The perimeter of the rectangle is 24 cm. Find the value of x.

Jennifer and Joshua meet for dinner at a restaurant. After dinner, Joshua drives 15 miles south while Jennifer drives 12 miles w

Natasha_Volkova [10]

Answer:

19.209 miles from each other.

Step-by-step explanation:

${a}^{2} + {b}^{2} = {c}^{2}$

Using this we get:

${15}^{2} + {12}^{2} = {x}^{2}$

$225 + 144 = 369 = {x}^{2}$

$\sqrt{369 } = 19.209$

6 0

3 years ago

United Airlines' flights from Denver to Seattle are on time 50 % of the time. Suppose 9 flights are randomly selected, and the n

Ivanshal [37]

Answer:

a) The probability that exactly 4 flights are on time is equal to 0.0313

b) The probability that at most 3 flights are on time is equal to 0.0293

c) The probability that at least 8 flights are on time is equal to 0.00586

Step-by-step explanation:

The question posted is incomplete. This is the complete question:

United Airlines' flights from Denver to Seattle are on time 50 % of the time. Suppose 9 flights are randomly selected, and the number on-time flights is recorded. Round answers to 3 significant figures.

a) The probability that exactly 4 flights are on time is =

b) The probability that at most 3 flights are on time is =

c)The probability that at least 8 flights are on time is =

<h2>Solution to the problem</h2>

a) Probability that exactly 4 flights are on time

Since there are two possible outcomes, being on time or not being on time, whose probabilities do not change, this is a binomial experiment.

The probability of success (being on time) is p = 0.5.

The probability of fail (note being on time) is q = 1 -p = 1 - 0.5 = 0.5.

You need to find the probability of exactly 4 success on 9 trials: X = 4, n = 9.

The general equation to find the probability of x success in n trials is:

$P(X=x)=_nC_x\cdot p^x\cdot (1-p)^{(n-x)}$

Where $_nC_x$ is the number of different combinations of x success in n trials.

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

Hence,

$P(X=4)=_9C_4\cdot (0.5)^4\cdot (0.5)^{5}$

$_9C_4=\frac{4!}{9!(9-4)!}=126$

$P(X=4)=126\cdot (0.5)^4\cdot (0.5)^{5}=0.03125$

b) Probability that at most 3 flights are on time

The probability that at most 3 flights are on time is equal to the probabiity that exactly 0 or exactly 1 or exactly 2 or exactly 3 are on time:

$P(X\leq 3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)$

$P(X=0)=(0.5)^9=0.00195313$ . . . (the probability that all are not on time)

$P(X=1)=_9C_1(0.5)^1(0.5)^8=9(0.5)^1(0.5)^8=0.00390625$

$P(X=2)=_9C_2(0.5)^2(0.5)^7=36(0.5)^2(0.5)^7=0.0078125$

$P(X=3)= _9C_3(0.5)^3(0.5)^6=84(0.5)^3(0.5)^6=0.015625$

$P(X\leq 3)=0.00195313+0.00390625+0.0078125+0.015625=0.02929688\\\\ P(X\leq 3) \approx 0.0293$

c) Probability that at least 8 flights are on time 

That at least 8 flights are on time is the same that at most 1 is not on time.

That is, 1 or 0 flights are not on time.

Then, it is easier to change the successful event to not being on time, so I will change the name of the variable to Y.

$P(Y=0)=_0C_9(0.5)^0(0.5)^9=0.00195313\\ \\ P(Y=1)=_1C_9(0.5)^1(0.5)^8=0.0039065\\ \\ P(Y=0)+P(Y=1)=0.00585938\approx 0.00586$

6 0

4 years ago

What are the solution(s) to the quadratic equation 50 – x2 = 0?

Dmitrij [34]

Answer:

x = ± $5\sqrt{2}$

Step-by-step explanation:

We have been given the quadratic equation;

$50-x^{2}=0$

The first step is to subtract 50 from both sides of the equation;

$50-x^{2}-50=0-50$

$-x^{2}=-50$

Multiplying both sides by -1 yields;

$x^{2}=50$

The final step is to obtain square roots on both sides;

$\sqrt{x^{2} }=\sqrt{50}\\x=+/-\sqrt{50}$

Therefore, x = ± $5\sqrt{2}$

5 0

3 years ago

June made a design with 6 equal tiles. One tile is yellow, 2 tiles are blue, and 3 tiles are purple. What fraction of the tiles

ludmilkaskok [199]

Answer: $\frac{2}{3}$

Step-by-step explanation:

yellow or purple

$\frac{1}{6}$ + $\frac{3}{6}$

= $\frac{4}{6}$

= $\frac{2}{3}$

6 0

3 years ago

Please help me figure out the answer to this I'm a bit confused

scZoUnD [109]

Answer:

y= 1/2x + 1

Step-by-step explanation:

Refer to y=mx+b, m=slope and b= y-intercept

First, you find the slope: you can find the slope by finding the rise over run between two points. Rise= 1, Run=2. The slope is rise/run (rise over run), so the slope would be 1/2 (one half).

Next, find the y-intercept. It is where the line touches the y-axis. Here, it would be 1.

Finally, put these in y=mx+b form:

y=(slope)x+(y-intercept) ---> y= 1/2x + 1

I tried my best to explain everything, I hope you found this helpful!

8 0

3 years ago

Read 2 more answers