A rectangular paperboard measuring long and wide has a semicircle cut out of it, as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed? (Use the value for , and do not round your answer. Be sure to include the correct unit in your answer.)

Answer:

x = 60°

y = 60°

Step-by-step explanation:

The three angles of a triangle add up to 180°
In ΔWXY, 60 + 60 + x = 180°
=> 120 + x = 180

=> x = 180 - 120 = 60°

Since lines WZ and XY are parallel, x and y which are alternate interior angles must be equal

So y = x = 60°

Answer:

[(8x+6)=(20+6x) as M is the midpoint

8x-6x=20-6

2x=14

x=7

LN=(8x+6)+(20+6x)

LN= 8(7)+6+20+6(7)

LN= 56+6+20+42

LN= 124

LN =124 units

\(\text{To get the total surface area, all we have to do is multiply } 18 \text{ by } 12, \text{which gets us}\)\($18\cdot12 = \boxed{216\text{ ft}^2}\).

\(\text{So, our answer is } \boxed{216\text{ ft}^2}.\)

Larry needs 216 square feet of carpeting for her rectangular living room.

To find the amount of carpeting Larry needs, we need to calculate the area of her rectangular living room. The area of a rectangle can be found by multiplying its length by its width. In this case, the length of the living room is 18 feet and the width is 12 feet.

So, the area of the living room is:

Area = Length * Width

Area = 18 feet * 12 feet

Area = 216 square feet

Therefore, Larry needs 216 square feet of carpeting for her living room.

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Answer:

0

Step-by-step explanation:

The 2 lines never intersect so there are 0 solutions

Answer:

3

Step-by-step explanation:

4(t +3)=24

4t +12 =24

4t =24 - 12

4t =12

t =12 :4

t =3

Answer:

t = 3

Step-by-step explanation:

Original Equation:

4(t + 3) = 24

Use distributive property

4 x t = 4t

4 x 3 = 12

Your equation:

4t + 12 = 24

Subtract 12 from both sides

4t = 12

Divide both sides by 4

t = 3

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One major difference in the style Shakespeare uses for Lady Macbeth's sleepwalking scene is the use of prose instead of verse. He does this to emphasize her confusion and disorientation, as well as create a sense of tension in the scene.

Shakespeare uses text rather than verse for Lady Macbeth's sleepwalking episode, which is a significant departure from his usual usage of verse. In addition to heightening the tension in the moment, he does this to highlight her confusion and disorientation.

Shakespeare uses prose to represent Lady Macbeth's disturbed mental state and her inability to express her thoughts coherently. In contrast, Macbeth speaks in verse throughout the play, expressing his thoughts in a logical and articulate manner. This contrast serves to further highlight Lady Macbeth's mental state and to illustrate the dramatic change in her character following the murder of Duncan.

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1. The inequality that models this situation is given as follows: 28 + 8x ≤ 80.

2. The solution is x ≤ 6. graphed on the image given at the end of the answer.

3. The meaning is that he can buy at most 6 t-shirts.

4. In this case, the number of t-shirts that he can buy is of at most 3.

The maximum amount that he can spend is of:

$80.

The equation that models his spending is given as follows:

28 + 8x.

As:

Then the inequality is given as follows:

28 + 8x ≤ 80.

The solution is then obtained as follows:

8x ≤ 52

x ≤ 52/8

x ≤ 6.5.

As the number of t-shirts is a countable amount, the solution can also be given as:

x ≤ 6.

Meaning that he can buy at most 6 t-shirts.

Considering the sunglasses, the inequality will be of:

8x ≤ 52 - 21

x ≤ 31/8

x ≤ 3.875.

Meaning that he can then buy at most 3 t-shirts.

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a). We have proved all the given conditions.

b). It is true that condition 3 holds for all regular languages L1 and L2.

(a) Regular languages L1 and L2 can be suggested as follows:

Let \(L_1={0^{(n+1)} | n\geq 0}\)

and

\(L_2={1^{(n+1)} | n\geq 0}\)

We have to prove three conditions:1. L1 ⊈ L2:

The given languages L1 and L2 both are regular but L1 does not contain any string that starts with 1.

Therefore, L1 and L2 are distinct.2. L2  L1:

The given languages L1 and L2 both are regular but L2 does not contain any string that starts with 0.

Therefore, L2 and L1 are distinct.3. (L1 ∪ L2)* = L1* ∪ L2*:

For proving this condition, we need to prove two things:

First, we need to prove that (L1 ∪ L2)* ⊆ L1* ∪ L2*.

It is clear that every string in L1* or L2* belongs to (L1 ∪ L2)*.

Thus, we have L1* ⊆ (L1 ∪ L2)* and L2* ⊆ (L1 ∪ L2)*.

Therefore, L1* ∪ L2* ⊆ (L1 ∪ L2)*.

Second, we need to prove that L1* ∪ L2* ⊆ (L1 ∪ L2)*.

Every string that belongs to L1* or L2* also belongs to (L1 ∪ L2)*.

Thus, we have L1* ∪ L2* ⊆ (L1 ∪ L2)*.

Therefore, (L1 ∪ L2)* = L1* ∪ L2*.

Therefore, we have proved all the given conditions.

(b)It is true that condition 3 holds for all regular languages L1 and L2.

This can be proved by using the fact that the union of regular languages is also a regular language and the Kleene star of a regular language is also a regular language.

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Answer:

If its multiple choice then any number between 7 and 8 but closer the 8 should be the answer. If not, then I don't know

Step-by-step explanation:

92.54/12 = 7.71

The mean price per item is 7.712 $

What is average ?

It is calculated by dividing the sum of the values in a set by their number in order to determine the central or typical value in the set, particularly the mean, median, or mode.

It is given that the total amount spend on grocery store is 92.54$ for purchasing 12 items in total and to find the mean that is average price per item we divide the total amount by number of items :

mean price per item = total amount spend on grocery/ total number of items

                       mean =  92.54$/ 12

                                 = 7.712 $

Therefore, the mean price per item is 7.712 $

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Answer:

The 3rd one

Step-by-step explanation:

Answer:

They are corresponding angles

Step-by-step explanation:

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Answer:

below

Step-by-step explanation:

the perpendicular line bisects the side. so x=√11/2

Answer:

135°

Step-by-step explanation:

You want QRT. So if you look at it you have a straight line, which equals 180°. you already have an angle at 45° so all you do is 180-45 and that equals 135°

Answer:

+/- x over 12

Step-by-step explanation:

The rate of the rowing team in clam water and the rate of current is 8 km/hour and 9 km/hour respectively.

Given information:

Distance traveled in clam water = 16 km

Time Taken = 2 hour

Rate in Clam water = Distance/Time = 16/2 = 8 km/hour

Distance traveled against the current = 18 km

Time Taken = 2 hour

Rate of current = Distance/Time = 18/2 = 9 km/hour

Hence, The rate of the rowing team in clam water and the rate of current is 8 km/hour and 9 km/hour respectively.

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Answer:

hi

Step-by-step explanation:

It take 21.2 minutes longer to fill both the pipe together if both were opened at the same time.

In mathematics, fractions are used to represent proportions/parts of a whole. represent the same part of the whole. The top number is called the numerator and the bottom number is called the denominator. The numerator express the number of equal parts and the denominator defines the total number of equal parts of the whole.

Based on the given condition- formulation is-

1/1/45+1/40

We have to find the common denominator and then we can write the numerators above the common denominator

1/(8/45×8 + 9/40×9)

Now we have to calculate the product

1/(8/360+9/40×9)

1/(8+/360+9/360)

We have to write the numerators over common denominator

1/ 8+9/360

= 1/17/360

Divide a fraction by multiplying it's reciprocal

=360/17

= 21.2 m

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Answer: 1/8 pounds of roasted almonds

Step-by-step explanation:

There are six friends and each of them are to receive and equal piece out of a 3/4 pound of roasted almonds.

The almonds each friend will get will therefore be the 3/4 pack divided by 6:

= 3/4 ÷ 6

= 3/4 * 1/6

= 3/24

= 1/8 pounds of roasted almonds

When dividing by a number, you can instead multiply by the inverse of that number.

There is a 25% chance that you will win the grand prize of $393, a 25% chance of getting your mon and a 50% chance of getting nothing. The expected payoff of a single spin on the wheel for $95 is $61.50.

In this scenario, there are three possible outcomes: winning the grand prize of $393, getting the initial amount of $95 back, or receiving nothing. Each outcome has a specific probability associated with it: 25% chance of winning the grand prize, 25% chance of getting the initial amount back, and 50% chance of getting nothing.

To calculate the expected payoff, we multiply each outcome by its respective probability and sum them up. For the grand prize, the expected payoff is (0.25 * $393) = $98.25. For getting the initial amount back, the expected payoff is (0.25 * $0) = $0. Finally, for receiving nothing, the expected payoff is (0.50 * -$95) = -$47.50.

Adding up the expected payoffs, we get ($98.25 + $0 - $47.50) = $50.75. However, since the question asks for the payoff as the winnings less the wager, we subtract the initial amount of $95 from the expected payoff to get the final answer: $50.75 - $95 = -$44.25. Rounding this to two decimal places, the expected payoff of the spin is -$44.25, which means you can expect to lose $44.25 on average per spin.

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Answer:

x=27

Step-by-step explanation:

x-11=16

add 11 to both sides

x=27

Answer:

-0.25

Step-by-step explanation:

need to find the halfway point (average) between -0.75 and 0.25 (same as 1/4)

To get average, add them together: (-0.75) + (0.25) = -0.5, divide by two since there are two numbers, to get average -0.25

Two or more angles are said to be supplementary if and only if they add up to \(180^{o}\).

Thus the required statements and appropriate reasons are stated below:

Two lines are said to be perpendicular when the measure of the angle between them is a right angle. Thus all right angle is congruent.

Angles are said to be congruent if and only if they have equal measure.

Thus in the given question, it can be deduced that:

                     STATEMENT                             REASONS

1. AC ⊥ BD, <1 ≅ <4                                  Given

2. <BCA = \(90^{o}\), <DCA = \(90^{o}\)                       Definition of perpendicular lines

3. <BCA ≅ <DCA                                      Right angles are congruent

4. <BCA = <1 + <2                                     Angle addition property

5. <DCA = <3 + <4                                    Angle addition property

6. <1 + <2 = <3 + <4                                   Distributive property

7. <1 + <2 = <4 + <3                                    Substitution property

8. <2 ≅ <3                                                 Reflexive property

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There are 342 ways to pick a representative who is either a mathematics major or a computer science major from a college that has 17 mathematics majors and 325 computer science majors.

To determine the number of ways to pick a representative who is either a mathematics major or a computer science major, we need to calculate the sum of the two groups.

The number of ways to pick a mathematics major representative is 17, and the number of ways to pick a computer science major representative is 325.

By adding these two numbers together, we obtain the total number of ways to pick a representative from either group.

Therefore, the total number of ways to pick a representative who is either a mathematics major or a computer science major is 17 + 325 = 342.

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Answer this is so easy im not even gonna answer

Step-by-step explanation:

Given:

Total produce = 80 liters

15% Acid solution and 25% acid solution

Find-:

How many litres of each

Explanation-:

Let

Total 80 litres

eq(2) - 3eq(1) is:

So, the value of "y" is:

So x is 40

Then,

The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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Answer:

The cost of the car is 26 lei and for ball it is 14 lei respectively

Step-by-step explanation:

The computation of the car and the ball is given below:

Given that

3 balls + 4 cars = 146 lei

3 balls + 7 cars = 224 lei

Based on the above information

3 balls = 146 - 4 cars

3 balls = 224-7 cars

Now

146 -  4cars = 224 - 7 cars

7 cars - 4 cars = 224 - 146

3 cars = 78

1 car = 78: 3 = 26

3 balls = 146 - 4 × 26

3 balls = 146-104

3 balls = 42

a ball = 42: 3 = 14

The cost of the car is 26 lei and for ball it is 14 lei respectively

Weight of a 24 square foot, 2 inch thick aluminum plate will be: 720 lbs.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Given:

To find: weight of a 24 square foot, 2 inch thick aluminum plate

Finding:

By unitary method, we get:

Weight of 1 square foot aluminum plate = 15 lbs.

Weight of 24 square foot aluminum plate = 15(24) lbs = 360 lbs.

Again, by unitary method, we get:

Weight of 1 square foot, 1 inch thick aluminum plate = 15 lbs.

Weight of 24 square foot, 1 inch thick aluminum plate = 15(24) lbs = 360 lbs.

Weight of 24 square foot, 2 inch thick aluminum plate = 360(2) lbs = 720 lbs.

Hence, Weight of 24 square foot, 2 inch thick aluminum plate = 720 lbs.

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\(x^2 + 12x=-33 \\ \\ x^2 + 12x+36=3 \\ \\ \boxed{(x+6)^2=3} \\ \\ x+6=\pm \sqrt{3} \\ \\ \boxed{x=-6 \pm \sqrt{3}}\)