Luna's dining room is 19 feet wide and 22 feet long. Luna wants to install wooden trim
around the top of the room. The trim costs $0.06 per foot. How much will it cost Luna to buy
enough trim?

The negations of the given statements with the application of De Morgan's law and/or conditional law.

a) ∃x (¬P(x) ∨ ¬R(x))

De Morgan's law:

∃y ∀z(¬P(y) ∧ ¬Q(z))

b) ∃y ∀z(¬P(y) ∧ ¬Q(z))

The double negation:

∃y ¬∃z(P(y) ∨ Q(z))

c) ¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

The conditional law:

¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

Let's form the negation of the given statements and apply De Morgan's law and/or conditional law, when applicable:

a) ∀x (P(x) ∧ R(x))

The negation of this statement is:

∃x ¬(P(x) ∧ R(x))

Now let's apply De Morgan's law:

∃x (¬P(x) ∨ ¬R(x))

b) ∀y∃z(¬P(y) → Q(z))

The negation of this statement is:

∃y ¬∃z(¬P(y) → Q(z))

Using the conditional law, we can rewrite the negation as:

∃y ¬∃z(¬¬P(y) ∨ Q(z))

c) ∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

The negation of this statement is:

¬∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

Using the conditional law, we can rewrite the negation as:

¬∃x (P(x) ∨ (∀z (R(z) ∨ ¬Q(z))))

Applying De Morgan's law:

¬∃x (P(x) ∨ (∀z ¬(¬R(z) ∧ Q(z))))

Simplifying the double negation:

¬∃x (P(x) ∨ (∀z ¬(R(z) ∧ Q(z))))

Using De Morgan's law again:

¬∃x (P(x) ∨ (∀z (¬R(z) ∨ ¬Q(z))))

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Answer:

$30.62

Step-by-step explanation:

12% of 40 is 4.8

(10% is 4, 2% is 0.8)

40- 4.8= 35.2

13% of 35.2 is 4.576

(10% is 3.52, 3% is 1.056)

35.2- 4.576= 30.624

then rounded to 2 decimal places

30.62

Answer:

-10.5-30x

Step-by-step explanation:

explanation is in the image above

Answer:

\({ \tt{0.5 - 3( - 2x - \frac{1}{3} + 4 + 8x) }}\)

» First solve the bracket by simplification rule. Arrange x terms together and constants together.

\({ \tt{ \dashrightarrow \: 0.5 - 3{ \huge \{}( - 2x + 8x) + (4 - \frac{1}{3} ){ \huge{ \}}}}}\)

» Then solve the sub brackets in the parent bracket:

\( \dashrightarrow \: { \tt{0.5 - 3(6x + \frac{11}{3} )}} \)

» Open the bracket following distributive property [ Multiply -3 to each constant in the bracket ]

\( \dashrightarrow \: { \tt{0.5 - 18x - 11}}\)

» Then simplify:

\({ \tt{ \dashrightarrow \: - \frac{21}{2} - 18x}} \\ \)

Answer:

\(x=\frac{y+4}{6}\)

Step-by-step explanation:

y=6x−4

Swap sides so that all variable terms are on the left hand side.

6x−4=y

Add 4 to both sides.

6x=y+4

Divide both sides by 6.

\(\frac{6x}{6}=\frac{y+4}{6}\)

Dividing by 6 undoes the multiplication by 6.

\(x=\frac{y+4}{6}\)

Divide y+4 by 6.

\(x=\frac{y}{6} +\frac{2}{3}\)

ANSWER:

x=1/6y + 2/3

y= 6x - 4

Answer:1285.7 meters per second.

Step-by-step explanation: divide 900,000 meters by 700 seconds

Answer:

A plane travels 360,000 meters in 900 seconds

Step-by-step explanation:

$40

1) Since Noah has a coupon (30% off) we can write the following

Since Noah has paid $28 after we can write the following equation to find the regular price.

jeans' price = j

j(1-0.3) = 28 We can write the discount of 30% as 0.3

j(0.7) =28 Divide both sides by 0.7

j=28/0.7

j=40

Notice that we have to subtract that percentage (0.3) from 1. To find the factor

2) Hence, the regular price of that pair of jeans is $40

Answer:

1 : 8

Step-by-step explanation:

Answer:

$8 per hour

Step-by-step explanation:

First you have to do 16/2 or 32/4 to get your answer which is 8

Hope this helps!

Answer:

the median of 0 1 2 3 16 38 34 12 is 9.5

Answer: 4(4b - 5)(b + 5)

Step-by-step explanation:

All have a common factor of 4

4(4b^2 + 15b - 25)

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

Now you need to find two numbers that:

a) multiply to -100 (the a term * the c term = 4 * -25)

b) add to 15 (the b term)

After a little thinking, we can determine that the two numbers are:

20 and -5

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

Now we can rewrite the middle term as 20b - 5b (notice how it still equals 15b)

4(4b^2 + 20b - 5b - 25)

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

4((4b^2 + 20b) + (-5b - 25))

Group the terms (associative property)

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

Take out a common factor from each

4(4b(b + 5) - 5 (b + 5))

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

Now we can factor by grouping

4(4b - 5)(b + 5)

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

Answer: 1/40

Step-by-step explanation:

The equivalent value of the fraction is A = 1/40

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first fraction be p

Let the second fraction be q

Now , A = p/q

when the value of p = 1/8

And , when the value of q = 5

On simplifying the equation , we get

A = ( 1/8 ) / 5

So , the left hand side of the equation is equated to the right hand side by the value of ( 1/8 ) / 5

A = ( 1/8 ) / 5

A = ( 1/8 ) ( 1/5 )

On simplifying , we get

A = 1/40

A = 0.025

Therefore , the value of A = 1/40 = 0.025

Hence , the fraction is A = 1/40

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The polynomial, f(x) = x² + 4·x - 1, has a value of -5 when x = -2

A polynomial consists of terms comprising of variables and numbers with positive integer indices with operations including additions, subtractions, multiplications.

The specified polynomial is f(x) = x² + 4·x - 1

The point at which the polynomial is evaluated is; x = -2

The value of the specified polynomial at x = -2 is therefore;

f(-2) = (2)² + 4 × (-2) - 1 = -5

The polynomial can also be evaluated by graphing polynomial and finding the point of intersection of the line x = -2 and the graph of the polynomial as follows;

The attached graph created with MS Excel, indicates that at the point x = -2 (represented by the point where the vertical line, x = -2, intersects the polynomial, x² + 4·x - 1) is the point where, f(x) = -5

The value of the polynomial, f(x) = x² + 4·x - 1, when x = -2 is -5.

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Answer:

Two Angles can be said to be Complementary when they add up to 90° ;a Right Angle.

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

4 * 2 + 3 - 2 =

= 8 + 1 =

= 9

The end-points of the line segment will be negative 1.25 and 0.25.

A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.

The length of the line segment is 1.50 units and the midpoint of the line segment is negative 0.50. Then the end-points of the line segment are given as,

⇒ - 0.50 ± (1.50) / 2

Simplify the expression, then we have

⇒ - 0.50 ± (1.50) / 2

⇒ - 0.50 - (1.50) / 2, - 0.50 + (1.50) / 2

⇒ - 0.50 - 0.75, - 0.50 + 0.75

⇒ - 1.25, 0.25

The end-points of the line fragment will be negative 1.25 and 0.25.

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Answer:1/8

Step-by-step explanation:

Answer:

1/8

Step-by-step explanation:

1/2 x 1/2 x 1/2 = 1/8

Answer:

below smallest to greatest:

Step-by-step explanation:

1)  1/4--> 3/8 --> 1/2

b) 4/9 --> 1/2 --> 2/3 -->5/6

c) 1/5--> 7/10 --> 3/4--> 4/5

Answer:

1.25

Step-by-step explanation:

you have to take the 9 pages and divide by 7 and then divide that by 60 and u get 1.25

Answer:

8

Step-by-step explanation:

72 ÷ 9 = 8

Answer:

8

Step-by-step explanation:

72 divided by 9 is 8

Answer:

12-4r

Step-by-step explanation:

4r<12 because r<3 so you flip it.

Answer:

320

Step-by-step explanation:

32 bottles  in 6 minutes add a 0 so you get 320 bottles in 60 minuts.

Answer:

D 320

Step-by-step explanation:

Since 60 minutes is 10 times 6 minutes, the machine can make 10 time more water bottles in 60 minutes than it can make is 6 minutes.

10 * 32 = 320

Answer: D 320

You can also solve by using a proportion.

32/6 = x/60

6x = 60 * 32

Divide both sides by 6.

x = 10 * 32

x = 320

Answer: D 320

\(\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies SA=4\pi (4)^2\implies SA\approx 201.1~in^2 \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3}\implies V\approx 268.1~in^3\)

Answer:

5

Step-by-step explanation:

Explanation: All the edges of a cube have the same length, and the volume of a cube is the length of an edge taken to the third power. So the length of the edge of a cube with a volume of 125 is 5.

Answer:

13.5 = 9.5 + x

x=4

Step-by-step explanation:

In this problem, the price of the baseball cap, which is $9.50, and a baseball, whose price is unknown (and therefore must be the variable), total $13.50. So, to set up the equation add the two prices and set them equal to the total, 9.5+x=13.5.

Then, using the subtraction property of equality subtract 9.5 from both sides. This means x=4, so the baseball cost 4 dollars.

cos(tan^(-1)(-2/3)) simplifies to 3√13 / 13.

To evaluate the expression cos(tan^(-1)(-2/3)), we can use the trigonometric identity:

cos(tan^(-1)(x)) = 1 / √(1 + x^2)

In this case, x is -2/3. Substituting the value into the identity:

cos(tan^(-1)(-2/3)) = 1 / √(1 + (-2/3)^2)

Now, let's calculate the value:

cos(tan^(-1)(-2/3)) = 1 / √(1 + 4/9)

                   = 1 / √(13/9)

                   = 1 / (√13/3)

                   = 3 / √13

                   = 3√13 / 13

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Answer:

1. 8t

2. 510 + 6t

3. 510 - 2t

Step-by-step explanation:

1. Since the hare moves at a speed of 8 metres per second, the distance it moves from the starting line is d = speed × time = 8t

2. Since the rabbit moves at a speed of 6 metres per second, and gets a head start of 510 metres, the distance it moves from the starting line is d = 510 m + speed × time = 510 + 6t

3. The distance the tortoise is ahead of the hare is thus, distance moved by rabbit - distance moved by hare in time, t.

d' = 510 + 6t - 8t

= 510 - 2t  

Answer:

60 dollars to the two girls each, and 30 dollars to John.

Step-by-step explanation:

If the two girls have 60 dollars (each), then that is twice as much as 30.

60 + 60 = 120.

120 + 30 = 150.

Given that,

The area of the rectangle, \(A=x^2-114\)

Length of the rectangle, \(l=x+12\ m\)

To find,

The width of the rectangle.

Solution,

The formula for the area of a rectangle is given by :

A = lb

b is width of the rectangle

\(b=\dfrac{A}{l}\\\\b=\dfrac{x^2-114}{x+12}\\\\b=\dfrac{x^2-12^2}{x+12}\\\\b=\dfrac{(x-12)(x+12)}{(x+12)}\\\\=(x-12)\ m\)

So, the width of the rectangle is (x-12) m.

Answer:

6,240

Step-by-step explanation:

You start off with 5200, if she earns 4% each year for the next 5 years, she would earn a total of 20% more than what she had now.

You would multiply 5,200 by 1.20 Which equals the answer (above)

Answer:

Odd

Step-by-step explanation:

The graph is odd because one side of the graph falls to the left and the other falls to the right. They are going in opposite directions.

According to the information, the missing number from the box is number 40.

To find the missing number of the table we must take into account different elements. In particular we must look at the totals and the columns and rows in which the empty space is. Once we identify the totals we can subtract the other values from the total and find the missing number in the table.

According to the above we can infer that the missing number is 40.

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