Calculate (-3 5/6)

Formulate a conjecture about how the next step in this pattern would be found: 4,16,36, 64,100

scoray [572]

Each number is the square of 2*the number, in other words
(1+1)²=4
(2+2)²=16
(3+3)²=36
(4+4)²=64
etc...

5 0

4 years ago

An automobile manufacturer has discovered that 20% of all the transmissions it installed in a particular style of truck are defe

Hatshy [7]

Answer:

0.148 = 14.8% probability that they will need to order at least one more new transmission

Step-by-step explanation:

For each transmission, there are only two possible outcomes. Either it is defective after a year of use, or it is not. The probability of a transmission being defective is independent of any other transmission. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

20% of all the transmissions it installed in a particular style of truck are defective after a year of use.

This means that $p = 0.2$

Sold seven trucks:

This means that $n = 7$

It has two of the new transmissions in stock. What is the probability that they will need to order at least one more new transmission?

This is the probability that at least 3 are defective, that is:

$P(X \geq 3) = 1 - P(X < 3)$

In which

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{7,0}.(0.2)^{0}.(0.8)^{7} = 0.2097$

$P(X = 1) = C_{7,1}.(0.2)^{1}.(0.8)^{6} = 0.3670$

$P(X = 2) = C_{7,2}.(0.2)^{2}.(0.8)^{5} = 0.2753$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2097 + 0.3670 + 0.2753 = 0.852$

$P(X \geq 3) = 1 - P(X < 3) = 1 - 0.852 = 0.148$

0.148 = 14.8% probability that they will need to order at least one more new transmission

6 0

3 years ago

The prism shown has a volume of 798 cm3.

a_sh-v [17]

Answer:

10.5 cm

Step-by-step explanation:

Volume = base area × height

798 = (9.5 × 8) × height

height = 798/76

height = 10.5

4 0

3 years ago

The equation y = 2x + 1 is a function rule. x y 0 1 2 3

Nimfa-mama [501]

Answer:

when you multypluie uwqhejqw

Step-by-step explanation:

qwveqeqweqvqeqve

8 0

3 years ago

Write an equation of The line that passes through the given point and is parallel to the given line (4;5);y=-3/2x+3

mojhsa [17]

9514 1404 393

Answer:

y = -3/2x +11

Step-by-step explanation:

The slope of the parallel line is the same as the slope of the given line, so ...

m = -3/2

The y-intercept of the parallel line can be found from ...

b = y -mx

b = 5 -(-3/2)(4) = 11

So, the desired equation is ...

y = mx +b

y = -3/2x + 11

_____

Additional comment

Since you know the slope and a point on the desired line, you can write down the equation directly using the point-slope form. No additional math is required.

y -5 = -3/2(x -4)

6 0

3 years ago

Calculate (-3 5/6) - 4 1/2