Brian bought a pair of jeans that was on sale for one third of its original price. Including the 3.76 sales tax, he paid $29.17. What was the original price of the jeans?

Emma will need to invite 32 guests for both venues to cost the same amount, which will be $3,394 in total for either venue.

Emma is comparing the cost of two venues for her surprise party and wants to find out after how many guests the costs for both the venues will be the same, as well as the total cost at that point. To solve this, we can set up an equation where the total cost for both venues is equal, with x representing the number of guests.

Let's denote Hall A's cost with an initial reservation fee of $862 plus $76 per dinner as A(x), and Hall B's cost with an initial reservation fee of $894 plus $75 per dinner as B(x).

Therefore, we can write the following equation for the point where both costs are the same:

A(x) = B(x)

862 + 76x = 894 + 75x

After solving this equation for x, we find:

76x - 75x = 894 - 862

x = 32

So, Emma will have to invite 32 guests for the cost of both venues to be the same. At this number of guests, the total cost for either venue can be calculated:

Total cost for Hall A: 862 + 76(32) = $3,394

Total cost for Hall B: 894 + 75(32) = $3,394

Both venues will cost her $3,394 when hosting 32 guests.

The required inequality is -6n - 5 ≥ 8. Option (C) is correct.

Inequality shows relation between two expression which are not equal to each others.

Given that,

When 5 is subtracted from the product of number n and -6 is at least 8.

The product of number n and - 6  = -6n

Subtract 5 from product of number n and -6 = -6n - 5

To write the inequality that shows that 5 less than -6n is at least 8,

Implies that, -6n - 5 can be grater than or equal to 8.

The inequality can be expressed as,

-6n - 5 ≥ 8

Hence, option (C) is correct.

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Answer

The owner lose is $100 .

Reason

As given

A man comes into a store and steals $100 from the register without the owner knowledge.

Comes back and buys $70 worth of stuff and the owner gives him $30 in change.

i.e First man steals $100  than give back to owner when he buys  $70 worth of stuff and  the owner gives him $30 in change.

Therefore the total owner lose is the sum of  $70 worth of stuff and  $30 in change.

Total owner lose = $70 + $30

                            = $100

Therefore the owner lose be  $100 .

Hence proved

Answer:

The total cost is $58.14.

Step-by-step explanation:

Given : A pair of shoes for $57 with a sales tax of 2%.

To find : What are two ways to find the total cost ?

Solution :

Cost price CP=$57

Sales tax S=2%

One way :

The total cost is given by,

[tex]C=CP+2\%\text{ of } CP[/tex]

[tex]C=57+\frac{2}{100}\times 57[/tex]

[tex]C=57+1.14[/tex]

[tex]C=58.14[/tex]

The total cost is $58.14.

Another way :

Using selling price formula,

[tex]SP=\frac{100+S\%}{100}\times CP[/tex]

[tex]SP=\frac{100+2}{100}\times 57[/tex]

[tex]SP=1.02\times 57[/tex]

[tex]SP=58.14[/tex]

The total cost is $58.14.

Option C) is the correct statement as the Theoretical Probability of the coin landing on tails is 1/2

Theoretical probability is the ratio of favorable outcomes to the total number of outcomes.

Experimental probability or empirical probability is based on a particular experiment using the same formula.

Experimental probability of getting heads

= Frequency of heads/Total observations

= 35/100 = 7/20

Experimental probability of getting tails

= Frequency of tails/Total observations

= 65/100 = 13/20

The theoretical probability of getting a heads

= Favorable outcomes of getting heads/Total possible outcomes

= 1/2

The theoretical probability of getting a tails

= Favorable outcomes of getting tails/Total possible outcomes

= 1/2

When we cross-check with the options,

A) Incorrect, as the Theoretical Probability of the coin landing on heads = 1/2

B) Incorrect, as the Experimental Probability of the coin landing on tails = 13/20

C) Correct, as the Theoretical Probability of the coin landing on tails = 1/2

D) Incorrect, as the Experimental Probability of the coin landing on heads = 7/20

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The number of tiles along the edge of a square room with a hundred square tiles is 10.

First, we need to recognize that a square room means all sides are of equal length. Since the room is tiled with square tiles throughout, the number of tiles along one edge will be the same as the other.

If there are a hundred square tiles in total, this represents the area of the square which is the product of the lengths of its sides (since the area of a square is given by side x side).

To find the length of a side, we take the square root of the total number of tiles. In this case, the square root of 100 is 10.

Therefore, there are 10 tiles along the edge of the square room.

To find the amount of milk a cow can produce in 500 days at the rate of 2000 gallons every 365 days, you can set up a proportion and solve for x.

To find the amount of milk a cow can produce in 500 days at the rate of 2000 gallons every 365 days, we can set up a proportion. The correct proportion to use is:

365 days / 2000 gallons = 500 days / x gallons

To solve for x, we need to cross multiply and then divide:

365 * x = 2000 * 500

x = (2000 * 500) / 365

So the correct proportion to find x is 365 days / 2000 gallons = 500 days / x gallons.

The formula for dividing fractions.

= a/b ÷ c/d

= a/b x d/c

= (axd) / (bxc)

The 1/2 ÷ 3 situation that represents can be:

Half of the cake is left and the leftover cake is divided among 3 people.

The solution of 1/2 ÷ 3 is 1/6

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

1/2 ÷ 3

This expression situation can be represented as:

Half of the cake is left and the leftover cake is divided among 3 people.

The formula for dividing fractions.

= a/b ÷ c/d

= a/b x d/c

= (axd) / (bxc)

The solution for 1/2 ÷ 3.

= (1/2) / 3

= 1/(2x3)

= 1/6

Thus,

The 1/2 ÷ 3 situation that represents can be:

Half of the cake is left and the leftover cake is divided among 3 people.

The solution of 1/2 ÷ 3 is 1/6

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To solve 5x13 using the distributive property, we can distribute 5 to both terms inside the parentheses and simplify the expression.

Using the distributive property, we can solve 5x13 as:

5x13 = (5 x 10) + (5 x 3)

= 50 + 15 = 65.

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In the given equation P-2+qp, when you substitute p=7 and q=4, the final result calculated is 33.

The given equation is P-2+qp. In this expression, we are to use p=7, and q=4. Substituting these values in our equation, it becomes: 7 - 2 + 7 * 4. Now, let's simplify it further step by step. First, calculate the multiplication: 7 * 4 = 28. So, the expression becomes 7 - 2 + 28. Now, perform the addition and subtraction: 7 + 28 = 35; and then 35 - 2 equates to 33. So, when you plug p = 7 and q = 4 into the equation P-2+qp, the result is 33.

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"Пятерку я получил не на третьем уроке" - ложь. Значит, пятерку Вася получил на третьем уроке.

"Четверку получил на втором" - тоже ложь. Значит, четверку Вася мог получить на перовом или на третьем уроке.

Выше мы выяснили, что на третьем уроке он получил пятерку, следовательно, четверку Вася получил на первом уроке.

Свободны остались только второй урок и тройка.

Ответ: Вася получил тройку на втором уроке.