To assess the accuracy of a laboratory scale, a standard weight known to weigh 1 gram is repeatedly weighed a total of n times How large should n be so that a 95% confidence interval for µ has a margin of error of ± 0.0001?

Answer:

The value of [tex]x_{1}[/tex] is given by [tex]\frac{10}{3}[/tex]. Hence, the answer is A.

Step-by-step explanation:

This exercise represents a case where the Newton-Raphson method is used, whose formula is used for differentiable function of the form [tex]f(x) = 0[/tex]. The expression is now described:

[tex]x_{n+1} = x_{n} - \frac{f(x_{n})}{f'(x_{n})}}[/tex]

Where:

[tex]x_{n}[/tex] - Current approximation.

[tex]x_{n+1}[/tex] - New approximation.

[tex]f(x_{n})[/tex] - Function evaluated in current approximation.

[tex]f'(x_{n})[/tex] - First derivative of the function evaluated in current approximation.

If [tex]f(x) = x^{2} - 4[/tex], then [tex]f'(x) = 2\cdot x[/tex]. Now, given that [tex]x_{0} = 6[/tex], the function and first derivative evaluated in [tex]x_{o}[/tex] are:

[tex]f(x_{o}) = 6^{2} - 4[/tex]

[tex]f(x_{o}) = 32[/tex]

[tex]f'(x_{o})= 2 \cdot 6[/tex]

[tex]f'(x_{o}) = 12[/tex]

[tex]x_{1} = x_{o} - \frac{f(x_{o})}{f'(x_{o})}[/tex]

[tex]x_{1} = 6 - \frac{32}{12}[/tex]

[tex]x_{1} = 6 - \frac{8}{3}[/tex]

[tex]x_{1} = \frac{18-8}{3}[/tex]

[tex]x_{1} = \frac{10}{3}[/tex]

The value of [tex]x_{1}[/tex] is given by [tex]\frac{10}{3}[/tex]. Hence, the answer is A.

Answer:

Brainleist!

Step-by-step explanation:

12/3.5

3.42857142857

round down so its 3!

Answer:

The probability that one red chip was selected is 0.0053.

Step-by-step explanation:

Let the random variable X be defined as the number of red chips selected.

It is provided that the selections of the n = 5 chips are done with replacement.

This implies that the probability of selecting a red chip remains same for each trial, i.e. p = 6/9 = 2/3.

The color of the chip selected at nth draw is independent of the other selections.

The random variable X thus follows a binomial distribution with parameters n = 5 and p = 2/3.

The probability mass function of X is:

[tex]P(X=x)={5\choose x}\ (\frac{2}{3})^{x}\ (1-\frac{2}{3})^{5-x};\ x=0,1,2...[/tex]

Compute the probability that one red chip was selected as follows:

[tex]P(X=1)={5\choose 1}\ (\frac{2}{3})^{1}\ (1-\frac{2}{3})^{5-1}[/tex]

                [tex]=5\times\frac{2}{3}\times \frac{1}{625}\\\\=\farc{2}{375}\\\\=0.00533\\\\\approx 0.0053[/tex]

Thus, the probability that one red chip was selected is 0.0053.

Answer:

0.0412

Step-by-step explanation:

Total chips = 6 red + 3 black chips

Total chips=9

n=5

Probability of (Red chips ) can be determined by

=[tex]\frac{6}{9}[/tex]

=[tex]\frac{2}{3}[/tex]

=0.667

Now we used the binomial theorem

[tex]P(x) = C(n,x)*px*(1-p)(n-x).....Eq(1)\\ putting \ the \ given\ value \ in\ Eq(1)\ we \ get \\p(x=1) = C(5,1) * 0.667^1 * (1-0.667)^4[/tex]

This can give 0.0412

Answer:

Solution,

<ABE+<ABC=180

<ABE=180-97

<ABE=83°

<ABC=<ACB=83°

<ABC+<ACB+<CAB=180

<CAB=180-83-83

<CAB=14

<DAC+<CAB=180

<DAC+14=180

<DAC=180-14

<DAC(X)=166°

Hope this helps...

Good luck on your assignment...

Answer:

The answer is -4.

Step-by-step explanation:

You should get this answer if you do 3 - 7.

Answer:

[tex]x\approx 50^\circ[/tex]

Step-by-step explanation:

[tex]c^2 = a^2 + b^2 - 2ab(cos(C))[/tex]

See the figure below to get the values as:

[tex]7^2=7^2+9^2-2\left(7\right)\left(9\right)cos\left(x\right)\\\\cos(x)=\frac{7^2+9^2-7^2}{2\cdot \:7\cdot \:9}\\\\x\approx 50^\circ[/tex]

There are multiple concepts to solve this problem. This is one of the concept used in high school. Other concept to solve this problem is to use the concept of isosceles triangle. An isosceles triangle is a triangle with (at least) two equal sides. The angles shared by the two equal sides are also equal. So that the sum of all the three angles will add up to 180.

[tex]x+x+80=180\\\\2x=100\\\\x=50^{\circ}[/tex]

Best Regards!

Answer:

y = x - 3

Step-by-step explanation:

Do rise/run to find the slope

8/8 = 1

y = x + b

Plug in a point to find the y-intercept

-5 = -2 + b

-3 = b

The equation will be y = x - 3

Answer:

6 years is the correct answer.

Step-by-step explanation:

Given that

Principal, P =  £8000

Rate of interest, R = 3% compounding annually

Amount, A >  £9500

To find: Time, T = ?

We know that formula for Amount when interest in compounding:

[tex]A = P \times (1+\dfrac{R}{100})^T[/tex]

Putting all the values:

[tex]A = 8000 \times (1+\dfrac{3}{100})^T[/tex]

As per question statement, A >  £9500

[tex]\Rightarrow 8000 \times (1+\dfrac{3}{100})^T > 9500\\\Rightarrow (1+0.03)^T > \dfrac{9500}{8000}\\\Rightarrow (1.03)^T > 1.19[/tex]

Putting values of T, we find that at T = 6

[tex]1.03^6 = 1.194 > 1.19[/tex]

[tex]\therefore[/tex] Correct answer is T = 6 years

In 6 years, the amount will be more than £9500.

Answer: 4,582,656

Step-by-step explanation:

A coin is tossed 4 times,

2^4 outcomes: 16

and then a standard six-sided die is rolled 3 times, 6^3

216 outcomes:

and finally, a group of two cards is drawn from a standard deck of 52 cards without replacements

It says a “group”, so, I guess the order doesn’t matter… So it is “52 choose 2”

52*51/ (2*1) = 26*51

how many different outcomes are possible?

16*216*26*51 = 4,582,656

162 inches is 13.5 feet or 13 feet 6 inches, so it would not fit underneath the bridge

Answer:

The truck cannot pass safely under the bridge. The truck is 13 inches taller than the maximum height.

Answer:

There are 36 education paths available to Carlos based on the schools around where he lives.

Step-by-step explanation:

Complete Question

Carlos is almost old enough to go to school. Based on where he lives, there are 6 elementary schools, 3 middle schools, and 2 high schools that he has the option of attending. How many different education paths are available to Carlos? Assume he will attend only one of each type of school.

Solution

We can use mathematics or manually writing out the possible combinations of elementary, middle and high school that Carlos can attend.

Using Mathematics

There are 6 elementary schools, meaning Carlos can make his choice in 6 ways.

There are 3 middle schools, meaning Carlos can make his choice in 3 ways.

Together with the elementary school choice, Carlos can make these two choices in 6 × 3 ways.

There are 2 high schools, Carlos can make his choice in 2 ways.

Combined with the elementary and middle school choices, Carlos can make his choices in 6×3×2 ways = 36 ways.

Manually

If we name the 6 elementary schools letters A, B, C, D, E and F.

Name the 3 middle schools letters a, b and c.

Name the 2 high schools numbers 1 and 2.

The different combinations of the 3 choices include

Aa1, Aa2, Ab1, Ab2, Ac1, Ac2

Ba1, Ba2, Bb1, Bb2, Bc1, Bc2

Ca1, Ca2, Cb1, Cb2, Cc1, Cc2

Da1, Da2, Db1, Db2, Dc1, Dc2

Ea1, Ea2, Eb1, Eb2, Ec1, Ec2

Fa1, Fa2, Fb1, Fb2, Fc1, Fc2

Evident now that there are 36 ways in which the 3 stages of schools can be combined. There are 36 education paths available to Carlos based on the schools around where he lives assuming that he will attend only one of each type of school.

Hope this Helps!!!

Answer:

36 education paths

Step-by-step explanation:

Hope this helps!

Answer:

2√3

Step-by-step explanation:

Step 1: Find perfect square roots

√4 x √3

Step 2: Convert

2 x √3

Step 3: Answer

2√3

Answer:

[tex] P(X>8)[/tex]

And for this case we can use the cumulative distribution function given by:

[tex] F(x) = 1- e^{-\lambda x}[/tex]

And if we use this formula we got:

[tex] P(X>8)= 1- P(X \leq 8) = 1-F(8) = 1- (1- e^{-\frac{1}{8.9} *8})=e^{-\frac{1}{8.9} *8}= 0.4070[/tex]

Step-by-step explanation:

For this case we can define the random variable of interest as: "The life of an electric component " and we know the distribution for X given by:

[tex]X \sim exp (\lambda =\frac{1}{8.9}) [/tex]

And we want to find the following probability:

[tex] P(X>8)[/tex]

And for this case we can use the cumulative distribution function given by:

[tex] F(x) = 1- e^{-\lambda x}[/tex]

And if we use this formula we got:

[tex] P(X>8)= 1- P(X \leq 8) = 1-F(8) = 1- (1- e^{-\frac{1}{8.9} *8})=e^{-\frac{1}{8.9} *8}= 0.4070[/tex]

Answer: f(-6) = 10.

Step-by-step explanation: This above equation is the only one that contains both coordinates of one of the ordered pairs in the correct order, so it is the answer.

Step-by-step explanation:

we can use o as the center of the circle

OB=13

EB=12

OE=?

OE^2 +EB^2=OB^2

OE^2+12^2=13^2

OE^2=169-144

OE=

√25

OE=5

OC=OE+EC

EC =13-5

EC=8

Answer:

It would decrease by 9.

Step-by-step explanation:

52 is the original mean or the initial mean.

43 is the final mean.

52-43 = 9

So 9 is the difference.

Hope this helped!

Answer:

21

Step-by-step explanation:

Since angle ABC is an inscribed angle, its measure is half that of arc AC. Therefore:

[tex]2(3x-1.5)=3x+9 \\\\6x-3=3x+9 \\\\3x-3=9 \\\\3x=12 \\\\x=4 \\\\AC=3(4)+9=12+9=21[/tex]

Hope this helps!

Use the Inscribed Angle theorem to get the measure of AC. The intercepted arc AC is,  21°.

We know that, Inscribed Angle Theorem stated that the measure of an inscribed angle is half the measure of the intercepted arc.

Given that,

The inscribed angle is, (3x - 1.5)

And the Intercepted arc AC is, (3x + 9)

So, We get;

(3x - 1.5) = 1/2 (3x + 9)

2 (3x - 1.5) = (3x + 9)

6x - 3 = 3x + 9

3x =  9 + 3

3x = 12

x = 4

Thus, The Intercepted arc AC is,

(3x + 9) = 3×4 + 9

           = 21°

Learn more about the Inscribed Angle theorem visit:

brainly.com/question/5436956

#SPJ2

Answer:

Option (D)

Step-by-step explanation:

Formula for the area of a triangle is,

Area of a triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

For the given triangle ABC,

Area of ΔABC = [tex]\frac{1}{2}(\text{AB})(\text{CD})[/tex]

Length of AB = [tex](y_2-y_1)[/tex]

Length of CD = [tex](x_3-x_1)[/tex]

Now area of the triangle ABC = [tex]\frac{1}{2}(y_2-y_1)(x_3-x_1)[/tex]

Therefore, Option (D) will be the answer.

Answer:

Step-by-step explanation:

Null hypothesis: u = 39.8

Alternative: u =/ 39.8

Using a one sample z test: the formula is

z = x-u / (sd/√n)

Where x = 33.1 u = 39.8, sd= 16.2 and n = 38

Thus we have:

z = 33.1-39.8 / (16.2/√38)

z = -6.7 / (16.2/6.1644)

z = -6.7/ 2.6280

z= -2.5495

To be able to arrive at a conclusion, we have to find the p value, the p value at a 0.1 significance level for a two tailed test is 0.0108. This is way less than 0.1 thus we will reject the null and conclude that there has been a change (either way) in the average number of e-mails received per day per employee. Yes, the new policy had an effect.

Answer:

The greatest possible length is 14 cm.

The total number of smaller pieces is 37.

Step-by-step explanation:

The greatest common factor of these three numbers is 14.

Total number of smaller pieces = 10+12+15 = 37

Best Regards!

Answer:

3^4

Step-by-step explanation:

3^2*3^2

3*3*3*3

3^4

Answer:

Area = 108 cm^2

Perimeter = 44 cm

Step-by-step explanation:

Area, -->

24 + 30 + 24 + 30 -->

24(2) + 30(2)

48 + 60 = 108 cm^2

108 = area

10 + 12 + 10 + 12, -->

10(2) + 12(2) = 44 cm

44 = perim.

Hope this helps!

Answer:

Step-by-step explanation:

Draw the diagram.

This time put in the only one line for the height. That is only 1 height is 8 cm. That's it.

The base is 6 +  6 = 12 cm.

The slanted line is 10 cm

That's all your diagram should show. It is much clearer without all the clutter.

Now you are ready to do the calculations.

Area

The Area = the base * height.

base = 12

height = 8

Area = 12 * 8 = 96

Perimeter.

In a parallelagram the opposite sides are equal to one another.

One set of sides = 10 + 10 = 20

The other set = 12 + 12 = 24

Both sets = 20 + 24

Both sets = 44

Answer

Area = 96

Perimeter = 44

Answer:

The 90% confidence interval for the mean production rate fro the new method is (75.9, 84.1).

Step-by-step explanation:

We have to calculate a 90% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=80.

The sample size is N=18.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{10}{\sqrt{18}}=\dfrac{10}{4.24}=2.36[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=18-1=17[/tex]

The t-value for a 90% confidence interval and 17 degrees of freedom is t=1.74.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=1.74 \cdot 2.36=4.1[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 80-4.1=75.9\\\\UL=M+t \cdot s_M = 80+4.1=84.1[/tex]

The 90% confidence interval for the mean production rate fro the new method is (75.9, 84.1).

Answer:

Step-by-step explanation:

[tex](\sqrt{b^{2}})^{3}=b^{3}\\\\[/tex]

or If it is

[tex]\sqrt[3]{b^{2}} =(b^{2})^{\frac{1}{3}}=b^{2*\frac{1}{3}}=b^{\frac{2}{3}}[/tex]

Answer: -13

Step-by-step explanation:

c-2y

= -5-2(4)

= -5 - 8

= -13

Answer:

-13

Step-by-step explanation:

[tex]c=-5\\y=4\\c-2y=\\-5-(4*2)=\\-5-8=\\-13[/tex]

The expression is equal to -13 when [tex]c=-5[/tex] and [tex]y=4[/tex].

Answer:

Step-by-step explanation:

The vertical asymptotes of the rational expression are the places where the denominator is zero:

  x^2 -16 = 0

  (x -4)(x +4) = 0 . . . . . true for x=4, x=-4

  x = 4, x = -4 are the equations of the vertical asymptotes

__

The zeros of a rational expression are the places where the numerator is zero:

  4x = 0

  x = 0 . . . . . . divide by 4

Answer: (f-g)(x)= -138

Step-by-step explanation:

Answer:

216

Step-by-step explanation:

To find the volume of the pyramid we have to do length * width * height / 3

The length is 9yd

The width is 8yd

The height is 9yd

So 9 * 9 * 8 = 648

648 / 3 = 216

Answer:

Approximately 0% probability that the average price for 15 gas stations is over $4.99.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 4.74, \sigma = 0.16, n = 16, s = \frac{0.16}{\sqrt{16}} = 0.04[/tex]

What is the approximate probability that the average price for 15 gas stations is over $4.99?

This is 1 subtracted by the pvalue of Z when X = 4.99. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{4.99 - 4.74}{0.04}[/tex]

[tex]Z = 6.25[/tex]

[tex]Z = 6.25[/tex] has a pvalue very close to 1.

1 - 1 = 0

Approximately 0% probability that the average price for 15 gas stations is over $4.99.