Compare the decimals 14.40 and 14.04.

The tickets for a dance recital cost $5.00 for adults and $2.00 for children. If the total number of tickets sold was 295 and th

dem82 [27]

To solve, you would need to make two equations and substitute one in for the other. Let a = # of adults, and c = # of children

5a + 2c = 1,220
a + c = 295

a + c = 295
-c -c
a = 295 - c

5(295 - c) + 2c = 1,220
1,475 - 5c + 2c = 1,220
1,475 - 3c = 1,220

1,475 - 3c = 1,220
-1,475 -1,475
-3c = -255

-3c/-3 = -255/-3
c = 85

a + c = 295
a + 85 = 295
-85 -85
a = 210

210 adults attended the dance recital

Hope this helps!

6 0

3 years ago

A rectangular site measures 125 feet (frontage) by 256 feet (depth), of which 26 feet is in the public right of way. what is the

alexandr1967 [171]

Answer:

32,000 square feet gross area and 28,750 square feet net area

Step-by-step explanation:

Given a rectangular site measures 125 feet (frontage) by 256 feet (depth), of which 26 feet is in the public right of way. We have to find the the gross and net site area.

As, 26 feet width is in the public right of way which excluded in the net area but included in gross area.

For gross area,

Length=125 feet

Width=256 feet

$Area=Length\times width=125\times 256=32000 square feet$

For net area,

Length=125 feet

Width=256-26=230 feet

$Area=Length\times width=125\times 230=28750 square feet$

Hence, last option is correct.

The answer is: 32,000 square feet gross area and 28,750 square feet net area

6 0

3 years ago

We have two fair three-sided dice, indexed by i = 1, 2. Each die has sides labeled 1, 2, and 3. We roll the two dice independent

Bogdan [553]

Answer:

(a) P(X = 0) = 1/3

(b) P(X = 1) = 2/9

(c) P(X = −2) = 1/9

(d) P(X = 3) = 0

(a) P(Y = 0) = 0

(b) P(Y = 1) = 1/3

(c) P(Y = 2) = 1/3

Step-by-step explanation:

Given:

- Two 3-sided fair die.

- Random Variable X_1 denotes the number you get for rolling 1st die.

- Random Variable X_2 denotes the number you get for rolling 2nd die.

- Random Variable X = X_2 - X_1.

Solution:

- First we will develop a probability distribution of X such that it is defined by the difference of second and first roll of die.

- Possible outcomes of X : { - 2 , -1 , 0 ,1 , 2 }

- The corresponding probabilities for each outcome are:

( X = -2 ): { X_2 = 1 , X_1 = 3 }

P ( X = -2 ): P ( X_2 = 1 ) * P ( X_1 = 3 )

: ( 1 / 3 ) * ( 1 / 3 )

: ( 1 / 9 )

( X = -1 ): { X_2 = 1 , X_1 = 2 } + { X_2 = 2 , X_1 = 3 }

P ( X = -1 ): P ( X_2 = 1 ) * P ( X_1 = 3 ) + P ( X_2 = 2 ) * P ( X_1 = 3)

: ( 1 / 3 ) * ( 1 / 3 ) + ( 1 / 3 ) * ( 1 / 3 )

: ( 2 / 9 )

( X = 0 ): { X_2 = 1 , X_1 = 1 } + { X_2 = 2 , X_1 = 2 } + { X_2 = 3 , X_1 = 3 }

P ( X = -1 ):P ( X_2 = 1 )*P ( X_1 = 1 )+P( X_2 = 2 )*P ( X_1 = 2)+P( X_2 = 3 )*P ( X_1 = 3)

: ( 1 / 3 ) * ( 1 / 3 ) + ( 1 / 3 ) * ( 1 / 3 ) + ( 1 / 3 ) * ( 1 / 3 )

: ( 3 / 9 ) = ( 1 / 3 )

( X = 1 ): { X_2 = 2 , X_1 = 1 } + { X_2 = 3 , X_1 = 2 }

P ( X = 1 ): P ( X_2 = 2 ) * P ( X_1 = 1 ) + P ( X_2 = 3 ) * P ( X_1 = 2)

: ( 1 / 3 ) * ( 1 / 3 ) + ( 1 / 3 ) * ( 1 / 3 )

: ( 2 / 9 )

( X = 2 ): { X_2 = 1 , X_1 = 3 }

P ( X = 2 ): P ( X_2 = 3 ) * P ( X_1 = 1 )

: ( 1 / 3 ) * ( 1 / 3 )

: ( 1 / 9 )

- The distribution Y = X_2,

P(Y=0) = 0

P(Y=1) = 1/3

P(Y=2) = 1/ 3

- The probability for each number of 3 sided die is same = 1 / 3.

7 0

3 years ago

Suppose there is a 13.9 % probability that a randomly selected person aged 40 years or older is a jogger. In addition, there is

Blababa [14]

Answer:

There is a 2.17% probability that a randomly selected person aged 40 years or older is male and jogs.

It would be unusual to randomly select a person aged 40 years or older who is male and jogs.

Step-by-step explanation:

We have these following probabilities.

A 13.9% probability that a randomly selected person aged 40 years or older is a jogger, so $P(A) = 0.13$ .

In addition, there is a 15.6% probability that a randomly selected person aged 40 years or older is male comma given that he or she jogs. I am going to say that P(B) is the probability that is a male. $P(B/A)$ is the probability that the person is a male, given that he/she jogs. So $P(B/A) = 0.156$

The Bayes theorem states that:

$P(B/A) = \frac{P(A \cap B)}{P(A)}$

In which $P(A \cap B)$ is the probability that the person does both thigs, so, in this problem, the probability that a randomly selected person aged 40 years or older is male and jogs.

So

$P(A \cap B) = P(A).P(B/A) = 0.156*0.139 = 0.217$

There is a 2.17% probability that a randomly selected person aged 40 years or older is male and jogs.

A probability is unusual when it is smaller than 5%.

So it would be unusual to randomly select a person aged 40 years or older who is male and jogs.

4 0

3 years ago

What is the reciprocal of 7/12

Artemon [7]

The reciprocal is just when you flip the number that you're given. the reciprocal of 7/12 is 12/7

6 0

3 years ago