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3 years ago

A window is 21 inches wide, and its perimeter is 112 inches. What is the length of the window?

Mathematics

1 answer:

Kazeer [188]3 years ago

8 0

Answer:

The length of the window is 35 inches.

Step-by-step explanation:

Perimeter of an object can be found using the general formula: P = 2W + 2L, where P = perimeter, W = width and L= length. Since both the width and perimeter of the window are given, we can plug these values into the formula to solve for the missing variable 'L': 112 = 2(21) + 2L, or 112 = 42 + 2L. We can then use inverse (opposite) operations to isolate the variable and solve. Whatever we do to one side of the equation, we do to the other. We will start by subtracting 42 from each side: 112 - 42 = 42 - 42 + 2L or 70 = 2L. Next, we divide both sides by 2 to solve for L: 70/2 = 2L/2 or L = 35. So, the final length of the window is 35 inches.

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How do I set up the equation for this?

Masteriza [31]

Answer:

Speed = Distance ÷ Time

time = distance ÷ speed

Step-by-step explanation:

248 ÷ 55 * 60 = 270.54 minutes

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3 years ago

After the drama club sold 100 tickets to a show, it had $300 in profit. After the next show, it had sold a total of 200 tickets

Alinara [238K]

Answer:

Option a : $y-300 = 4(x - 100)$

Step-by-step explanation:

Given :

The drama club sold 100 tickets to a show, it had $300 in profit.

The next show, it had sold a total of 200 tickets and had a total of $700 profit.

To Find : Equation models the total profit, y, based on the number of tickets sold, x

Solution :

For 100 tickets he had $300 in profit .

⇒ ( $x_{1} ,y_{1}$ )=(100,300)

For 200 tickets he had $700 in profit .

⇒ ( $x_{2} ,y_{2}$ )=(200,700)

We will use point slope form i.e.

$y-y_{1} = m(x - x_{1})$ --(A)

Now, to calculate m we will use slope formula :

$m = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }$

$m = \frac{700 -300}{200-100}$

$m =4$

Now, putting values in (A)

$y-300 = 4(x - 100)$

Thus Option a is correct i.e. $y-300 = 4(x - 100)$

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3 years ago

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3 years ago

Two cards are drawn with replacement, one after the other, and the outcomes recorded. What is the probability that at least one

babymother [125]

Answer:

The probability is 0.231

Step-by-step explanation:

In this question, we are tasked with calculating the probability that out of two cards drawn with replacement from a pack of cards , at least one of the two is a face card.

In a standard pack of cards, there are 52 cards.

Now let’s calculate the number of face cards we have.

There are 12 face cards in a pack of cards. There are 4 of each of Jack, Queen or King

The probability of drawing a face card is 12/52 = 3/13

Now, we want to calculate the probability of at least one of the cards drawn are face cards.

Mathematically, what we are needing to calculate is

Probability of drawing a single face card or probability of the two being a face card

Now let’s calculate.

The probability of the first card drawn being a face card is 3/13. The probability of the second card not being a face card will be 1-3/13 = 10/13

The joint probability under this first set of condition will be 3/13 * 10/13 = 30/169

Now, for the second condition, here we are considering that both cards drawn are face cards. What we have is 3/13 * 3/13 = 9/169

Now in probabilities, whenever we are having the statement or, we add the probabilities together

Thus, the probability here would be 30/169 + 9/169 = 39/169 = 3/13

In decimal this will be 0.231

8 0

2 years ago

A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess

maxonik [38]

Answer:

Total weight of the wheat placed on 45th square will be = $1.26\times 10^{6}tons$

Step-by-step explanation:

King rewarded the inventor of chess by giving grain of wheat on every square of the chess board. He places one grain of wheat on first square, 2 on second, 4 on 3rd, 8 on 4th and so on.

In fact he places grains of wheat in a progression S = 1, 2, 4, 8, 16.........n terms where value of n is 64.

We can rewrite the progression as S = 2°, 2, 2², 2³,.........n terms (n = 64)

In a geometric progression we know the nth term = $a(r^{n-1})$