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Roman55 [17]
3 years ago
14

A fraction is less than 1. Choose a counterexample that will prove this conjecture false​

Mathematics
1 answer:
Vesnalui [34]3 years ago
7 0

Answer:

1st option

Step-by-step explanation:

Here we are trying to prove that not all fractions are less than 1. So we have to choose an example in which the fraction is more than 1.

1) \frac{8}{7}  = 1 \frac{1}{7}

This fraction is greater than 1 hence it can prove that the conjecture is false.

2) ½ is lesser than 1 and will not prove that the conjecture is false.

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The Boy Scouts self popcorn Ethan sold 9 small
NARA [144]

Answer:

The cost of 1 small bag of popcorn = $2.95

The cost of 1 large bag of popcorn   = $4.75

Step-by-step explanation:

Here, let us assume the cost of 1 small bag of popcorn = $ m

And,  the cost of 1 large bag of popcorn = $ n

So, the cost of 9 small bag = 9 x ( cost of 1 small bag)  = 9 x (m) = 9 m

and  the cost of 2 large bag = 2 x ( cost of 1 large bag)  = 2 x (n) = 2 n

Also, cost of 9 small + 2 large bag of popcorn sold by  Ethan for   $ 36.05 .

⇒ Total cost of 9 small + 2 large bag of popcorn =  9 m + 2 n

⇒ 9  m +  2 n =  $ 36.05  ..........  (1)

Also, the cost of 5 small bag = 5 x ( cost of 1 small bag)  = 5 m

and  the cost of 7 large bag = 7 x ( cost of 1 large bag)  = 7 n

Also, cost of 5 small + 7 large bag of popcorn sold by  Jack for   $ 48 .

⇒ Total cost of 5 small + 7 large bag of popcorn =  5 m + 7 n

⇒ 5 m +  7 n =  $ 48 ..........  (2)

Now, solving (1) and (2) for the values of m and n , we get

9  m +  2 n =   36.05

5 m +  7 n =  48

Multiply (1) with (-7) and (2) by 2 , add both equation we get:

-63 m - 14 n  + 10 m + 14 n =  -252.35 + 96

or, - 53 m = -156.35

or, m =   2.95

Now, put the value of m in (1), we get:  5 ( 2.95) + 7 n =  48

or, n =  33.25 /7 = 4.75

Hence the cost of 1 small bag of popcorn = $2.95

The cost of 1 large bag  = $4.75

6 0
3 years ago
Read 2 more answers
What is the quotient of x and 8
Naily [24]
It means x should be divided by 8
x/8
6 0
3 years ago
How many times will a 37inch tire rotate on a 5 mile road?
Ilya [14]

circumference of the tire = 37 x Pi = 116.24 inches

1 mile = 5280 feet = 63360 inches

63360/116.24 = 545.08 revolutions per mile

545.08 x 5 = 2725.4 revolutions in 5 miles


 Round answer as needed.

7 0
3 years ago
The temperature was 10°F. It dropped so that the temperature was 0°F. ​___°F represents the change in temperature. Is it 10 or -
yan [13]

Answer:

Change = - 10^{\circ}F

Step-by-step explanation:

Given

Initial = 10^{\circ}F

New = 0^{\circ}F

Required

Determine the change in temperature

This is calculated by:

Change = New - Initial

Substitute values for New and Initial Temperatures

Change = 0^{\circ}F - 10^{\circ}F

Change = - 10^{\circ}F

Hence, the change in temperature is: - 10^{\circ}F

4 0
3 years ago
Si lanzas una moneda justa 4 veces, ¿cuál es la probilidad
Alexeev081 [22]

Answer:

The probability of getting exactly 2 soles is 0.375.

Step-by-step explanation:

The question is:

If you toss a fair coin 4 times, what's the probability that you get exactly 2 soles?

Solution:

A fair coin has two parts.

On tossing a coin once there is 50-50 odds of both the sides.

So, the probability of one side is, <em>p</em> = 0.50.

It is provided that a fair coin is tossed <em>n</em> = 4 times.

The event of any of the sides showing up after the toss are independent of each other.

The random variable <em>X</em> defined as soles, follows a Binomial distribution with parameters <em>n</em> = 4 and <em>p</em> = 0.50.

The probability mass function of <em>X</em> is:

P(X=x)={4\choose x}\ (0.50)^{x}\ (1-0.50)^{4-x};\ x=0,1,2,3,4

Compute the probability of getting exactly 2 soles as follows:

P(X=2)={4\choose 2}\ (0.50)^{2}\ (1-0.50)^{4-2}

                =6\times 0.25\times 0.25\\\\=0.375

Thus, the probability of getting exactly 2 soles is 0.375.

5 0
3 years ago
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