In a histogram, are the lengths of the rectangles proportional to the width of the bars?​

Answer:

(a) The confidence level desired by the researchers is 95%.

(b) The sampling error is 0.001 microcurie per millilitre.

(c) The sample size necessary to obtain the desired estimate is 36.

Step-by-step explanation:

The mean and standard deviation of the amount of the radioactive​ element, cesium-137 present in a sample of n = 16 lichen specimen are:

[tex]\bar x=0.009\\s=0.003[/tex]

Now it is provided that the researchers want to increase the sample size in order to estimate the mean μ to within 0.001 microcurie per millilitre of its true​ value, using a​ 95% confidence interval.

The (1 - α)% confidence interval for population mean (μ) is:

[tex]CI=\bar x \pm z_{\alpha/2}\times \frac{s}{\sqrt{n}}[/tex]

(a)

The confidence level is the probability that a particular value of the parameter under study falls within a specific interval of values.

In this case the researches wants to estimate the mean using the 95% confidence interval.

Thus, the confidence level desired by the researchers is 95%.

(b)

In case of statistical analysis, during the computation of a certain statistic, to estimate the value of the parameter under study, certain error occurs which are known as the sampling error.

In case of the estimate of parameter using a confidence interval the sampling error is known as the margin of error.

In this case the margin of error is 0.001 microcurie per millilitre.

(c)

The margin of error is computed using the formula:

[tex]MOE=z_{\alpha/2}\times \frac{s}{\sqrt{n}}[/tex]

The critical value of z for 95% confidence level is:

[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]

*Use a z-table.

Compute the sample size value as follows:

[tex]MOE=z_{\alpha/2}\times \frac{s}{\sqrt{n}}[/tex]

      [tex]n=[\frac{z_{\alpha/2}\times s}{MOE}]^{2}[/tex]

          [tex]=[\frac{1.96\times 0.003}{0.001}]^{2}[/tex]

          [tex]=34.5744\\\approx36[/tex]

Thus, the sample size necessary to obtain the desired estimate is 36.

The sample size necessary to estimate the mean within the desired sampling error can be calculated using the formula: n = (z * σ / E)^2, where n is the sample size, z is the z-score corresponding to the desired confidence level, σ is the standard deviation, and E is the desired sampling error. In this case, the sample size is approximately 11,447.

To determine the sample size necessary to estimate the mean within the desired sampling error, we can use the formula:

n = (z * σ / E)^2

Where n is the sample size, z is the z-score corresponding to the desired confidence level (in this case, 1.96 for a 95% confidence level), σ is the standard deviation, and E is the desired sampling error.

Plugging in the values, we get:

n = (1.96 * 0.003 / 0.001)^2

Simplifying, we find that n is approximately 11,447. Therefore, the sample size necessary to obtain the desired estimate is 11,447 (rounded to the nearest whole number).

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Answer:

1391000000

Step-by-step explanation:

Answer:

A ^2 + B^2 =C^2. The Pythagorean Theorem is a statement about triangles containing a right angle

Step-by-step explanation:

Answer:

  x = y = 26 cm; z = 13 cm

Step-by-step explanation:

The generic solution for the minimum material in an open-top box is that the box is square and half as high as it is wide. It is half a cube of twice the volume.

The dimensions of the square base are ...

  ∛(2·8788 cm³) = 26 cm

Then the height is half that, or 13 cm.

  x = y = 26 cm; z = 13 cm

_____

If you need to see the development, you can use the method of Lagrange multipliers to find the minimum area for the given volume;

  area = xy +2(xz +yz)

  volume = xyz = 8788

We require each of the partial derivatives of L with respect to x, y, z, and λ to be zero.

  L = xy +2(xz +yz) +λ(xyz -8788)

  partial with respect to x: 0 = y+2z +λyz

  partial with respect to y: 0 = x +2z +λxz

  partial with respect to z: 0 = 2x+2y +λxy

  partial with respect to λ: 0 = xyz -8788

From the first two equations, we have ...

  λ = (y +2z)/(yz) = 1/z +2/y

  λ = (x +2z)/(xz) = 1/z +2/x

Equating these expressions for λ, we find ...

  1/z +2/y = 1/z +2/x   ⇒   x = y

The third equation then tells us ...

  λ = (2x +2y)/(xy) = 2/y +2/x

Comparing this to either of the first two expressions for λ, we see ...

  1/z +2y = 2/x +2/y   ⇒   z = x/2

This is the result we started the answer with:

  x = y = 2z = ∛(2·8788 cm³)

The rate of increase is 1.2 as it represents b in the equations A+b power of x+c then +D.

Answer:

y=7.46496

Step-by-step explanation:

Answer:

2345

Step-by-step explanation:

because3456

Step-by-step explanation:

For a community service project, the no of the students in a class bring paper towels  = [tex]\frac{3}{4}[/tex]

The students bring towels and soap = [tex]\frac{2}{5}[/tex]

The students who bring paper towels = [tex]\frac{3}{4}[/tex]

The fraction of students who bring paper towels also bring soap =  [tex]\frac{2}{5}[/tex]

Answer:

4 units to the right & 1 unit up.

Answer: it’s B)

The answer is the second one

Answer:

4 * x - 33

Step-by-step explanation:

four times as old as she was 33 years ago

let x represent how old she is now

4 * x - 33

Four ( 4 ) times ( * ) as old as she was 33 years ago ( x - 33 )

Final answer:

The phrase "4 times as old as she was 33 years ago" can be represented algebraically as the equation x = 4(x - 33), where x is the current age of the person.

Explanation:

To translate the phrase "4 times as old as she was 33 years ago" into algebraic terms, we first denote the current age of the person as a variable, let's call it x. The age of the person 33 years ago would then be expressed as x - 33. To articulate that someone is now four times as old as they were 33 years ago, we create the algebraic expression 4(x - 33), which represents the current age being four times the age 33 years prior.

Example:

If we want to set up an equation where someone's current age is four times their age from 33 years ago, it would look like this:

Let x = current age

Then x - 33 = age 33 years ago

The phrase translates to the equation x = 4(x - 33)

By multiplying both sides by the same factor, we can manipulate this equation if necessary to solve for x. As an example, multiplying both sides by 1 does not change the equation, but it can sometimes be helpful in other contexts to multiply both sides to simplify or to get rid of fractions.

Answer:

a) The null hypothesis is represented as

H₀: μ ≤ 23

The alternative hypothesis is given as

Hₐ: μ > 23

b) Check the Explanation

The conditions for a t-test to be performed are satisfied or not?

- Yes, because the students were randomly sampled.

- Yes, the sample size is larger man 30.

And the central limit theorem allows us to approximate that the random sample obtained from the population is a normal distribution.

c) Are the sampled values independent of each other?

Yes, because each student's test score does not affect other students' test scores.

d) p-value obtained = 0.004

Reject the null hypothesis because the P-value a less than the alpha = 0.10 level of significance

e) There is sufficient evidence to conclude that the population mean is greater than 23.

Step-by-step explanation:

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, we want to check if results suggest that students who complete the core curriculum are ready for college-level mathematics.

The only condition to be ready for college is scoring above 23.

So, the null hypothesis would be that the mean of test scores of students that complete core curriculum is less than or equal to 23. That is, there isn't significant evidence to conclude that the results suggest that students who complete the core curriculum are ready for college-level mathematics.

And the alternative hypothesis would be that there is significant evidence to conclude that the results suggest that students who complete the core curriculum are ready for college-level mathematics. That is, the mean score of those that complete the core curriculum is above 23 and are ready for college-level mathematics.

Mathematically

The null hypothesis is represented as

H₀: μ ≤ 23

The alternative hypothesis is given as

Hₐ: μ > 23

b) The conditions required before performing t-test.

- The sample should be a random sample

- The dependent variable should be approximately normally distributed.

- The observations are independent of one another.

- The dependent variable should not contain any outliers

All of these conditions are satisfied for our distribution.

c) Are the sampled values independent of each other?

Yes, because each student's test score does not affect other students' test scores.

d) To do this test, we will use the t-distribution because no information on the population standard deviation is known

So, we compute the t-test statistic

t = (x - μ₀)/σₓ

x = sample mean = 23.6

μ₀ = 23

σₓ = standard error = (σ/√n)

where n = Sample size = 200

σ = Sample standard deviation = 3.2

σₓ = (3.2/√200) = 0.226

t = (23.6 - 23) ÷ 0.226 = 2.65

checking the tables for the p-value of this t-statistic

- Degree of freedom = df = n - 1 = 200 - 1 = 199

- Significance level = 0.10

- The hypothesis test uses a one-tailed condition because we're testing only in one direction.

p-value (for t = 2.65, at 0.10 significance level, df = 199, with a one tailed condition) = 0.004348 = 0.004 to 3 d.p.

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.10

p-value = 0.004

0.004 < 0.10

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis and say that there is significant evidence to conclude that the results suggest that students who complete the core curriculum are ready for college-level mathematics. That is, the mean score of those that complete the core curriculum is above 23 and are ready for college-level mathematics.

e) The result of the p-value obtained is that there is significant evidence to conclude that the results suggest that students who complete the core curriculum are ready for college-level mathematics. That is, the mean score of those that complete the core curriculum is above 23 and are ready for college-level mathematics.

Hope this Helps!!!

Complete Question:

For a healthy human, a body temperature follows a normal distribution with Mean of 98.2 degrees Fahrenheit and Standard Deviation of 0.26 degrees Fahrenheit. For an individual suffering with common cold, the average body temperature is 100.6 degrees Fahrenheit with Standard deviation of 0.54 degrees Fahrenheit. Simulate 10000 healthy and 10000 unhealthy individuals and answer questions 14 to 16.

14. If person A is healthy and person B has a cold, which of the events are the most likely? Pick the closest answer.  

a. Person B will have higher temperature than 101 degrees.

b. Person A will have temperature higher than 99 degrees

c. Person B will have temperature lower than 100 degrees

d. ​​Person A will have temperature lower than 97.5 degrees

15. What would be a range [A to B], which would contain 68% of healthy individuals? Pick the closest answer.  

a. Between 97.9 and 98.46

b. Between 99.5 and 101.6

c. Between 100.06 and 101.14

d. Between 100.1 and 102.2

16. What is the approximate probability that a randomly picked, unhealthy individual (one with the cold) would have body temperature above 101 degrees Fahrenheit? Pick the closest answer.  

a. About 10%

b. About 15%

c. About 22%

c. About 34%

Answer:

14. option a

15. option a

16. option a

explanation:

14 option (a)

person B have higher temperature than 101 degrees,  

(b) cannot be true if person a has higher temperature than 99 then he has cold most likely and as mentioned by the standard dev and mean of healthy people  

(c) AND (d) also cannot be true as they also do not satisfy the given standard dev and mean

15 option (a) because of the A to B range and not B to A range ....... as the healthy person's standard dev is 0.26. Hence the 68% data will lie in 97.94 - 98.46

but, if it was B to A, then the (c) option will be true

16 option (a) because most of the unhealthy individuals above the 0.54 standard dev will come somewhat near 90%

Answer:

A. There is sufficient evidence to prove and conclude that the true average percentage differs from desired percentage.

B. P(Z<-4.93333) = 0.0000

C. n = 5945 samples

Step-by-step explanation:

A)

The rightnull and alternative hypotheses are given as below:

Null hypothesis H0: µ = 5.5

Alternative hypothesis Ha: µ ≠ 5.5

Conducting the one sample z test for population mean.

Test statistic formula is given as below:

Z = (Xbar - µ)/[σ/√(n)]

Given,

Xbar = 5.23

µ = 5.5

σ = 0.30

n = 16

Z = (5.23 – 5.5) / [ 0.30 /√(16)]

Z = -3.6000

P-value = 0.0003

α value = 0.05

P-value < α value

So, we reject the null hypothesis. There is sufficient evidence to prove and conclude that the true average percentage differs from desired percentage.

B

From the information given

Xbar = 5.23

µ = 5.6

σ = 0.30

n = 16

α value = 0.01

Z = (Xbar - µ)/[σ/√(n)]

Z = (5.23 - 5.6)/(0.30/√(16))

Z = -4.93333

P(Z<-4.93333) = 0.0000

Required probability = 0.0000

C

We are given α =0.01

Therefore, critical Z value = 2.57

E = 0.01

σ = 0.30

n = (Z*σ/E)^2

n = (2.57*0.30/0.01)^2 = 5944.41

n = 5945 samples

Answer:

Point of estimate of the true Proportion 'p' = 0.1941

Step-by-step explanation:

Explanation:-

Given data a random sample of 340 people in Chicago showed that 66 listened to WJKT-1450, a radio station in South Chicago Heights.

Given sample size 'n'= 340

Point of estimate of the true Proportion P  = [tex]\frac{x}{n}[/tex]

Properties of Estimation

An estimator is not expected to estimate the Population parameter without error.

An estimator should be close to the true value of un-known parameter.

Point of estimate of the true Proportion   = [tex]p = \frac{66}{340}= 0.1941[/tex]

Conclusion:-

Point of estimate of the true Proportion = 0.1941

Answer:

[tex]t=\frac{424-420}{\frac{26}{\sqrt{61}}}=1.202[/tex]    

[tex]p_v =2*P(t_{(60)}>1.202)=0.234[/tex]  

If we compare the p value and the significance level given [tex]\alpha=0.01[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the true mean is NOT different from  420. So the specification is satisfied.

Step-by-step explanation:

Data given and notation  

[tex]\bar X=424[/tex] represent the sample mean

[tex]s=26[/tex] represent the sample standard deviation

[tex]n=61[/tex] sample size  

[tex]\mu_o =420[/tex] represent the value that we want to test

[tex]\alpha=0.01[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is different from 420 or not, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 420[/tex]  

Alternative hypothesis:[tex]\mu \neq 420[/tex]  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]t=\frac{424-420}{\frac{26}{\sqrt{61}}}=1.202[/tex]    

P-value

The first step is calculate the degrees of freedom, on this case:  

[tex]df=n-1=61-1=60[/tex]  

Since is a two sided test the p value would be:  

[tex]p_v =2*P(t_{(60)}>1.202)=0.234[/tex]  

Conclusion  

If we compare the p value and the significance level given [tex]\alpha=0.01[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the true mean is NOT different from  420. So the specification is satisfied.

Answer:

x = -5/4    x=1

Step-by-step explanation:

5x^2 -x -4 =0

Factor

(5x+4) (x-1)=0

Using the zero product property

5x+4 =0  x-1 =0

5x=-4       x=1

x = -5/4    x=1

Answer:

x = -0.8, 1

Step-by-step explanation:

5x² - x - 4 = 0

5x² - 5x + 4x - 4 = 0

5x(x - 1) + 4(x - 1) = 0

(5x + 4)(x - 1) = 0

x = -⅘, 1

Answer:

Копиравать

Step-by-step explanation:

Копиравать ладно

Answer:

218

Step-by-step explanation:

327*2/3=218

Stokes' theorem says the integral of the curl of [tex]\vec F[/tex] over a surface [tex]S[/tex] with boundary [tex]C[/tex] is equal to the integral of [tex]\vec F[/tex] along the boundary. In other words, the flux of the curl of the vector field is equal to the circulation of the field, such that

[tex]\displaystyle\iint_S\nabla\times\vec F\cdot\mathrm d\vec S=\int_C\vec F\cdot\mathrm d\vec r[/tex]

We have

[tex]\vec F(x,y,z)=x^2\,\vec\imath+4x\,\vec\jmath+z^2\,\vec k[/tex]

[tex]\implies\nabla\times\vec F(x,y,z)=4\,\vec k[/tex]

Parameterize the ellipse [tex]S[/tex] by

[tex]\vec s(u,v)=\dfrac{u\cos v}{\sqrt5}\,\vec\imath+\dfrac{u\sqrt5\sin v}4\,\vec\jmath[/tex]

with [tex]0\le u\le1[/tex] and [tex]0\le v\le2\pi[/tex].

Take the normal vector to [tex]S[/tex] to be

[tex]\dfrac{\partial\vec s}{\partial\vec u}\times\dfrac{\partial\vec s}{\partial\vec v}=\dfrac u4\,\vec k[/tex]

Then the flux of the curl is

[tex]\displaystyle\iint_S4\,\vec k\cdot\dfrac u4\,\vec k\,\mathrm dA=\int_0^{2\pi}\int_0^1u\,\mathrm du\,\mathrm dv=\boxed{\pi}[/tex]

1 meter = 1,000 millimeter

We can solve this by making two proportion or millimeter over meter:  [tex]\frac{millimeter}{meter}[/tex]

[tex]\frac{19.5 mm}{x meter} = \frac{1,000 mm}{1 m}[/tex]

Now you must solve for the unknown meter under the first proportion:

(1,000)(x meter) = 19.5 * 1

1,000(x meter) = 19.5

x meter = 0.0195 m

19.5 mm = 0.0195 m

Hope this helped! Let me know if you have any further questions

~ Just a girl in love with Shawn Mendes

Answer:

a and c

Step-by-step explanation:

Looking at the pieces of information, the pieces of information that can be gathered from these box plots are:

Olympics actually refers to the major international event which usually features different sports and normally holds once in every four years. It is also known as the Games of the Olympiad.

From the pieces of information given, we can actually conclude that the above options can be gathered from the information.

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Given:

The given two functions are [tex]f(x)=\frac{4 x^{2}+24 x}{x^{2}-11 x+30}[/tex]  and  [tex]g(x)=\frac{x-5}{x^{2}}[/tex]

We need to determine the value of R(x)

Value of R(x):

The value of R(x) can be determined by R(x) = f(x) × g(x)

Substituting the values, we get;

[tex]R(x)=\frac{4 x^{2}+24 x}{x^{2}-11 x+30} \cdot \frac{x-5}{x^{2}}[/tex]

Multiplying the fractions, we have;

[tex]R(x)=\frac{\left(4 x^{2}+24 x\right)(x-5)}{\left(x^{2}-11 x+30\right) x^{2}}[/tex]

Let us factor out the common term 4x from the term (4x² + 24x)

Thus, we have;

[tex]R(x)=\frac{4 x(x+6)(x-5)}{\left(x^{2}-11 x+30\right) x^{2}}[/tex]

Let us factor the term (x² -11x + 30), we get;

[tex]R(x)=\frac{4(x+6)(x-5)}{x(x-5)(x-6)}[/tex]

Cancelling the common term, we have;

[tex]R(x)=\frac{4(x+6)}{x(x-6)}[/tex]

Thus, the value of R(x) is [tex]\frac{4(x+6)}{x(x-6)}[/tex]

Answer:

See the image below.

The lower of cost or market rule states that a business must record the cost of inventory at whichever cost is lower – the original cost or its current market price.

To determine the carrying value of inventory under the lower of cost or market (LCM) rule, we compare unit cost and unit replacement cost for each product and choose the lower value. We then multiply these values with their respective quantities and sum them to get the total carrying value. For inventory write-downs, we record an adjustment entry.

The carrying value of inventory for Forester Company at the end of December 31, 2018, involves two scenarios. In the first scenario, we apply the lower of cost or market (LCM) rule to individual products (product A through E). For each product, we compare its unit cost and unit replacement cost and choose the lower value. The total carrying value under this scenario is obtained by summing the products of the chosen values and the respective quantities.

In the second scenario, we apply the LCM rule to the entire inventory. Here, we compare the total cost and the total replacement cost of all products, and choose the lesser value as the carrying value of inventory. Inventory write-downs are typical business practice for Forester, in this case, we record an adjusting entry to recognize the loss resulting from decline in the value of inventory.

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Answer: the answer is zero my bad

Step-by-step explanation:

Answer:

g = - 30

Step-by-step explanation:

[tex] - 15 - \frac{g}{3} = - 5 \\ - \frac{g}{3} = - 5 + 15 \\ - \frac{g}{3} = 10 \\ - g = 10 \times 3 \\ - g = 30 \\ \huge \red{ \boxed{g = - 30}}[/tex]

Answer:

Fraction

Step-by-step explanation:

Answer:

fraction

Step-by-step explanation:

pls mark brainliest

The number of people in attendance are:

Children=70

Parents=140

Grandparents=190

Let

C represent children

P represent parents

G represent grandparents

Hence:

children+parents+ grandparent=400

P=2G

C=P+50 = 2G+50

2G+50 + 2G + G =400

5G=400-50

5G = 350

G=350/5

G =70 grandparents

P=70×2

P =140 parents

C=140+50

C =190 children

Inconclusion The number of people in attendance are:

Children=70

Parents=140

Grandparents=190

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The question is a math problem requiring a system of linear equations to solve. There were 70 grandparents, 140 parents, and 190 children at the family reunion. This was determined by assigning variables to each group and using the given conditions to form equations, which were then solved sequentially.

This problem can be solved using a system of linear equations. We can represent each group at the family reunion (children, parents, and grandparents) with a variable. To create equations from the information provided:

First, replace P and C in the total equation with the equivalent as per the other equations so it reads (2G + 50 + 2G + G = 400). Simplify this equation and you get 5G + 50 = 400. Solving for G, we find that there were 70 grandparents.

Plug the value of G (70) back in the equation for P (2*70), we find that there were 140 parents.

Similarly plug P (140) in the equation for C, we find that there were 190 children.

So, in conclusion, there were 70 grandparents, 140 parents, and 190 children at the family reunion.

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The average rate of change can be calculated using the formula: (g(b) - g(a)) / (b - a), substituting -5 for a and 5 for b in our case.

In order to find the average rate of change of a function, in this case, function g, from x = -5 to x = 5, we use the formula: (g(b) - g(a)) / (b - a), where b is the ending value and a is the starting value. This gives us the slope of the tangent line that connects these two points on the graph, which reflects the average rate of change of the function over the interval. In this case, to find the average rate of change of function g from x = -5 to x = 5, we would substitute -5 for a and 5 for b in the formula to get: (g(5) - g(-5)) / (5 - (-5)). From here we can solve based on the known values of g(5) and g(-5).

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Answer:

top 83 1/5

bottom 1,248

Step-by-step explanation:

i got it right

Answer:

Top 83 1/5

Bottom 1,248

Step-by-step explanation:

Just took it