:

4.5 feet * 30 feet = 6 feet * x

135 feet = 6x

Divide both sides by 6:

x = 135 feet / 6

Simplifying the division:

x = 22.5 feet

Therefore, in the painting, the tree should stand 22.5 feet tall.

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Answer:

-34

Step-by-step explanation:

All you have to do is subtract by 4 until you count to 15 which then leads you to the number -34

Answer:

x is 49

Step-by-step explanation:

Answer:

49

Step-by-step explanation:

i just took the test

Answer:

(3, -2)

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

(x, y) (__,-2)

-2 = -2r + 4

-2-4 = -2r

-6 = -2r

divide -2r on both sides

r=3 ---> x=3

(3,-2)

Answer:

x=7

Step-by-step explanation:

2x-4+2x-7=17

4x-11=17

4x=28

x=7

Example 1:

An example of a group in which all non-identity elements have infinite order is the additive group of integers, denoted as (Z, +). In this group, the operation is ordinary addition. Every non-zero integer can be written as the sum of 1 repeated infinitely many times or -1 repeated infinitely many times, resulting in infinite orders for all non-identity elements. For instance, consider the element 1 in this group. If we add 1 to itself repeatedly, we obtain the sequence 1, 2, 3, 4, and so on, which extends infinitely. Similarly, adding -1 to itself repeatedly generates the sequence -1, -2, -3, -4, and so forth. Thus, every non-zero element in the additive group of integers has an infinite order.

Example 2:

An example of a group in which for every positive integer n, there exists an element of order n is the multiplicative group of positive rational numbers, denoted as (Q+, ×). In this group, the operation is ordinary multiplication. For any positive integer n, we can find an element whose exponentiation by n gives the identity element 1. Specifically, let's consider the element 2^(1/n). If we multiply this element by itself n times, we get (2^(1/n))^n = 2^(n/n) = 2^1 = 2, which is the identity element in the group. Therefore, the element 2^(1/n) has an order of n. This applies to every positive integer n, meaning that for any n, we can find an element in the multiplicative group of positive rational numbers with an order of n.

In summary, the additive group of integers (Z, +) exemplifies a group where all non-identity elements have infinite order, while the multiplicative group of positive rational numbers (Q+, ×) demonstrates a group where for every positive integer n, there exists an element with an order of n.

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Using the given factorization A = PDP⁻¹ and D₁ = [3 0 0 5], the matrix P₁ is calculated as [25, -8, 7, -7], satisfying A = P₁D₁P⁻¹₁.

To find the matrix P₁ given the factorization A = PDP⁻¹, we can use the formula P₁ = P.D₁⁻¹.D.P⁻¹.

Given

A = [9 -12 2 1]

P = [1 -2 1 -3]

D = [5 0 0 3]

P⁻¹ = [3 -2 1 -1]

D₁ = [3 0 0 5]

First, we need to find D₁⁻¹, which is the inverse of D₁:

D₁⁻¹ = [1/3 0 0 1/5]

Now, we can compute P₁ using the formula:

P₁ = P.D₁⁻¹.D.P⁻¹

Substituting the given values, we have:

P₁ = [1 -2 1 -3] * [1/3 0 0 1/5] * [5 0 0 3] * [3 -2 1 -1]

Performing the matrix multiplication, we get:

P₁ = [1/3 -4/5 1/3 -3/5] * [15 0 0 9] * [3 -2 1 -1]

Simplifying further, we have:

P₁ = [5 -4 5 -3] * [3 -2 1 -1]

Performing the final matrix multiplication, we get:

P₁ = [15 + 8 + 5 - 3, -10 + 4 - 5 + 3, 5 - 2 + 5 - 1, -5 + 2 - 5 + 1]

Simplifying the calculation, we get:

P₁ = [25, -8, 7, -7]

Therefore, the matrix P₁ for the given factorization A = PDP⁻¹ and D₁ = [3 0 0 5] is:

P₁ = [25, -8, 7, -7]

Hence, we have found the matrix P₁ using the provided information.

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Answer:

{-2, 0, 1, 2, 8}

Step-by-step explanation:

The range is {-2, 3, 4, 5}

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

We are given the set as;

{-2, 3, 4, 5}

Since the Range is the set of y-values that are outputted by function f(x)

The Builder Set Notation {x}

According to the given graph, our y-values are 3, 4, 5 and -2. Since they are all closed dots, they are inclusive in the range:

Note to put it in number line order.

{-2, 3, 4, 5}

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Answer:

The answer is 324

Step-by-step explanation:

I don't know if it's the correct answer but I hope it helps

pls mark me as brainliest

Answer:

no photo

Step-by-step explanation:

we need a photo to decide if answer is correct or not

The value of x in the equation is x = -1 ±√19

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

4(x+1)^2-31=45

Add 31 to both sides of the equation

This gives

4(x+1)^2 = 76

Divide by 4

So, we have

(x + 1)^2 = 19

take the square roots of both sides

x + 1 = √19

So, we have

x = -1 ±√19

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Answer:

hi JJHJHJHDJHOSDIHSKOREIHOISOJ

Step-by-step explanation:

Answer:

-x12

Step-by-step explanation:

cause I know

Answer:

Monday

Tuesday

Wednesday

Thursday

Friday     only!

Step-by-step explanation:

Answer:

Monday

Tuesday

Wednesday

Thursday

Hope it helped!!

The best answer regarding the effects of carbon monoxide is option c, CO results in less oxygen loading hemoglobin but unloading is not changed.

Carbon monoxide binds up more tightly to the hemoglobin as compared to the oxygen molecules. This reduces the oxygen-carrying capacity of the blood and results in less oxygen loading onto hemoglobin.

However, once oxygen is already bound to hemoglobin, CO does not significantly affect its release or unloading. Therefore, option c is the most accurate statement among the given choices.

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Answer:

Answer 1: a. Moonlight: C=75n+1000

Riverside: C=50n+1500

Answer 2: c. The solution coordinates are c. (20, 2500)

Answer 3: c. When there are 20 guests attending the price is $2500.

Step-by-step explanation:

Moonlight Hall:

Fixed cost = $1000

Cost per guest = $75

Cost of 'n' guests = 75 \(\times n\)

Total cost of moonlight hall = Fixed cost + Cost of 'n' guests

\(\Rightarrow 1000 + 75 \times n\)

Riverside Hall:

Fixed cost = $1500

Cost per guest = $50

Cost of 'n' guests = 50 \(\times n\)

Total cost of moonlight hall = Fixed cost + Cost of 'n' guests

\(\Rightarrow 1500 + 50 \times n\)

Hence, Answer 1:

a. Moonlight: C=75n+1000

Riverside: C=50n+1500

Answer 2: Coordinates of solution:

Option c. (20,2500) satisfies both the equation.

When there are 20 number of guests, the cost of both moonlight and riverside hall comes out to be 2500.

Moonlight Hall cost

\(75 \times 20 + 1000\\\Rightarrow \$2500\)

Riverside Hall cost

\(50 \times 20 + 1500\\\Rightarrow \$2500\)

Answer 3: c. When there are 20 guests attending the price is $2500.

The solution is done in Answer 2.

So,

Answer 1: a. Moonlight: C=75n+1000

Riverside: C=50n+1500

Answer 2: c. The solution coordinates are c. (20, 2500)

Answer 3: c. When there are 20 guests attending the price is $2500.