Compare the quantities in column A and Columb B,

Tyler selects one card from the three(4,5, and a King), and rolls a number cube. What is the probability that she selects the 5,

Svet_ta [14]

$\frac{1}{3}$ Answer:

2/9

Step-by-step explanation:

given that Tyler selects one card from the three(4,5, and a King), and rolls a number cube.

We find that A the event of selecting one card and B getting a number on rolling a number cube are independent events.

No of cards = 3

Prob of selecting 5 from 3 cards = $P(1,2,3, or 4) = \frac{2}{3}$

When rolling a number cube (assuming fair) there is equally likely for all numbers to appear from 1 to 6

Prob of getting 5 = $\frac{1}{6}$

Prob of getting less than 5 =

Since these two events are independent,

the probability that she selects the 5, and rolls a number less than 5

= Product of probabilities

= $\frac{1}{3}$ * $\frac{2}{3}$

= $\frac{2}{9}$

6 0

3 years ago

Cable Strength: A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the ca

KatRina [158]

Answer:

95% confidence interval for the mean breaking strength of the new steel cable is [763.65 lb , 772.75 lb].

Step-by-step explanation:

We are given that the engineers take a random sample of 45 cables and apply weights to each of them until they break. The mean breaking weight for the 45 cables is 768.2 lb. The standard deviation of the breaking weight for the sample is 15.1 lb.

Since, in the question it is not specified that how much confidence interval has be constructed; so we assume to be constructing of 95% confidence interval.

Firstly, the Pivotal quantity for 95% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean breaking weight = 768.2 lb

s = sample standard deviation = 15.1 lb

n = sample of cables = 45

$\mu$ = population mean breaking strength

Here for constructing 95% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-2.02 < $t_4_4$ < 2.02) = 0.95 {As the critical value of t at 44 degree

of freedom are -2.02 & 2.02 with P = 2.5%}

P(-2.02 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.02) = 0.95

P( $-2.02 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.02 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.02 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.02 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-2.02 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.02 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $768.2-2.02 \times {\frac{15.1}{\sqrt{45} } }$ , $768.2+2.02 \times {\frac{15.1}{\sqrt{45} } }$ ]

= [763.65 lb , 772.75 lb]

Therefore, 95% confidence interval for the mean breaking strength of the new steel cable is [763.65 lb , 772.75 lb].

3 0

3 years ago

20 years from now I will be 4 times as old as my present age what is my present age ?

Shkiper50 [21]

Step-by-step explanation:

your present age = 20/4 =5

4 0

2 years ago

Read 2 more answers

How do I solve this and answer?

kodGreya [7K]

Step-by-step explanation:

at first solve first triangle with Pythagorean solving witch it c²=a²+b²

you have to change a bit so it will be c²-b²=a²

you start with 8 and 10 triangle and then you get line which is in the middle and yo udo just the same with triangle 8 and the solved side and you get x in the second triangle you have to use c²-a²=b²

6 0

3 years ago

Simplify the expression.

geniusboy [140]

Answer:

2 x 2 + 8 + 3 x 2 + 4x - 10

4 + 8 + 8 + 6 + 4x - 10

26 + 4x - 10

20 + 4x

The answer is 20 + 4x

5 0

3 years ago