Determine whether the following problem involves a permutation or combination.​ (It is not necessary to solve the​ problem.)
How many different ​-letter passwords can be formed from the letters ​S, T​, U​, ​W, X​, Y​, and Z if no repetition of letters is​ allowed?

The problem involves (combination or permiation) because the (order or number) of letters selected (does or does not) matter.

Answer:

The company should use a mean of 12.37 ounces.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The distribution for the amount of beer dispensed by the machine follows a normal distribution with a standard deviation of 0.17 ounce.

This means that [tex]\sigma = 0.17[/tex]

The company can control the mean amount of beer dispensed by the machine. What value of the mean should the company use if it wants to guarantee that 98.5% of the bottles contain at least 12 ounces (the amount on the label)?

This is [tex]\mu[/tex], considering that when [tex]X = 12[/tex], Z has a p-value of [tex]1 - 0.985 = 0.015[/tex], so when [tex]X = 12, Z = -2.17[/tex].

Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-2.17 = \frac{12 - \mu}{0.17}[/tex]

[tex]12 - \mu = -2.17*0.17[/tex]

[tex]\mu = 12 + 2.17*0.17[/tex]

[tex]\mu = 12.37[/tex]

The company should use a mean of 12.37 ounces.

Answer:

Test Statistic = 10

Critical Value = 9.488

Step-by-step explanation:

Given :

Grade A _ B _ C _ D _ F

_____14 _ 18 _32_ 20_16

H0 : distribution of grade is uniform

H1 : Distribution of grade is not uniform

Using the Chisquare statistic :

χ² = (observed - Expected)² / Expected

The expected value :

(14+18+32+20+16) / 5 = 20

χ² = (14-20)^2 / 20 + (18-20)^2 / 20 + (32-20)^2 / 20 + (20-20)^2 / 20 + (16-20)^2 / 20

χ² statistic = 10

The χ² critical at df = (n - 1) = 5 - 1 = 4

χ² Critical(10, 4) = 9.488

Answer:

n ≥  3

Step-by-step explanation:

Applying the remainder term in evaluating the minimum order of the Taylor polynomial

absolute error ≤ 10^-2

[tex]\sqrt{1.06}[/tex]

∴ n ≥   ?

The remainder term is the leftover term after computation ( dividing one polynomial with another )

attached below is the detailed solution

The minimum order of the Taylor polynomial, n≥3

Taylor polynomial is a series of functions that has an infinite sum of terms that are expressed in terms of the function's derivatives.

[tex]\rm f(a)+\frac{f'(a)}{1!} (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +....,[/tex]

Applying the Taylor series polynomial, the minimum order of the Taylor polynomial, centered at 0

[tex]\rm f(0)+\frac{f'(0)}{1!} (x-0)+\frac{f''(0)}{2!} (x-0)^{2} +....,[/tex]

f(x) = [tex]\sqrt{x+1}[/tex]

[tex]f'(x)=\frac{1}{2}[/tex]

[tex]f''(x)=3/8[/tex]

substituting in the Taylors series

T(x) = [tex]1+\frac{x}{2} -\frac{x^{2} }{8} +\frac{x^{3} }{16}[/tex]......

T(0.06) = [tex]1+\frac{0.06}{2} -\frac{0.06^{2} }{8} +\frac{0.06^{3} }{16}...[/tex]

T(0.06) =1.03

f(0.06) =

[tex]\sqrt{0.06+1}\\= 1.03[/tex]

Therefore, the minimum order of the Taylor polynomial, n≥3

Learn more about Taylor polynomial;

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Answer:

4.5%

Step-by-step explanation:

The tax rate=(2152.6/47800)*100=4.5%

Subtracting 10 from the original equation will shift the graph down 10 units

The answer is D.

Answer:

232.045

Step-by-step explanation:

217 + 253 + 214 + 247 + 217 + 253 + 232 + 246 + 223 + 227 + 229 + 247 + 206 + 241 + 239 + 223 + 222 + 216 + 252 + 209 + 236 + 256 = 5105

5105 / 22 = 232.045454545

5(2x+1)+4=6(3x+2)-7

10x+5+4=18x+12-7

10x-18x=12-7-5-4

-8x=-4 (-1)

8x=4

x=4/8 (/4)

x=1/2

Answer:

x = 1/2

Step-by-step explanation:

5(2x + 1) + 4 = 6 (3x + 2) - 7

~Simplify both sides

10x + 9 = 18x + 5

~Subtract 9 from both sides

10x = 18x - 4

~Subtract 18x to both sides

-8x = -4

~Divide -8 to both sides

x = 1/2

Best of Luck!

Answer:

12

Step-by-step explanation:

2²×3

I hope its correct

Answer:

4

[tex] {( - 2 + 1)}^{2} + 5(12 \div 3) - 9 \\ 2 + 1 + 5 \times 4 - 9 \\ 3 + 20 - 9 \\ 23 - 9 \\ 14[/tex]

Answer:

Step-by-step explanation:

Slope of the given line: m=4/3

Slope of the perpendiclar : m'=-3/4 (the inverse of the opposed of m)

Equation of the perpendiclar line: (passing through (-7,2))

[tex]y-2=(x+7)*\dfrac{-3}{4} \ or\\\\ y=-\dfrac{3x}{4} -\dfrac{13}{4}[/tex]

Answer:

X = 64

Step-by-step explanation:

All of the angles are right angles (because of the square at one of the angles shown above). This means each angle equals 90 degrees. If X + 26 = 90, then X = 64 because 90 - 26 = 64. I hope this helps!

Answer: X = 64

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

The cube root parent function:

Horizontally stretched by a factor of 4:

Translated 5 units right:

Translated 3 units up:

Answer:

-2 from both sides

Step-by-step explanation:

32=5x+2

-2        -2

________

30=5x

__=__

5      5

6=x

The first step to solve for X is to use subtraction property of equality to subtract 2 from both sides.

We are given the algebraic equation;

32 = 5X + 2

The first step to solve for X is to use subtraction property of equality to subtract 2 from both sides to get;

32 - 2 = 5X + 2 - 2

30 = 5X

Divide both sides by 5 using division property of equality to get;

X = 6

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#SPJ6

Answer:

± 3

Step-by-step explanation:

let n be the number then the number squared is n² , so

6n² = 54 ( divide both sides by 6 )

n² = 9 ( take the square root of both sides )

n = ± [tex]\sqrt{9}[/tex] = ± 3

That is the number is 3 or - 3

Answer:

Here the answer is given as follows,

Answer:

28 blue marbles

Step-by-step explanation:

yellow: blue

8               4

To get to 56 yellow marbles multiply by 7  

yellow: blue

8*7           4*7

56             28

There will be 28 blue marbles

Answer: plz marl brainilist

3966

Step-by-step explanation:

(98 × 63 - 32 × 69

98 * 63) - (32 * 69)

Answer: See explanation

Step-by-step explanation:

From the information given in the question, we are informed that a newsletter publisher believes that less than 61% of their readers own a laptop.

The null hypothesis will be: H0: p ≥ 0.61

The alternative hypothesis will be: Ha: p < 0.61.

The correct answer to the given question is "[tex]\bold{392.47\ < \mu <\ 427.53}[/tex],[tex]\bold{0.28 \ < P <\ 0.34}[/tex], and for Interpret results go to the C part.

Following are the solution to the given parts:

A)

[tex]\to \bold{(n) = 16}[/tex]

[tex]\to \bold{(\bar{X}) = 410}[/tex]

[tex]\to \bold{(\sigma) = 40}[/tex]

In the given question, we calculate [tex]90\%[/tex] of the confidence interval for the mean weight of shipped homemade candies that can be calculated as follows:

[tex]\to \bold{\bar{X} \pm t_{\frac{\alpha}{2}} \times \frac{S}{\sqrt{n}}}[/tex]

[tex]\to \bold{C.I= 0.90}\\\\\to \bold{(\alpha) = 1 - 0.90 = 0.10}\\\\ \to \bold{\frac{\alpha}{2} = \frac{0.10}{2} = 0.05}\\\\ \to \bold{(df) = n-1 = 16-1 = 15}\\\\[/tex]

Using the t table we calculate [tex]t_{ \frac{\alpha}{2}} = 1.753[/tex]  When [tex]90\%[/tex] of the confidence interval:

[tex]\to \bold{410 \pm 1.753 \times \frac{40}{\sqrt{16}}}\\\\ \to \bold{410 \pm 17.53\\\\ \to392.47 < \mu < 427.53}[/tex]

So [tex]90\%[/tex] confidence interval for the mean weight of shipped homemade candies is between [tex]392.47\ \ and\ \ 427.53[/tex].

B)

[tex]\to \bold{(n) = 500}[/tex]

[tex]\to \bold{(X) = 155}[/tex]

[tex]\to \bold{(p') = \frac{X}{n} = \frac{155}{500} = 0.31}[/tex]

Here we need to calculate [tex]90\%[/tex] confidence interval for the true proportion of all college students who own a car which can be calculated as

[tex]\to \bold{p' \pm Z_{\frac{\alpha}{2}} \times \sqrt{\frac{p'(1-p')}{n}}}[/tex]

[tex]\to \bold{C.I= 0.90}[/tex]

[tex]\to\bold{ (\alpha) = 0.10}[/tex]

[tex]\to\bold{ \frac{\alpha}{2} = 0.05}[/tex]

Using the Z-table we found [tex]\bold{Z_{\frac{\alpha}{2}} = 1.645}[/tex]

therefore [tex]90\%[/tex] the confidence interval for the genuine proportion of college students who possess a car is

[tex]\to \bold{0.31 \pm 1.645\times \sqrt{\frac{0.31\times (1-0.31)}{500}}}\\\\ \to \bold{0.31 \pm 0.034}\\\\ \to \bold{0.276 < p < 0.344}[/tex]

So [tex]90\%[/tex] the confidence interval for the genuine proportion of college students who possess a car is between [tex]0.28 \ and\ 0.34.[/tex]

C)

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Answer:

Length:8

Width:5.5

Step-by-step explanation:

We're given area = 44m^2, and the formula for the area of a rectangle is the length multiplied by the width. So,

A = L * w = 44

We're given that the length is 3m shorter than 2 times the width, which is 2w - 3. "2w" is the same as "2 times the width", and the 3 is subtracted because it says 3m shorter than 2 times the width. So L = 2w - 3, and we can substitute that into our equation above.

(2w - 3)(w) = 44

2w^2 - 3w - 44 = 0

Use the quadratic formula here.

x = {3 ± √(-3)^2 - 4(-44)(2)}/2(2)

= {3 ± √9 + 352}/4

= (3 ± 19)/4

You'll get two answers, but remember, we're measuring the length of the sides of shapes, so it has to be positive. It's impossible to have negative lengths, so we're going to stick with the (3 + 19)/4 answer, which is 22/4, which is 5.5. However, we are not finished yet. This is just the width. Now we need to plug it into the equation for length, which was 2w - 3

2(5.5) - 3 = 11 - 3 = 8

The length is 8m and the width is 5.5m.

Answer:

henc X = 30°

Step-by-step explanation:

here is the proof

when X=30° then

sin2x = sin2×30

=sin 60°

= √3/2

or else,

putting value of X = 30° then

sin2x= 2sinxcosx

= 2×sin30°×cos30°

=2×1/2×√3/2

= 2√3/4

= √3/2

hence proved sin2x= √3/2.

Answer:

0.08y - 0.0144

Step-by-step explanation:

We need to solve the below expression i.e.

(y - .18) x .08

It can be done as follows :

Using distributive property to solve it.

(y - .18) x .08 = 0.08(y) - 0.18(0.08)

= 0.08y - 0.0144

So, the equivalent expression is 0.08y - 0.0144.

Given:

The five number summary of two data sets are given as:

a) 0, 4, 12, 14, 20

b) 2, 8, 14, 18, 20

To find:

The range for the outliers.

Solution:

We know that,

An observation is considered an outlier if it is below [tex]Q_1-1.5(IQR)[/tex]

An observation is considered an outlier if it is above [tex]Q_3+1.5(IQR)[/tex]

Where, IQR is the interquartile range and [tex]IQR=Q_3-Q_1[/tex].

The five number summary of two data sets are given as:

0, 4, 12, 14, 20

Here, [tex]Q_1=4[/tex] and [tex]Q_3=14[/tex].

Now,

[tex]IQR=14-4[/tex]

[tex]IQR=10[/tex]

The range for the outliers is:

[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[4-1.5(10),14+1.5(10)][/tex]

[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[4-15,14+15][/tex]

[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[-11,29][/tex]

An observation is considered an outlier if it is below -11.

An observation is considered an outlier if it is above 29.

The five number summary of two data sets are given as:

2, 8, 14, 18, 20

Here, [tex]Q_1=8[/tex] and [tex]Q_3=18[/tex].

Now,

[tex]IQR=18-8[/tex]

[tex]IQR=10[/tex]

The range for the outliers is:

[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[8-1.5(10),18+1.5(10)][/tex]

[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[8-15,18+15][/tex]

[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[-7,33][/tex]

An observation is considered an outlier if it is below -7.

An observation is considered an outlier if it is above 33.

Answer:

dư 0... 7^300 chia 7 đc 7^299 mà

Answer:

R x 1= price of 1 locker

Step-by-step explanation:

it would continue the same way. Just multiply R and the number of lockers.

Is there a certain situation it was asking about?

Answer:

384

Step-by-step explanation:

Answer:

384 words

Step-by-step explanation:

Number of words typed in 1 minute = 48

So, number of words typed in 8 minutes

= Number of words typed in 1 minute × 8

= 48 × 8

= 384

So, Curtis types 384 words in 8 minutes.

Answer:

The width is 36 feet

Step-by-step explanation:

If the width of the fence is x then its length is x+3.

The perimeter is 150 feet, so we have the equation:

2(x + x + 3) = 150

4x + 6 = 150

x = 144/4 = 36 feet

9514 1404 393

Answer:

  |x| = 1/2

Step-by-step explanation:

Perhaps the simplest equation is ...

  |x| = 1/2

__

You could get more elaborate:

  |2x| = 1

  3 -|6x| = 0