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3 years ago

12. The table shows the number of people who attended a

Mathematics

1 answer:

Nataly_w [17]3 years ago

7 0

Answer:

1. See the graph attached

2. 13,400 thousands people will attend the new movie on the 8th day, if the pattern shown in the graph continues.

Explanation:

The <em>table </em>that shows the number of people who attend a new movie ofver teh course of a week is:

Day Attendance (thousands)

1 12,200

3 12,600

5 13,000

7 13,400

8 x

The <em>graph</em> showing that pattern is attached.

It is a discrete graph because days can take only positive integer values.

You can see that the relation is linear and can calculate the change in the number of people every two days by subracting any two consecutive pairs of data:

12,600 - 12,200 = 400

13,000 - 12,600 = 400

13,400 - 13,000 = 400

Hence, every two days the increase in the number of people is 400 thousands.

For one day the increase is: 400 thousands / 2 days = 200 thousands/day.

Since you know the attendance for the day 7, you can calculate the attendance for the day 8 adding 200 thousands to 13,400:

13,400 thousands + 200 thousands = 13,600 thousands.

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3 coffees and 4 donuts cost $10.05. In the same cafeteria, 5 coffees and 7 donuts cost $17.15. How much do you have to pay for 4

MakcuM [25]

Answer

You need to pay $14.20 to get 4 coffees and 6 donuts.

Explanation

Let's say that the price of one coffee and x and the price of one donut is y.

In the first instance, 3x+4y=10.05.

In the second instance, 5x+7y=17.15.

You can use these equations to find the value of a coffee and the value of a donut.

We can find x and y using elimination. To do this, you should add or subtract one equation from another to "get rid" of a variable (I'll "get rid" of x). We can't just add or subtract the equations right now, since that wouldn't lead to 0x.

Multiply the first equation by 5, and the second equation by 3. After this, both equations will have 15x. Make sure to multiply each term by 5 and 3.

15x+20y=50.25. This means that 15 coffees and 20 donuts is $50.25.

15x+21y=51.45. This means that 15 coffees and 21 donuts is 51.45.

Now since there are an equal number of coffees, we can subtract these equations.

(15x+21y=51.45)-(15x+20y=50.25) equals y=1.20 (a donut costs $1.20).

Plug the price of the donut into y to find x; 3x+4(1.20)=10.05. The value of x is 1.75. The price of a coffee is 1.75.

You can multiply 1.75 by 4 to find the price of 4 coffees and 1.20 by 6 to find the price of 6 donuts.

1.75*4 is 7.00 and 1.20*6 is 7.20.

You can add those to find the total price; 7.00+7.20=14.20.

5 0

3 years ago

To avoid detection at customs, a traveler places 6 narcotic tablets in a bottle containing 9 vitamin tablets that are similar in

lukranit [14]

Answer: $\dfrac{26}{27}$

Step-by-step explanation:

Given : To avoid detection at customs, a traveler places 6 narcotic tablets in a bottle containing 9 vitamin tablets that are similar in appearance.

Proportion of success : $p=\dfrac{6}{9}=\dfrac{2}{3}$

Sample size taken by customs oﬃcial : n= 3

Let x be a binomial variable that represents the tablets in the bottle.

Using Binomial probability formula :-

$P(X=x)=^nC_xp^x(1-p)^{n-x}$

The probability that the traveler will be arrested for illegal possession of narcotics = $P(x\geq1)=1-P(x=0)$

$1-^3C_0(\dfrac{2}{3})^0(1-\dfrac{2}{3})^3\\\\=1-(1)(1)(\dfrac{1}{3})^3\ [\becuase ^nC_0=1]\\\\=1-\dfrac{1}{27}=\dfrac{26}{27}$

Hence, the probability that the traveler will be arrested for illegal possession of narcotics = $\dfrac{26}{27}$

8 0

3 years ago

Work out the percentage change to 2 decimal places when a price of £57.99 is decreased to £49.99.

IRISSAK [1]

Answer:

Percentage change in price = 13.80%

Step-by-step explanation:

Given that:

Original price = £57.99

Decreased price = £49.99

Difference = Original price - Decreased price

Difference = 57.99 - 49.99

Difference = £8.00

Percent change = $\frac{Difference}{Original\ price}100$

Percent change = $\frac{8.00}{57.99}*100$

Percent change in price = 13.80%

Hence,

Percentage change = 13.80%

5 0

3 years ago

Find sin 2x,cos2x and tan2x,if tanx=-(3)/(4)and x terminates in quadrant IV

Montano1993 [528]

Answer:PLEASE HELP ME

Step-by-step explanation:

here can you guys please help me with this question.

I have been asking help from so many people but no one is nice enough to give it so im hoping that anyone over here can help me. this is the problem

Carl is standing at the base of a zip line which is 400 ft away from the base of the building that is connected to the top of a building. Standing 5.5 ft tall, he looks up to the top of the building at an angle of elevation of 25 degrees. A weight is released and travels down the zip line to his feet. How far did the weight travel? Round to nearest 10th of a foot and do not use units in your answer.

Please show work

7 0

2 years ago

Marco purchased a large box of comic books for $300. He gave 15 of the comic books to his brother and then sold the rest on an i

Yuri [45]

Answer: There are 75 books.

Price of each book = $4.

Step-by-step explanation:

Let x = Number of books in the box.

Then as per given,

Cost of x books = $300

Cost of one book = $\$(\dfrac{300}x)$

Books left after giving 15 of them = x-15

Selling price of (x-15) books= $330

Selling price of one book = $\$(\dfrac{330}{x-15})$

Profit on each book= $1.50

Profit = selling price - cost price

$\Rightarrow 1.50=\dfrac{330}{x-15}-\dfrac{300}{x}\\\\\Rightarrow\ 1.50=\dfrac{330(x)-300(x-15)}{x(x-15)}\\\\\Rightarrow\ 1.50=\dfrac{330x-300x+4500}{x^2-15x}\\\\\Rightarrow\ 1.50(x^2-15x)=30x+4500\\\\\Rightarrow\ 1.50x^2-22.5x=30x+4500\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ x^2-25x-3000=0\ \ [\text{divide by 1.5}]$

$\Rightarrow (x+40)(x-75)=0\\\\\Rightarrow\ x=-40,75$

Number of books cannot be negative.

So, there are 75 books.

Price of each book = $\dfrac{300}{75}=\$4$

So price of each book = $4.

5 0

3 years ago