A four-digit number is formed using four of the eight eight digits 1, 2, 3, 4, 5, 6, 7, 8. No digit can be used once. Find how many different four - digit number can be formed if

There are no restriction

The probability associated with failing to reject the null hypothesis when it is false is called the Type II error rate.

This error rate is the likelihood of incorrectly accepting the null hypothesis when the alternative hypothesis is actually true. It is denoted as beta (β) and is often calculated before conducting a hypothesis test. The probability of making a Type II error depends on several factors, including the sample size, the significance level, and the effect size.
It is important to minimize the Type II error rate in order to increase the power of a hypothesis test, which is the probability of correctly rejecting the null hypothesis when it is false. A higher power means that the test is more likely to detect a true effect and avoid false negative results. However, reducing the Type II error rate usually requires increasing the sample size or relaxing the significance level, which may not be feasible or desirable in some cases. Therefore, it is crucial to carefully consider the trade-offs between the Type II error rate, the power, and the practical implications of the hypothesis test before making any conclusions.

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Answer:

\(9n - 12 \rightarrow \frac{1}{3} (9n - 12) \\ = \frac{3}{3} (3n - 4) \\ l = 3n - 4\)

The perimeter of an equilateral triangle is 9n - 12. Write an expression to represent the length of each side.

\( = \frac{9n-12}{3} \\ = \frac{3(3n - 4)}{3} \\ = 3n - 4\)

The length of each side of the triangle is 3n-4.

Hope it helps!!

The probability of getting 0 lemons in the sample is 0.8836, the probability of getting 1 lemon in the sample is 0.1060, and the probability of getting 2 lemons in the sample is 0.0564.

The probability distribution of x can be calculated as follows:

Given that 6% of all cars produced at a large auto company are lemons. This means that out of every 100 cars manufactured at the company, 6 of them are lemons.Let x denote the number of lemons in this sample. Then, x can take the values 0, 1, or 2. To find the probability of each value of x, we use the binomial probability formula, which is:

P(x) = (nCx) * p^x * (1-p)^(n-x)

where n is the sample size, p is the probability of success, and x is the number of successes.

The sample size is 2 because we are selecting two cars at random from the production line. The probability of success (getting a lemon) is 0.06. Using the binomial probability formula, we get:

P(0) = (2C0) * 0.06^0 * (1-0.06)^(2-0) = 0.8836

P(1) = (2C1) * 0.06^1 * (1-0.06)^(2-1) = 0.1060

P(2) = (2C2) * 0.06^2 * (1-0.06)^(2-2) = 0.0564

Therefore, the probability distribution of x is:X P(x) 0. 0.8836 1. 0.1060 2. 0.0564

In conclusion, the probability of getting 0 lemons in the sample is 0.8836, the probability of getting 1 lemon in the sample is 0.1060, and the probability of getting 2 lemons in the sample is 0.0564.

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Using the given equation, the number of miles the family has already driven would be = 268,258,248 and 234 miles.

The substitution method of solving equation is defined as the method whereby by a known number is substituted into an equation to solve for the unknown.

The values given to be substituted in order to find out the miles the family has already driven are as follows:

where m ;

= 111 = 255- 111 + 124 = 144+124 = 268

121 = 255 - 121 +124 = 134 + 124 = 258

131 = 255 - 131 +124 = 124 + 124 = 248

141 = 255 - 141 + 124 = 114 + 124 = 234

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Answer and Step-by-step explanation:

given

Distance from n to m is 1/5 and

N (-3, -2),  M (1, 1)

In the graph we can see that the distance from M to R is 4,

And the distance between N to R is 3.

So, 1/5 MR = 1/5 (4)

                     =4/5

And, 1/5 NR=1/5 (3)

                      =3/5

By putting these values in N (-3, -2),

We get a point p on MN.

                           -3 + 4/5 = -2.2

                          and -2 + 3/5 = -1.4

Hence p(-2.2, -1.4) is the point on segment mn,

By using multiplication and division, it can be calculated that-

The multiple according to the number 3 = 162

The submultiple according to the number 7 = 7

What is multiplication and division?

Repeated addition is called multiplication. Multiplication is used to find the product of two or more numbers.

Division is the process in which a value of single unit can be calculated from the value of multiple unit.

The number to be divided is called dividend. The  number by which dividend is divided is the divisor. The result obtained is called quotient and the remaining part is the remainder.

This is a problem of multiplication and division.

One segment measures 161 cm

So, to find the multiple according to the number 3, we have to divide 161 by 3

161 \(\div\) 3 = 53.67

Nearest integer of 53.67 is 54

The multiple according to the number 3 = 54 \(\times\) 3 = 162

To find the submultiple according to the number 7, we have to divide 161 by 7

161 \(\div\) 7 = 23

Nearest integer of 23 is 23

The submultiple according to the number 7 = 161 \(\div\) 23 = 7

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the Department of Education receives about 65 percent of the federal funds transferred to state governments.

First, you need to identify what type of information is being asked for in the question. In this case, the question is asking which department receives a certain percentage of federal funds transferred to state governments.

Next, you need to research the answer. You can find the answer to this question by looking at the U.S. Department of Education website or other reliable sources.

The answer is that the Department of Education receives about 65 percent of the federal funds transferred to state governments.

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The probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled is \(0.01667496\).

What is probability?

Probability is defined as the possibility of an event to occur.

An automated weight monitor can detect underfilled cans of beverages with probability \(0.98\)

Thus probability of success will be \(p=0.98\)

So probability of failure \(q=1-p=1-0.98=0.02\)

To find the first wrong detection happening on the tenth trial the first nine trials must be success followed by failure in the tenth trial.

Thus, required probability \(=p^9q^1=(0.98)^9(0.02)=0.01667496\)

Hence the probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled is \(0.01667496\).

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Answer: no

Step-by-step explanation: no I cannot

Answer:

The answer is 99/12 or 8 1/4

Step-by-step explanation:

2 1/4 × 3 2/3

Here,

2 1/4 = 9/4

3 2/3 = 11/3

Now,

9/4 × 11/3 = 99/12 or 8 1/4

Thus, The answer is 99/12 or 8 1/4

-TheUnknownScientist 72

Answer:

2  1/4 x 3  2/3

first, we have to get rid of the fraction, so multiply by the numerator and then add it to the denominator.

9/4 x 11/3

next, multiply them

9x11/4x3

factor the 9, and cancle the numbers that are the same

3x3x11/4x3

3x11/4

=33/4 or 8  1/4

Step-by-step explanation:

In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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Answer:

45

Step-by-step explanation:

x,30,24,16

since,they are in proportion

x/30=24/16

16x=720

x=720÷16

x=45

therefore the value of x is 45.

\( \: \: \: \: \: \: \)

\( = \: \: \: \: r = 5\)

Step-by-step explanation:

\(7 + 4(r + 3) = 9r - 6\)

\(7 + 4r + 12 = 9r - 6\)

\(19 + 4r = 9r - 6\)

\(19 + 9r = - 6\)

\(4r - 9 = - 6 - 19\)

\( - 5r = - 6 - 19\)

\( - 5r = - 25\)

\( = \: \: \: \: r = 5\)

Answer:

C. Yes, there is an outlier at 110. This means that one person's age was 110, which is 25 years older than the next closest age.

Step-by-step explanation:

An outlier is a data point that sticks out like a sore thumb. It's so different from the rest of the data that it makes you wonder if it's a mistake or a miracle. One way to spot an outlier is to use the 1.5IQR rule, where IQR stands for interquartile range. The interquartile range is the gap between the third quartile (Q3) and the first quartile (Q1) of the data. The 1.5IQR rule says that any data point that is more than 1.5*IQR above Q3 or below Q1 is an outlier.

In this case, the first quartile (Q1) is 75, the third quartile (Q3) is 85, and the interquartile range (IQR) is 10. So, any data point that is more than 1.5*10 = 15 above 85 or below 75 is an outlier. The only data point that does this is 110, which is 25 above 85. That means 110 is an outlier.

What does this outlier mean in this situation? It means that one person who came to the senior center that afternoon was way older than the rest of the folks. The average age of the visitors was not changed by this outlier, since it was just one out of 12 data points. But, the outlier does mess up the range and the standard deviation of the data, making them bigger than they would be without the outlier.

Answer:The answer is C

Step-by-step explanation:I did the test.

Answer:

-x² + 5x - 1

Step-by-step explanation:

separate the x², the x, and the constants (numbers without any x).

3x² - 4x² = -x²

2x - -3x = 2x + 3x = 5x

-5 - -4 = -5 + 4 = -1.

we have -x² + 5x - 1

Answer:

1) x+2y=7

+3x-2y=5

2)After adding like terms your answer is

4x-0=12

Divide the left side from the right by 4

and your x= 3.

3)Then add the x value(3) into one of the 2 equations

x+2y=7

3+2y=7, Subtract 3 from the left and right side=7-3=4

2y=4, divide by two and y= 2...

Use the elimination method..Substitute x=3 and y=2 into the second equation and you should come to the same answer...

(a)  The joint PMF of S₁, S₂, ..., Sn is: P(S₁ = s₁, S₂ = s₂, ..., Sₙ = sₙ) =\((1 - p)^{(s_1 + s_2 + ... + s_n) } \times p^n\)

(b)  The random variables S₁,..., Sn are  independent.

(c)  the cumulative distribution function (CDF) of U is:

\(F(u) = (1 - \sum (1 - p)^{(k)} \timesp)^n\)

To compute the joint probability mass function (PMF) of S₁, S₂, ..., Sn, we need to consider the number of failures before each success.

(a) Joint probability mass function (PMF) of S₁, S₂, ..., Sn:

Let's first define the random variable S as the sequence of failures until the first success:

S = (S₁, S₂, ..., Sn)

Now, let's calculate the PMF of S:

P(S = (s₁, s₂, ..., sₙ))

Since the random variables X₁, X₂, ..., Xₙ are independent Bernoulli random variables with success probability p.

The probability of getting s failures before the first success is given by:

\(P(S_1 = s_1) = (1 - p)^{s_1} \times p\)

The probability of getting s₂ additional failures before the second success is:

\(P(S_2 = s_2) = (1 - p)^{s_2} \times p\)

\(P(S_3 = s_3) = (1 - p)^{s_3} \times p\)

And so on, until the probability of getting sₙ additional failures before the nth success:

\(P(S= s) = (1 - p)^{s} \times p\)

Now, since the random variables S₁, S₂, ..., Sn are independent, the joint PMF is the product of the individual probabilities:

P(S = (s₁, s₂, ..., sₙ)) = P(S₁ = s₁) × P(S₂ = s₂)×... × P(Sₙ = sₙ)

Therefore, the joint PMF of S₁, S₂, ..., Sn is:

P(S₁ = s₁, S₂ = s₂, ..., Sₙ = sₙ) =\((1 - p)^{(s_1 + s_2 + ... + s_n) } \times p^n\)

(b)

To determine whether the random variables S₁, S₂, ..., Sn are independent, we need to check if the joint PMF factorizes into the product of the individual PMFs.

Let's consider three random variables, S₁, S₂, and S₃:

P(S₁ = s₁, S₂ = s₂, S₃ = s₃) = P(S₁ = s₁) ×P(S₂ = s₂) × P(S₃ = s₃)

Using the joint PMF calculated in part (a), we can rewrite this as:

\((1 - p)^{(s_1 + s_2 + s_3)} p^3 = (1 - p)^{(s_1)} \times p \times (1 - p)^{(s_2)} \times p \times (1 - p)^{(s_3)}\times p\)

Simplifying, we have:

\((1 - p)^{(s_1 + s_2 + s_3)} p^3 = (1 - p)^{(s_1 + s_2 + s_3)} p^3\)

Since the equation holds true for any values of s₁, s₂, and s₃, we can conclude that the random variables S₁, S₂, and S₃ are indeed independent.

(c)

To compute the CDF of U, we need to determine the probability that U is less than or equal to a given value u.

CDF of U:

F(u) = P(U ≤ u) = 1 - P(U > u)

Since U represents the maximum value among S₁, S₂, ..., Sn, we have:

P(U > u) = P(S₁ > u, S₂ > u, ..., Sn > u)

Using the independence of S₁, S₂, ..., Sn, we can express this probability as:

P(U > u) = P(S₁ > u)×P(S₂ > u) × ...× P(Sn > u)

The probability that a single random variable Si is greater than u (where Si represents the number of failures between the (i-1)th and the ith success) is:

P(Si > u) = 1 - P(Si ≤ u) = 1 - ∑(k=0 to u) P(Si = k)

Using the PMF derived in part (a), we can calculate this probability:

\(P(Si > u) = 1 - \sum (1 - p)^(^k^) \times p\) (k=0 to u)

Finally, substituting this back into the expression for P(U > u), we have:

\(P(U > u) = (1 - \sum (1 - p)^{(k)} \timesp)^n\) (k=0 to u)

Therefore, the cumulative distribution function (CDF) of U is:

\(F(u) = (1 - \sum (1 - p)^{(k)} \timesp)^n\)

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Outlet A sold the greatest number of copies of album x in July and August

The tables of values are given as:

July

Album X Album Y Album Z

Outlet A 14 8 6

Outlet B 7 13 4

Outlet C 2 11 1

August

Album X Album Y Album Z

Outlet A 12 14 10

Outlet B 5 12 8

Outlet C 16 12 7

In July, the total sales of album x are:

Outlet A  = 14

Outlet B = 7

Outlet C = 2

In August, the total sales of album x are:

Outlet A  = 12

Outlet B = 5

Outlet C = 16

Add both sales

A = 14 + 12 = 26

B = 7 + 5 = 12

C = 2 + 16 = 18

26 (in outlet A) is greater than 12 and 18

Hence, outlet A sold the greatest number of copies of album x in July and August

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Answer:

Outlet D

Step-by-step explanation:

they sold 28 of album x

outlet a only sold 26

Answer:

100%+15% = 115%

proportionally:

x - 100%

161 - 115%

x = (161 * 100%) / 115% = 140

Answer:

\(\Large\boxed{140}\)

Step-by-step explanation:

\(\sf Let \ x \ be \ the \ number.\)

\(\sf x \ increased \ by \ 15\% \ is \ 161.\)

\(x \times (1+15\%)=161\)

\(x \times (1+0.15)=161\)

\(x \times (1.15)=161\)

\(\displaystyle \frac{x \times (1.15)}{1.15}=\frac{161}{1.15}\)

\(x=140\)

Yes, you are correct!

8x⁴-6x³+2/2x²+3

= 4x² + -6x³-12x²+2/2x²+3

= 4x² - 3x + -12x²+9x+2/2x²+2

= 4x² - 3x - 6 + 9x+20/2x²+3

Best of Luck!

Answer: 27 students

Step-by-step explanation:

First take 45 + 90 = 135 students total

20% = 0.2

Then take 135 times 0.2 = 27 students

2x + 8 should be right

Answer:

5/6 of a mile

Step-by-step explanation:

1/2+1/3=?

1/2=3/6

1/3=2/6

3/6+2/6=5/6

Answer:

Jamie ran 5 1/4 miles in all

Step-by-step explanation:

Alternating current (AC) is a type of electrical current that changes direction periodically, unlike direct current (DC), which flows in only one direction.

The frequency of AC, or the number of times the current changes direction per second, is measured in Hertz (Hz). In the study of AC, the instantaneous voltage is modeled by the equation e = Emax sin \(2πft\),

where f is the frequency in Hz, Emax is the maximum voltage, and t is the time in seconds.In this equation, the sine function represents the alternating nature of the current, with the peak voltage occurring when sin \(2πft = 1\) and the lowest voltage occurring when sin\(2πft = -1\).

The value of f determines the number of complete cycles per second and is directly proportional to the frequency of the AC. The maximum voltage, Emax, represents the amplitude of the voltage wave and is measured in volts.

The equation \(e = Emax sin 2πft\) is widely used in the study of AC, and it can be used to calculate a variety of properties of AC circuits, such as the peak voltage, root-mean-square voltage, and phase angle.

By understanding the behavior of AC circuits, engineers and scientists can design and optimize electrical systems for a wide range of applications, from power generation and distribution to electronic devices and appliances.

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Answer:

R= {a,b,c}

S = {b, c, d}

T = {c, d, e},

Step-by-step explanation:

R U S U T. ={a,b,c}U{b, c, d}U{c, d, e},={a,b,c,d,e}

The solution is, the finally discounted price is 71.5.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

sale price = 90

15% discount, so, the price = 90* 85%

                                            =76.5

now, after 5 discount, price became = 76.5 - 5

                                                             = 71.5

Hence, The solution is, the finally discounted price is 71.5.

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Answer:

200 times

Step-by-step explanation:

The time taken for the water level in the tank to drop from 3 to 0.5 meters above the bottom cannot be determined without additional information.

To calculate the time taken, we need to know the flow rate or discharge rate of the water from the tank. This information is not provided in the question. The time taken to drain the tank depends on factors such as the diameter of the outlet pipe, the pressure difference, and any restrictions or obstructions in the flow path.

If we assume a known discharge rate, we can use the principles of fluid mechanics to calculate the time. The volume of water that needs to be drained is the difference in the volume of water between 3 meters and 0.5 meters above the bottom of the tank. The flow rate can be determined using the pipe diameter and other relevant factors. Dividing the volume by the flow rate will give us the time taken.

However, since the discharge rate is not given, we cannot perform the calculation and determine the time taken accurately.

Without knowing the discharge rate or additional information about the flow characteristics, it is not possible to calculate the time taken for the water level in the tank to drop from 3 to 0.5 meters above the bottom.

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Answer:

x=-5/3

y=-4/3

Step-by-step explanation:

Given:

x+y=-3

y=2x+2

Substitute y into the first equation

x+2x+2=-3

combine like terms

3x+2=-3

subtract 2 from both sides

3x=-5

divide both sides by 3

x=-5/3

Substitute in x for the second equation:

y=2(-5/3)+2

y= -4/3

Hope this helps! :)

The given expression is of the form y=mx+c. Comparing, we get the slope as 7.

The direction and steepness of a line are represented numerically by the slope or gradient of the line. It provides the ratio of how much y rises when x rises by a particular amount. The general form is therefore y=mx+c, where c represents the y-intercept and m represents the slope. This form gives the slope-intercept form.

Given the expression is  y=7x+3. Comparing this expression with the general form we get, slope or gradient as 7 and y-intercept as 3. Therefore, the required answer is 7.  

The complete question -

What is the gradient of the line y=7x+3?

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