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2 years ago

How many four-character passwords can be formed using the characters A, B, C, 1, 2 if the characters can be repeated

Mathematics

1 answer:

olga55 [171]2 years ago

7 0

<h3>Answer: 625</h3>

Work Shown:

The set {A,B,C,1,2} has five items. There are four slots to fill.

So we have 5^4 = 5*5*5*5 = 625 different possible passwords where the characters can be repeated.

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• A researcher claims that less than 40% of U.S. cell phone owners use their phone for most of their online browsing. In a rando

antiseptic1488 [7]

Answer:

We failed to reject H₀

Z > -1.645

-1.84 > -1.645

We failed to reject H₀

p > α

0.03 > 0.01

We do not have significant evidence at a 1% significance level to claim that less than 40% of U.S. cell phone owners use their phones for most of their online browsing.

Step-by-step explanation:

Set up hypotheses:

Null hypotheses = H₀: p = 0.40

Alternate hypotheses = H₁: p < 0.40

Determine the level of significance and Z-score:

Given level of significance = 1% = 0.01

Since it is a lower tailed test,

Z-score = -2.33 (lower tailed)

Determine type of test:

Since the alternate hypothesis states that less than 40% of U.S. cell phone owners use their phone for most of their online browsing, therefore we will use a lower tailed test.

Select the test statistic:

Since the sample size is quite large (n > 30) therefore, we will use Z-distribution.

Set up decision rule:

Since it is a lower tailed test, using a Z statistic at a significance level of 1%

We Reject H₀ if Z < -1.645

We Reject H₀ if p ≤ α

Compute the test statistic:

$Z = \frac{\hat{p} - p}{ \sqrt{\frac{p(1-p)}{n} }}$

$Z = \frac{0.31 - 0.40}{ \sqrt{\frac{0.40(1-0.40)}{100} }}$

$Z = \frac{- 0.09}{ 0.048989 }$

$Z = - 1.84$

From the z-table, the p-value corresponding to the test statistic -1.84 is

p = 0.03288

Conclusion:

We failed to reject H₀

Z > -1.645

-1.84 > -1.645

We failed to reject H₀

p > α

0.03 > 0.01

We do not have significant evidence at a 1% significance level to claim that less than 40% of U.S. cell phone owners use their phones for most of their online browsing.

8 0

2 years ago

. A 25-ft ladder is leaning against a wall. If we push the ladder toward the wall at a rate of 1 ft/sec, and the bottom of the l

Vlada [557]

Answer:

0.75 feet per second.

Step-by-step explanation:

Please find the attachment.

We have been given that a 25-ft ladder is leaning against a wall. We can see from the attachment that ladder forms a right triangle with respect to wall and ground.

So we can set a Pythagoras theorem as:

$x^2+y^2=25^2$

$x^2+y^2=625$

Now, we need to find the derivative of above equation with respect to time.

$2x\cdot \frac{dx}{dt}+2y\cdot \frac{dy}{dt}=0$

Since the adder is moving toward the wall at a rate of 1 ft/sec for 5 sec, so x after 5 seconds would be: $20-1(5)=20-5=15$

Let us solve for y using Pythagoras theorem.

$y^2+15^2=25^2$

$y^2+225=625$

$y^2=625-225$

$y^2=400$

Take positive square root:

$\sqrt{y^2}=\sqrt{400}$

$y=20$

Upon substituting our given values in derivative equation, we will get:

$2x\cdot \frac{dx}{dt}+2y\cdot \frac{dy}{dt}=0$

$2(15)\cdot(-1)+2(20)\cdot \frac{dy}{dt}=0$

$-30+40\cdot \frac{dy}{dt}=0$

$40\cdot \frac{dy}{dt}=30$

$\frac{dy}{dt}=\frac{30}{40}$

$\frac{dy}{dt}=0.75$

Therefore, the ladder is moving up at a rate of 0.75 feet per second.

3 0

2 years ago

Jason collects baseball cards. He bought one card for $25. Its current value is represented by the expression 25(1.02)t, where t

ki77a [65]

Is Jason’s baseball card going up by 2% every year for example

Jason’s baseball card after 1 year is
25×(1.02)^(1)=25.5
It increased by 0.5 in amount after one year

4 0

2 years ago

Nine new employees, two of whom are married to each other, are to be assigned nine desks that are lined up in a row. If the assi

meriva

Answer:

The probability is 0.8

Step-by-step explanation:

The key to answering this question is considering the fact that the two married employees be treated as a single unit.

Now what this means is that we would be having 8 desks to assign.

Mathematically, the number of ways to assign 8 desks to 8 employees is equal to 8!

Now, the number of ways the couple can interchange their desks is just 2 ways

Thus, the number of ways to assign desks such that the couple has adjacent desks is 2(8!)

The number of ways to assign desks among all six employees randomly is 9!

Thus, the probability that the couple will have adjacent desks would be ;

2(8!)/9! = 2/9

This means that the probability that the couple have non adjacent desks is 1-2/9 = 7/9 = 0.77778

Which is 0.8 to the nearest tenth of a percent

4 0

2 years ago

A 40-meter-long blade of a wind turbine makes one complete revolution in 10 seconds. To the nearest tenth, the linear velocity o

Pani-rosa [81]

The distance the tip travels is
2π·(40 m) = 80π m

Then its speed is
(80π m)/(10 s) = 8π m/2 ≈ 25.1 m/s

7 0

2 years ago

Read 2 more answers