Consider the following sequence: 8748, -2916, 972, -324, … What is the common ratio?

Marge cut 16 pieces of tape for mounting pictures on poster board. Each piece of tape was 3/8 inch long. How much tape did Marge

3241004551 [841]

Hello!

Let's convert 3/8 to a decimal and then multiply the length of each piece of tape by how many pieces Marge used.

To convert a fraction to a decimal, simply divide its numerator by its denominator:

3 ÷ 8 = 0.375

Next, multiply this by the amount of pieces Marge cut.

0.375 × 16 = 6

Therefore, Marge used 6 inches of tape.

8 0

3 years ago

The phone lines to an airline reservation system are occupied 40% of the time. Assume that the events that the lines are occupie

nikitadnepr [17]

Answer:

a) $P(X=3)$

And we can use the probability mass function and we got:

$P(X=3) = (10C3) (0.4)^3 (1-0.4)^{10-3} = 0.215$

b) For this case we want this probability:

$P(X \geq 1)$

and the probability that the one call would be not occupied is 1-0.4=0.6

And if we use the complement rule we got:

$P(X \geq 1)= 1-P(X$

$P(X=0) = (10C0) (0.6)^0 (1-0.6)^{10-0} = 0.000105$

$P(X \geq 1)= 1-P(X$

c) $E(X) = np = 10*0.4 = 4$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

a. What is the probability that for exactly three calls, the lines are occupied?

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=10, p=0.4)$

The probability mass function for the Binomial distribution is given as:

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

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And for this case we want this probability:

$P(X=3)$

And we can use the probability mass function and we got:

$P(X=3) = (10C3) (0.4)^3 (1-0.4)^{10-3} = 0.215$

b. What is the probability that for at least one call, the lines are not occupied?

For this case we want this probability:

$P(X \geq 1)$

and the probability that the one call would be not occupied is 1-0.4=0.6

And if we use the complement rule we got:

$P(X \geq 1)= 1-P(X$

$P(X=0) = (10C0) (0.6)^0 (1-0.6)^{10-0} = 0.000105$

$P(X \geq 1)= 1-P(X$

c. What is the expected number of calls in which the lines are all occupied?

For this case the expected value is given by:

$E(X) = np = 10*0.4 = 4$

8 0

3 years ago

Brandon wants to buy a new bike. The model he likes is on sale for 15% off its original price. His parents agree to pay for $50

Leno4ka [110]

Answer:

0.85x - $50

Step-by-step explanation:

Given that :

Brandon wants to buy a new bike. The model he likes is on sale for 15% off its original price. His parents agree to pay for $50 of the cost. If the original cost of the bike is x dollars, which of the expressions below represent the amount Brandon has to pay

Discount on price = 15%

Amount parents agreed to pay = $50

Cost of bike = x

Discount on bike = 0.15x

Cost after discount is removed = (x - 0.15x) = 0.85x

Parent pays $50 of cost price, amount Brandon will have to pay equals :

(0.85x - $50)

3 0

3 years ago

Solve for y: 6x-2y=-8

Stella [2.4K]

6x-2y=-8
-2y =-6x-8
y = 3x+4

y= 3x+4

4 0

4 years ago

Read 2 more answers

-X-6 constant. coefficient: variable

stepan [7]

Answer:

constant: -6

Coefficient: -1

Variable: x

Step-by-step explanation:

5 0

3 years ago