The common fruit fly Drosophila melanogaster is the most studied organism in genetic research because it is small, easy to grow, and reproduces rapidly. The length of the thorax (where the wings and legs attach) in a population of male fruit flies is approximately Normal with mean 0.800 millimeters (mm) and standard deviation 0.078 mm. Draw a Normal curve on which this mean and standard deviation are correctly located. (Hint: Draw an unlabeled Normal curve, locate one, two and three standard deviations away from the mean, then add number labels on the horizontal axis.)

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 6.8 psi

For the alternative hypothesis,

µ ≠ 6.8

This is a 2 tailed test

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 6.8

x = 6.9

σ = 0.7

n = 140

z = (6.9 - 6.8)/(0.7/√140) = 0.17

Therefore, the value of the test statistic us 0.17

Answer:

100 mL

Step-by-step explanation:

If x is the volume of 35% solution, then:

0.35x + 0.20(50) = 0.30(x + 50)

0.35x + 10 = 0.30x + 15

0.05x = 5

x = 100

You need 100 mL of 35% solution.

Answer:

a) Entries of A are non negative, that is ai,j ≥ 0 for all 1 ≤ i ≤ n and all 1 ≤ j ≤ n.

c) yes MS is stochastic

Step-by-step explanation:

a) A stochastic matrix is a square matrix whose columns are probability vectors. A probability vector is a numerical vector whose entries are real numbers between 0 and 1 whose sum is 1.

B)

a) Now, suppose Sx=λx for some λ>1. Since the rows of S are nonnegative and sum to 1, each element of vector Sx is a convex combination of the components of x, which can be no greater than maximum of x the largest component of x. On the other hand, at least one element of λx is greater than maximum of x, which proves that λ>1 is impossible and Hence  λ = 1.

b) Then [tex]S^{2}[/tex] =[tex]P^{2}_{ij}[/tex] is also stochastic; it is the two-step transition matrix for the chain {Xn, n = 0,1,…}. To every stochastic matrix S, there corresponds a Markov chain {Xn} for which S is the unit-step transition matrix.

However, not every stochastic matrix is the two-step transition matrix of a Markov chain.

c) Let A and B be two row-stochastic matrices and suppose we know the product of column stochastic matrices is column-stochastic. Observe that,

MS = [tex]((MS)^{T})^{T} = (S^{T}M^{T})^{T}[/tex]

by properties of transpose of a matrix. Let us consider [tex]S^{T} M^{T}[/tex]. It is easy to see that the transpose of a row-stochastic matrix is column-stochastic by definition (and vice versa). Thus, [tex]S^{T}[/tex]and [tex]M^{T}[/tex] are column stochastic and by our assumption, it must then be the case that [tex]S^{T} M^{T}[/tex] is column-stochastic. Since  [tex]S^{T} M^{T}[/tex]  is column-stochastic, then it's transpose [tex](S^{T} M^{T})^{T}[/tex]=MS is row stochastic.

Final answer:

The question touches on elements of sociology, dealing with social influence, group behavior, and persuasion as evidenced through scenarios where individuals are impacted by their group affiliations. It illustrates real-life applications of sociological principles such as persuasion in deciding on a dinner venue or peer pressure in case of vandalism.

Explanation:

The subject matter here touches upon aspects of sociology, specifically related to social influence, group behaviour, and persuasion. These examples illustrate how individuals are often influenced by the groups they belong to and how persuasive tactics can be employed by individuals within a social context. The scenarios highlight how group membership and social pressures can impact decisions, such as where to eat dinner or participating in group activities like vandalism. The statement by John Donne encapsulates the concept that no person is isolated; instead, each individual is part of a broader society, emphasizing the importance of social groups in shaping behavior and attitudes.

In the given examples, we encounter various situations where group dynamics play a role - from peer pressure to persuade Jake to hang out against his parents' wishes, to a group's collective decision about whether to dine at a particular restaurant. These are everyday applications of sociological principles, demonstrating the study of group life, group behavior, and group processes, which are key concepts in understanding how individuals behave within and are influenced by their social environment.

Answer:

The answer is 30 sq in i had that question, good luck :)

Answer:

Wag

Step-by-step explanation:

C72 или Wag ладно помогите

Step-by-step explanation:

By trigonometric conversion,

Cos -90° = 0

Cos -60° = 0.5

Cos -30° = 0.866

Cos 0° = 1

From the above values, Cos -90° to Cos 0° = 0 to 1

As theta increases from [tex]\frac{-theta}{2}[/tex] to 0, the value of cos theta will increase from 0 to 1 (Option 4)

Answer:

185

Step-by-step explanation:

sorry. had to do something but im bsck :)

The ASA and AAS are methods of proving triangle congruence. ASA requires two angles and the included side in one triangle to match the respective parts in the other triangle. AAS requires two angles and a non-included side in one triangle to match the respective parts in the other triangle.

The question refers to two of the many methods to prove that triangles are congruent: Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS). In triangle congruence, congruent means that two triangles have the same size and shape.

For the ASA congruence, two angles and the included side in one triangle must be congruent to the corresponding two angles and the included side in another triangle. For example, if we have two triangles, Triangle ABC and Triangle DEF, if angle A is congruent to angle D, angle B is congruent to angle E, and side AB is congruent to side DE, then the two triangles are congruent by ASA.

For AAS congruence, two angles and a non-included side in one triangle must be congruent to the corresponding two angles and the non-included side in another triangle. For instance, in Triangle ABC and Triangle DEF, if angle A is congruent to angle D, angle B is congruent to angle E, and side BC is congruent to side EF, then the two triangles are congruent by AAS.

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To estimate the product 137 multiplied by 18, we can round the numbers to the nearest ten. 137 is approximately 140, and 18 is approximately 20. The estimated product of 137 x 18 is 2800.

To estimate the product 137 multiplied by 18, we can round the numbers to the nearest ten. 137 is approximately 140, and 18 is approximately 20. Then, we multiply the rounded numbers: 140 x 20 = 2800. Therefore, the estimated product of 137 x 18 is 2800.

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Answer:

a)From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

And the standard error for the mean would be:

[tex]\sigma_{\bar X}= \frac{140}{\sqrt{100}} =14[/tex]

b) We want this probability:

[tex] P(\bar X >120) [/tex]

And we can use the z score formula given by:

[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And replacing we got:

[tex] z = \frac{120-90}{\frac{140}{\sqrt{100}}}= 2.143[/tex]

And we can find this probability with the complement rule and the normal standard deviation or excel and we got:

[tex] P( z>2.143) = 1-P(Z<2.143) = 1-0.984 = 0.016[/tex]

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Solution to the problem

Part a

From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

And the standard error for the mean would be:

[tex]\sigma_{\bar X}= \frac{140}{\sqrt{100}} =14[/tex]

Part b

We want this probability:

[tex] P(\bar X >120) [/tex]

And we can use the z score formula given by:

[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And replacing we got:

[tex] z = \frac{120-90}{\frac{140}{\sqrt{100}}}= 2.143[/tex]

And we can find this probability with the complement rule and the normal standard deviation or excel and we got:

[tex] P( z>2.143) = 1-P(Z<2.143) = 1-0.984 = 0.016[/tex]

Answer:

(A) The mean for the differences is 2.0.

(B) The test statistic is 1.617.

(C) At 90% confidence the null hypothesis should not be rejected.

Step-by-step explanation:

We are given that a random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance.

The following data (in miles per gallon) show the results of the test;

Driver         Manufacturer A               Manufacturer B

   1                      32                                       28

  2                      27                                       22

  3                      26                                       27

  4                      26                                       24

  5                      25                                       24

  6                      29                                       25

  7                       31                                       28

  8                      25                                       27

Let [tex]\mu_1[/tex] = mean MPG for the fuel efficiency of Manufacturer A brand

[tex]\mu_2[/tex] = mean MPG for the fuel efficiency of Manufacturer B brand

SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1-\mu_2=0[/tex]  or  [tex]\mu_1= \mu_2[/tex]    {means that there is a not any significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1-\mu_2\neq 0[/tex]  or  [tex]\mu_1\neq \mu_2[/tex]   {means that there is a significant difference in the mean MPG (miles per gallon) for the fuel efficiency of these two brands of automobiles}

The test statistics that will be used here is Two-sample t test statistics as we don't know about the population standard deviations;

                      T.S.  = [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex]  ~ [tex]t__n__1+_n__2-2[/tex]

where, [tex]\bar X_1[/tex] = sample mean MPG for manufacturer A = [tex]\frac{\sum X_A}{n_A}[/tex] = 27.625

[tex]\bar X_2[/tex] = sample mean MPG for manufacturer B =[tex]\frac{\sum X_B}{n_B}[/tex] = 25.625

[tex]s_1[/tex] = sample standard deviation for manufacturer A = [tex]\sqrt{\frac{\sum (X_A-\bar X_A)^{2} }{n_A-1} }[/tex] = 2.72

[tex]s_2[/tex] = sample standard deviation manufacturer B = [tex]\sqrt{\frac{\sum (X_B-\bar X_B)^{2} }{n_B-1} }[/tex] = 2.20

[tex]n_1[/tex] = sample of cars selected from manufacturer A = 8

[tex]n_2[/tex] = sample of cars selected from manufacturer B = 8

Also, [tex]s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2} }[/tex]   =  [tex]\sqrt{\frac{(8-1)\times 2.72^{2}+(8-1)\times 2.20^{2} }{8+8-2} }[/tex]  = 2.474

(A) The mean for the differences is = 27.625 - 25.625 = 2

(B) The test statistics  =  [tex]\frac{(27.625-25.625)-(0)}{2.474 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }[/tex]  ~  [tex]t_1_4[/tex]

                                     =  1.617

(C) Now at 10% significance level, the t table gives critical values between -1.761 and 1.761 at 14 degree of freedom for two-tailed test. Since our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that there is a not any significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles.

The mean for the differences is 2.5 MPG. The test statistic is 2.256. At 90% confidence, the null hypothesis should be rejected.

In order to determine if there is a significant difference in the mean MPG between the two manufacturers, we need to calculate the mean for the differences and the test statistic. The mean for the differences is calculated by subtracting the Manufacturer B MPG from the Manufacturer A MPG for each driver and then taking the average of those differences. In this case, the mean for the differences is 2.5 MPG. The test statistic is calculated by dividing the mean for the differences by the standard deviation of the differences and then multiplying by the square root of the sample size. In this case, the test statistic is 2.256.

At 90% confidence, we can compare the test statistic to the critical value for a two-tailed test. The critical value for a 90% confidence level is 1.645. Since the test statistic (2.256) is greater than the critical value (1.645), we reject the null hypothesis. Therefore, the answer to question C is: the null hypothesis should be rejected.

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Answer:

Unknown 1: -OH group at 3400-3600

Unknown 2: Ketone and alkene group

Step-by-step explanation:

Unknown 1:

This compound has a strong IR absorption at 3400 - 3600cm-¹; this indicates that it is an alcoholic group (OH)

No absorption between 1600 and 2900cm-¹: this rule out the presence of ketone (C = O)

Hence the unknown compound is OH group

Unknown 2:

This has strong IR absorption at 1680cm-¹: this indicates the presence of (C=O) group.

No absorptions above 3100cm-¹: this indicates the presence of C = C - H

So therefore, unknown 2 is most likely to be Ketone and alkene group

Answer:

For this case we want to determine  if pennies are really fair when flipped, meaning equally likely to land head up or tails, so then the correct system of hypothesis are:

Null hypothesis: [tex]p=0.5[/tex]

Alternative hypothesis: [tex]p \neq 0.5[/tex]

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".  

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".  

Solution to the problem

For this case we want to determine  if pennies are really fair when flipped, meaning equally likely to land head up or tails, so then the correct system of hypothesis are:

Null hypothesis: [tex]p=0.5[/tex]

Alternative hypothesis: [tex]p \neq 0.5[/tex]

Final answer:

The appropriate null hypothesis for the experiment is that pennies are fair when flipped, with the alternative hypothesis being that they are not.

Explanation:

The appropriate null hypothesis for this experiment is that the true probability of a penny landing heads up when flipped is 0.5, meaning that pennies are fair when flipped. The alternative hypothesis, denoted as the alternative to the null hypothesis, would be that the true probability of a penny landing heads up when flipped is not 0.5.

To summarize:

Null hypothesis (H0): p = 0.5

Alternative hypothesis (Ha): p ≠ 0.5

Answer:

b. There's no statistically significant linear relationship between the number of miles driven and the maintenance cost.

Step-by-step explanation:

The p value that is corresponding in line with the slope of regression line is 0.345, which is quite above the significance level of 0.05. as a result, we failed to discard the null hypothesis that there is no important association or connection between x and y variables.

Going by the above explanation we can then conclude that there's no statistically significant linear relationship between the number of miles driven and the maintenance cost.

Answer:

See down below.

Step-by-step explanation:

Theoretical probability is what we expect to happen. For example, we do a test of flipping a coin. You know that its either gonna be heads or tails.

Experimental probability is what actually happens when we try it out. It occurs when we are doing an experiment and then something happens.

Hope this helps!

Theoretical probability is calculated based on assumptions and mathematical calculations, while experimental probability is based on actual data and observations.

Theoretical probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. It is based on assumptions and mathematical calculations. For example, if you flip a fair coin, the theoretical probability of getting heads is 1 out of 2, or 0.5.

Experimental probability, on the other hand, is calculated by conducting an actual experiment and observing the outcomes. It is based on actual data and observations. For example, if you flip a coin 10 times and get heads 6 times, the experimental probability of getting heads is 6 out of 10, or 0.6.

In summary, theoretical probability is based on calculations and assumptions, while experimental probability is based on actual data and observations.

Final answer:

Different materials exhibit varying degrees of thermal expansion when subjected to a temperature change. Polymers such as polyethylene expand the most, followed by soft metals like lead and aluminum, with hard metals like platinum and minerals like quartz showing much less expansion.

Explanation:

When materials undergo a change in temperature, they typically experience a change in size, known as thermal expansion or contraction. This phenomenon happens because the kinetic energy of the particles within the material changes, consequently changing the distances between particles. The amount by which a material expands or contracts is dependent on its coefficient of thermal expansion, which varies widely among different materials. Polymers such as polyethylene show significant thermal expansion, more so than soft metals like lead and aluminum, and much more than hard materials like platinum and quartz. When temperature increases, thermal stress may arise in materials that are constrained and cannot freely expand, leading to deformation or even damage. Platinum, being a metal, would deform more than quartz due to its higher thermal expansion, but less than softer metals and polymers.

To rank the items based on the total change in length along the long axis of beams with a temperature change of 20 degrees, we would expect polyethylene to have the greatest change due to its high coefficient of thermal expansion, followed by soft metals like lead and aluminum. Platinum would have some expansion but considerably less than softer metals and polymers, and quartz would experience the least amount of expansion given its low thermal expansion characteristic.

Answer:

[tex]n=(\frac{2.58(1.2)}{0.25})^2 =153.36 \approx 154[/tex]

So the answer for this case would be n=154 rounded up to the nearest integer

Step-by-step explanation:

Assuming the following question: It is desired to estimate the mean GPA of each undergraduate class at a large university. How large a sample is necessary to estimate the GPA within 0.25 at the 99% confidence level? The population standard deviation is 1.2. If needed, round your final answer up to the next whole number.

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

[tex]\bar X[/tex] represent the sample mean for the sample  

[tex]\mu[/tex] population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =0.25 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.005;0;1)", and we got [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:

[tex]n=(\frac{2.58(1.2)}{0.25})^2 =153.36 \approx 154[/tex]

So the answer for this case would be n=154 rounded up to the nearest integer

Answer:

[tex]V = \frac{2L\sqrt{3}}{3} \pi}[/tex]

[tex]A = 4\pi + \sqrt{3L^{2} + 16}[/tex]

Step-by-step explanation:

Figure of cone is missing. See attachment

Given

Radius, R = 2m

Let L = KL=LM=KM

Required:

Volume, V and Surface Area, A

Calculating Volume

Volume is calculated using the following formula

[tex]V = \frac{1}{3} \pi R^{2} H[/tex]

Where R is the radius of the cone and H is the height

First, we need to determine the height of the cone

The height is represented by length OL

It is given that KL=LM=KM in triangle KLM

This means that this triangle is an equilateral triangle

where OM = OK = [tex]\frac{1}{2} KL[/tex]

OK = [tex]\frac{1}{2}L[/tex]

Applying pythagoras theorem in triangle LOM,

|LM|² =  |OL|² + |OM|²

By substitution

L² = H² + ( [tex]\frac{1}{2}L[/tex])²

H² = L² -  [tex]\frac{1}{4}L[/tex]²

H² = L² (1 -  [tex]\frac{1}{4}[/tex])

H² = L² [tex]\frac{3}{4}[/tex]

H² = [tex]\frac{3L^{2} }{4}[/tex]

Take square root of bot sides

[tex]H = \sqrt{\frac{3L^{2} }{4}}[/tex]

[tex]H = \frac{L\sqrt{3}}{2}[/tex]

Recall that [tex]V = \frac{1}{3} \pi R^{2} H[/tex]

[tex]V = \frac{1}{3} \pi 2^{2} * \frac{L\sqrt{3}}{2}[/tex]

[tex]V = \frac{1}{3} \pi * 4} * \frac{L\sqrt{3}}{2}[/tex]

[tex]V = \frac{1}{3} \pi} * {2L\sqrt{3}}[/tex]

[tex]V = \frac{2L\sqrt{3}}{3} \pi}[/tex]

in terms of [tex]\pi[/tex] an d L where L = KL = LM = KM

Calculating Surface Area

Surface Area is calculated using the following formula

[tex]H = \frac{L\sqrt{3}}{4}[/tex]

[tex]A=\pi r(r+\sqrt{h^{2} +r^{2} } )[/tex]

[tex]A=\pi * 2(2+\sqrt{((\frac{L\sqrt{3}}{2})^{2} +2^{2} } )[/tex])

[tex]A=\pi * 2(2+\sqrt{{\frac{3L^{2}}{4} } + 4 }[/tex] )

[tex]A=\pi * 2(2+\sqrt{{\frac{3L^{2}+16}{4} } })[/tex]

[tex]A=2\pi(2+\sqrt{{\frac{3L^{2}+16}{4} } })[/tex]

[tex]A = 2\pi (2 + \frac{\sqrt{3L^{2} + 16}}{\sqrt{4}} )[/tex]

[tex]A = 2\pi (2 + \frac{\sqrt{3L^{2} + 16}}{2} )[/tex]

[tex]A = 2\pi (2 + {\frac{1}{2} \sqrt{3L^{2} + 16})[/tex]

[tex]A = 4\pi + \sqrt{3L^{2} + 16}[/tex]

Answer:

The P-value for this test is P=0.2415.

Step-by-step explanation:

We have to perform an hypothesis testing on the mean of alla account balances.

The claim is that the mean of all account balances is significantly greater than $1,150.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=1150\\\\H_a: \mu>1150[/tex]

The sample size is n=20, with a sample mean is 110 and standard deviation is 125.

We can calculate the t-statistic as:

[tex]t=\dfrac{\bar x-\mu}{s/\sqrt{n}}=\dfrac{1170-1150}{125/\sqrt{20}}=\dfrac{20}{27.95}=0.7156[/tex]

The degrees of freedom fot this test are:

[tex]df=n-1=20-1=19[/tex]

For this one-tailed test and 19 degrees of freedom, the P-value is:

[tex]P-value=P(t>0.7156)=0.2415[/tex]

Answer:

96.08% probability that the average length of a randomly selected bundle of steel rods is less than 178.3-cm.

Step-by-step explanation:

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

Normal probability distribution

Problems of normally distributed samples are solved using 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 problem, we have that:

[tex]\mu = 177.5, \sigma = 1.2, n = 7, s = \frac{1.2}{\sqrt{7}} = 0.4536[/tex]

Find the probability that the average length of a randomly selected bundle of steel rods is less than 178.3-cm.

This is the pvalue of Z when X = 178.3. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{178.3 - 177.5}{0.4536}[/tex]

[tex]Z = 1.76[/tex]

[tex]Z = 1.76[/tex] has a pvalue of 0.9608

96.08% probability that the average length of a randomly selected bundle of steel rods is less than 178.3-cm.

Answer: the probability that the average length of a randomly selected bundle of steel rods is less than 178.3-cm is 0.96

Step-by-step explanation:

Since the lengths of the steel rods are normally distributed, then according to the central limit theorem,

z = (x - µ)/(σ/√n)

Where

x = sample mean lengths of the steel rods

µ = population mean length of the steel rods

σ = standard deviation

n = number of samples

From the information given,

µ = 177.5 cm

x = 178.3 cm

σ = 1.2 cm

n = 7

the probability that the average length of a randomly selected bundle of steel rods is less than 178.3-cm is expressed as

P(x < 178.3)

Therefore,

z = (178.3 - 177.5)/(1.2/√7) = 1.76

Looking at the normal distribution table, the probability corresponding to the z score is 0.96

Therefore,

P(x < 178.3) = 0.96

The researchers conducted an experiment to test the effectiveness of a placebo in reducing pain. A statistical test called the paired t-test can be used to analyze the data and determine if the mean BOLD measurements are higher in the first session than in the second. The results of this test will provide evidence to confirm or refute the effectiveness of the placebo.

The researchers conducted an experiment to test the effectiveness of a placebo in reducing pain. They measured the blood oxygen level-dependent (BOLD) signal during two consecutive sessions with electric shocks applied to the volunteers' arms. In the second session, a cream that was actually a placebo was applied to the volunteers. The mean and standard deviation of the differences in BOLD measurements were calculated to determine if there was evidence to confirm that the placebo was effective.

To test if the mean BOLD measurements were higher in the first session than in the second, a statistical test can be used. The paired t-test is suitable for this scenario, as it compares the means of two related samples. The t-test calculates a t-value which can be compared to a critical value to determine if there is evidence of a significant difference. In this case, with a significance level of α = 0.05, if the t-value is greater than the critical value, it would indicate evidence that the mean BOLD measurements are higher in the first session than the second.

If the calculated t-value is greater than the critical value, there is evidence to confirm that the placebo is effective in reducing pain. Conversely, if the calculated t-value is not greater than the critical value, there is not enough evidence to confirm that the placebo is effective. It is important to note that statistical significance does not necessarily imply practical significance, so further investigation may be required to understand the magnitude of the effect.

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Answer:

a

Step-by-step explanation:

first multiply 9*6.5*.5 for the triangle

Then multiply 9*4.5

Then add up to get 69.75

Answer:

a is your answer

Step-by-step explanation:

Answer:

The steps to finding the upper and lower quartiles are given in the first choice.

1.  Order the data from least to greatest. If you don't do this, the data is random.

2.  Find the median - you will do this so that you can find the midpoint of the data set (half of of the data is smaller and half of the data is larger).

3.  Find the lower quartile - this is the half of the lower half of numbers; think of it as breaking the lower half of the data into 2 sections.  

4.  Find the upper quartile - this is the half of the greater half of numbers; this will break the upper half of the data into 2 sections.  

Answer:

A.

Step-by-step explanation:

Just took the test:)

Answer:

A point in geometry is a location. It has no size i.e. no width, no length and no depth.

Step-by-step explanation:

If you need more definitions, I suggest you go to mathisfun which is an amazing website! Hope this helped :)

Answer:

a. The probability of getting an specific sequence would be

[tex](1/20)*(1/19)*(1/18)*(1/17)*(1/16)[/tex]

b. The probability  of having an specific sequence would be.

[tex]5/20 = 1/4[/tex]

Step-by-step explanation:

a. If you draw 5 marbles without replacement, the probability of getting an specific sequence would be

[tex](1/20)*(1/19)*(1/18)*(1/17)*(1/16)[/tex]

b. If you draw 5 marbles all at once without replacement, the probability  of having an specific sequence would be.

[tex]5/20 = 1/4[/tex]

Answer:

(6+2)/(-4+8)= 8/4= 2

y+2=2(x+8)

y+2=2x+16

y=2x+14

Step-by-step explanation:

Given:

Given that the measurements of the triangle.

We need to determine the value of x.

Value of x:

The value of x can be determined using by angle bisector theorem.

The angle bisector theorem states that "if the angle that bisects the triangle will divide the opposite sides into two segments that are proportional to the remaining two sides of the triangle".

Hence, applying the theorem, we have;

[tex]\frac{x}{20-x}=\frac{14}{11}[/tex]

Cross multiplying, we get;

[tex]11x=14(20-x)[/tex]

Simplifying, we get;

[tex]11x=280-14x[/tex]

[tex]25x=280[/tex]

   [tex]x=11.2[/tex]

Thus, the value of x is 11.2