People are entering a building at a rate modeled by f (t) people per hour and exiting the building at a rate modeled by g (t) people per hour, where t is measured in hours. The functions f and g are nonnegative and differentiable for all times t. Which of the following inequalities indicates that the rate of change of the number of people in the building is increasing at time t? o f (t) > 0 f (t)-9(t) > 0 o f (t)>0 of'(t)-g'(t) > 0

Answer:

D. [tex]\angle E \cong \angle E'[/tex] statement is true.

Step-by-step explanation:

Given:

Δ DEF was dilated by a scale factor 3 to create Δ D'E'F'

Solution:

A dilation is a transformation that produces an image that is the same shape as the original, but is of different size.

So, the shape of the triangles DEF and D'E'F' are the same.

Since the shape is similar the angle of the dilated triangle and considered triangle are the same.

A. Segment DF ≅ Segment D'F'

This statement is false as the triangles which are dilated by scale factor 3 cannot be congruent to each other

B.[tex]3 . m\angle D = m\angle D'[/tex]

This statement is false since the shape is similar the angle of the dilated triangle and considered triangle are the same.

C. Segment EF ≅ 3. Segment E'F'

This statement is false as dilation is a transformation that produces an image that is the same shape as the original, but is of different size so it cannot be congruent.

D.[tex]\angle E = \angle E'[/tex]

This statement is True as dilation is a transformation that produces an image that is the same shape as the original,Since the shape is similar the angle of the dilated triangle and considered triangle are the same.

Hence Option D.[tex]\angle E = \angle E'[/tex] is True

Answer:

(a) 0.87 (b) 0.3843

Step-by-step explanation:

We have the null and alternative hypotheses [tex]H_{0}: p = 0.56[/tex] and [tex]H_{a}: p\neq 0.56[/tex] (two-tailed alternative). There is a large sample size of n = 113 customers and a point estimate of p that is [tex]\hat{p} = 0.60[/tex] with an estimate standard deviation given by [tex]\sqrt{\hat{p}(1-\hat{p})/n} = \sqrt{0.60(1-0.60)/113} = 0.0461[/tex]. Then, the test statistic z which comes from a standard normal distribution is given by  

(a) [tex]z = \frac{\hat{p}-0.56}{\sqrt{\hat{p}(1-\hat{p})/n}}=(0.60-0.56)/0.0461 = 0.8677[/tex]

(b) The p-value is given by 2P(Z > 0.87) = 0.3843, this because we are dealing with a two-tailed alternative.

Answer:

-1/3

Step-by-step explanation:

Given that a simple game goes as follows: you pay one dollar and roll a die. If the roll is either a 1 or 2, you get your dollar back. If it is greater than 3 you lose the dollar you paid. If it is a 3, you get your dollar back and an additional dollar.

Your fee for the dollar would be 1 dollar always

If you roll 1 or 2, your gain is 0

If you roll 3, your gain is 1

If you roll 4 or 5 or 6you lose 1 dollar

Let X be the amount of gain.

X       0        1         -1

P       2/6     1/6      3/6  

E(x) = Sum of products of x with probabilities

= [tex]\frac{1}{6} -\frac{3}{6} \\=\frac{-2}{6} \\=\frac{-1}{3}[/tex]

Note:  this is not a fair game to play since expected gain is negative.

Answer: The purpose of statistical inference is to provide information about the population based upon information contained in the sample.

The mean and standard error of the mean are 200 and 2 respectively.

Step-by-step explanation:

Statistical inference is used to draw conclusions about the some unknown parameter based on samples that are drawn from the original population.

The formula for central limit theorem can be stated as follows:

[tex]\begin{array}{l}\\{\mu _{\bar x}} = \mu \\\\{\sigma _{\bar x}} = \frac{\sigma }{{\sqrt n }}\\\end{array}[/tex]

Here, [tex]\mu[/tex] is the population mean, [tex]\sigma[/tex] is the population standard deviation, [tex]{\mu _{\overline x }}[/tex]  is the sample mean, [tex]{\sigma _{\overline x }}[/tex]  is the sample variance and [tex]n[/tex] is the sample size.

The option (a), “sample based upon information contained in the population” is incorrect because the estimate is calculated based on sample.

The option (c), “population based upon information contained in the population” is incorrect because statistical inference helps to draw conclusions about some unknown parameter based on sample data.

The option (d), “mean of the sample based upon the mean of the population” is incorrect because statistical inference draws some conclusions about some unknown parameter of population based on sample and not based on mean of population.

As the statistical inference is used to draw some conclusions based on sample data, options (a), (c), and (d) are the incorrect answer choices.

Statistical inference draws some conclusions or estimate the unknown parameter based on sample drawn from population. That is, the conclusion about population is made based on the sample data. Hence, option (b), “population based upon information contained in the sample” is the correct answer in the provided scenario.

As the statistical inference draw some conclusions about the population based upon information contained in sample, option (b) can be considered as correct answer choice.

According to provided data, the population mean is equal to 200, population variance is equal to 18 and sample size is equal to 81.

The mean of sampling means can be calculated as:

[tex]\begin{array}{c}\\{\mu _{\bar x}} = \mu \\\\ = 200\\\end{array}[/tex] 

The standard error of the mean can be calculated as:

[tex]\begin{array}{c}\\{\sigma _{\bar x}} = \frac{\sigma }{{\sqrt n }}\\\\ = \frac{{18}}{{\sqrt {81} }}\\\\ = \frac{{18}}{9}\\\\ = 2\\\end{array}[/tex]

So, the options (a), (b) and (c) are considered as incorrect options because the values do not match with the obtained values of mean and the standard error of the mean..

The options (a), (b) and (c) are considered as incorrect answer choice because the obtained value of mean and standard error of the mean is 200 and 2 respectively.

The obtained value of mean and standard error of the mean is 200 and 2 respectively. So, it can be said that option (d) is the correct answer in the provided scenario.

Statistical inference aims to draw conclusions about a population based on sample data, and for random samples of size 81 from a population with a mean of 200 and standard deviation of 18, the mean and standard error of the sample mean are 200 and 2, respectively.

The purpose of statistical inference is to provide information about the population based upon information contained in the sample. This includes estimating a population parameter like the mean or proportion by analyzing a subset of collected data. When dealing with samples, specifically random samples, we use inferential statistics to make assumptions about the larger population from which the sample is drawn.

When you have random samples of size 81 from an infinite population with a known mean (μ = 200) and standard deviation (σ = 18), and the distribution of the population is unknown, the distribution of the sample means will approach a normal distribution according to the Central Limit Theorem. The mean of the sampling distribution of the sample mean will be the same as the population mean, so the correct answer is 200.

The standard error of the mean (SEM) is calculated as the population standard deviation divided by the square root of the sample size (n). Thus, SEM = σ/√n = 18/√81 = 18/9 = 2. Therefore, the answer is 200 for the mean and 2 for the standard error of the mean.

Answer: The population proportion is between 0.34 and 0.46 .

Step-by-step explanation:

Interpretation of 95% confidence interval : A person can be about 95% confident that the true population parameter lies in the interval.

A confidence interval is constructed for an unknown population proportion, p. A sample is collected, and the 95% confidence interval is calculated to be 0.40 ± 0.06.

i.e. Lower limit = [tex]0.40-0.06=0.34[/tex]

Upper limit =  [tex]0.40+0.06=0.46[/tex]

i.e. 95% confidence interval = (0.34, 0.46)

i.e. A person can be about 95% confident that the true population proportion (p) lies in the interval  (0.34, 0.46).

⇒ It is most accurate to say that there is approximately 95% confidence in the assertion that:

The population proportion is between 0.34 and 0.46 .

Answer:

Step-by-step explanation:

Which statement about the siege of Savannah and its outcome is correct?

A

The siege was a failed attempt by American forces to retake Savannah from the British.

B

The siege was a failed attempt by British forces to retake Savannah from the Americans.

C

The siege was a successful attempt by American forces to retake Savannah from the British.

D

The siege was a successful attempt by British forces to retake Savannah from the Americans.

Answer:

z-score is 2.16

98.46% of men are SHORTER than 6 feet 3 inches

Step-by-step explanation:

The heights of adult men in America are normally distributed, with a mean of 69.3 inches and a standard deviation of 2.64 inches.

Mean = [tex]\mu = 69.3 inches[/tex]

Standard deviation = [tex]\sigma = 2.64 inches[/tex]

a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)

x = 6 feet 3 inches

1 feet =12 inches

6 feet = 12*6 = 72 inches

So, x = 6 feet 3 inches  = 72+3=75 inches

Formula : [tex]Z=\frac{x-\mu}{\sigma}[/tex]

[tex]Z=\frac{75-69.3}{2.64}[/tex]

[tex]Z=2.159[/tex]

So, his z-score is 2.16

No to find percentage of men are SHORTER than 6 feet 3 inches

We are supposed to find P(x< 6 feet 3 inches)

z-score is 2.16

Refer the z table

P(x< 6 feet 3 inches) =0.9846

So, 98.46% of men are SHORTER than 6 feet 3 inches

Answer:

1.00 and 1.73

Step-by-step explanation:

1) Calculating the 1st and the 2nd leg using trigonometric function sine:

[tex]sin (30^{0})=\frac{c}{2}\Rightarrow \frac{1}{2}=\frac{c}{2}\Rightarrow 2*\frac{1}{2}=2*\frac{c}{2}\Rightarrow c=1\\sin(60^0)=\frac{b}{2}\Rightarrow \frac{\sqrt{3}}{2}=\frac{b}{2}\Rightarrow b=\sqrt{3}\Rightarrow\: b\approx \:1.73[/tex]

Once one leg is found there is another way to find the other leg, using Pythagorean Theorem too.

[tex]a^{2}=b^{2}+c^{2}\Rightarrow 2^{2}=b^{2}+1^{2}\Rightarrow 4-1=b^{2}\Rightarrow b=\sqrt{3} b\approx 1.73[/tex]

Sides

a hypotenuse: 2.00

-------------------------------

b leg: 1.73

--------------------------------

c leg: 1.00

--------------------------------

The question asks for an Oz function to parse and evaluate arithmetic expressions represented by tuples. The Eval function recursively breaks down the expressions into smaller parts until it‘s a single integer. Pattern matching is used to simplify the process of breaking down the expressions.

For this task, we are required to implement an Oz function named Eval that evaluates arithmetic expressions built using tuples. Each tuple represents an arithmetic operation, integer or variable. The function uses an environment record to map each variable to an integer.

Here is a specification and possible Oz implementation of the Eval function:

fun {Eval Exp Env}

case Exp of int(N) then N
mul(X Y) then {Mul {Eval X Env} {Eval Y Env}}
add(X Y) then {Add {Eval X Env} {Eval Y Env}}
var(A) then {Find A Env}
else raise system.error end

Here, the Eval function breaks down the expression based on its pattern and recursively reduces the expression until it's a single integer. The Find function is a helper function that looks up the value of a variable in the environment. We can use pattern matching to simplify the process of breaking down the expressions, which is a powerful feature in Oz.

https://brainly.com/question/34469129

#SPJ12

Answer:

y int = 6

Step-by-step explanation:

simplistic plotting in my head

A line is drawn on the coordinate plane that passes through the point (10,1) and has a slope given as -0.5. The y intercept will be 6.

The intersection of the graph of the function with the y-axis gives y-intercept of that function.

The y-intercept is the value of y on the y-axis at which the considered function intersects it.

Assume that we've got: y = f(x)

At y-axis, we've got x = 0, so putting it will give us the y-intercept.

Thus, y-intercept of y = f(x) is y = f(0)

A line is drawn on the coordinate plane that passes through the point (10,1) and has a slope given as -0.5.

So the equation of line

y = mx + c

1 = -0.5(10) + c

1 = -5 + c

c = 6

Hence, The cut-off point with the "y" axis is 6.

Learn more about y-intercept here:

https://brainly.com/question/16540065

#SPJ5

Answer:

There is an association between drying choice and illness

a.True

Step-by-step explanation:

H_0: There is no association between the drying choice and ilness

H_a: There is an association between drying choice and illness

(Two tailed chi square test)

Observations are given as per the following table

Observed    

Sick Not sick  

Paper 19 27 46

Hot air 10 42 52

29 69 98

Expected row total*col total/grand total  

Paper 13.6122449 32.3877551 46

Hot air 15.3877551 36.6122449 52

29 69 98

Chi square =(observed-expected)^2/Expected    

Paper 2.132484778 0.896261718 3.028746496

Hot air 1.886428842 0.792846905 2.679275747

4.01891362 1.689108623 5.708022243

Thus chi square = 5.708

degrees of freedom = (r-1)(c-1) = 1

p value = 0.0167

Since p <0.05 our alpha we reject null hypothesis

At 5% significance level, we can say

There is an association between drying choice and illness

a.True

For the first one, since the slope is 0 the line must be just a horizontal line that passes through the given point. The equation would be y=-4 because the y coordinate for the point is -4.

For the second problem, utilize y=mx+b, the parent equation for slope intercept form (m-slope, b-y intercept).

y=mx+b

-4=-1/3(5)+b

b=-2 1/3

equation: y=-1/3x - 2 1/3

Answer:

  C)  60°

Step-by-step explanation:

The sum of the acute angles in a right triangle is 90°, so we have ...

  α + β = 90

  (5x³ +20) +(2x³ +14) = 90

  7x³ = 56 . . . . . . subtract 34, collect terms

  x³ = 8 . . . . . . . . divide by 7

Using this value in the expression for α, we find its measure to be ...

  α = 5·8 +20 = 60

  α = 60°

The P-value is 0.0000; we reject the null hypothesis and conclude males consume more energy drinks than females.

We will conduct a hypothesis test for the difference between two means. Here are the steps we'll follow:

1. **State the Hypotheses**:

2. **Check the Conditions**:

3. **Calculate the Test Statistic**:

  We'll use the formula for the test statistic for two independent samples (assuming equal variances are not assumed):

  [tex]\[ t = \frac{(\bar{x}_1 - \bar{x}_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \][/tex]

  where:

4. **Calculate the Degrees of Freedom**:

  We'll use the Welch-Satterthwaite equation to approximate the degrees of freedom for the t-distribution:

[tex]\[ df = \frac{\left(\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}\right)^2}{\frac{\left(\frac{s_1^2}{n_1}\right)^2}{n_1 - 1} + \frac{\left(\frac{s_2^2}{n_2}\right)^2}{n_2 - 1}} \][/tex]

5. **Find the P-value**:

  Since we are conducting a one-tailed test, we will find the area to the right of our calculated t-value in the t-distribution with the calculated degrees of freedom.

6. **State the Conclusion**:

  We will compare the P-value to the significance level (usually 0.05) and decide whether to reject the null hypothesis.

Let's perform the calculations.

The test statistic (t-value) for the difference in the mean number of energy drinks consumed per month between male and female college students is approximately 4.3285. The degrees of freedom for this test is approximately 720.78.

The P-value for this one-tailed test is approximately 0.00000857 (rounded to four decimal places, this is 0.0000). Since the P-value is significantly less than the common alpha level of 0.05, we reject the null hypothesis.

**Conclusion**: We can conclude that there is significant evidence at the 0.05 level to suggest that the mean number of energy drinks consumed by male college students is greater than that consumed by female college students.

Answer:

(x + 3)^2 + (y + 2)^2 = 98.

Step-by-step explanation:

(x - h)^2 + (y - k) ^2 = r^2   ( center is (h, k) and r = radius.)

So we have:

(x + 3)^2 + (y + 2)^2 = r^2

When x = 4 y = 5, so

(4 + 3)^2 + (5 + 2)^2 = r^2

r^2 =  7^2 + 7^2 =  98

.

Answer:

Step-by-step explanation:

(x+2)^2+(y+3)^2=100

To find the probability that a butterfly will live between 12.04 and 18.38 days, calculate the z-scores for both values and use the standard normal distribution table. The probability is approximately 0.4203.

To find the probability that a butterfly will live between 12.04 and 18.38 days, we need to calculate the z-scores for both values and then use the standard normal distribution table. The z-score for 12.04 can be calculated as:

z = (12.04 - 18.8) / 2 = -3.38

The z-score for 18.38 can be calculated as:

z = (18.38 - 18.8) / 2 = -0.21

Using the standard normal distribution table, we can find the area under the curve between these two z-scores, which represents the probability of a butterfly living between 12.04 and 18.38 days. The probability is approximately 0.4203, which corresponds to option b) in the given choices.

https://brainly.com/question/32117953

#SPJ12

In a normal distribution of butterfly lifespan with mean of 18.8 and standard deviation of 2, the probability that a butterfly will live between 12.04 and 18.38 days is 0.4164.

In this problem, we are dealing with a normal distribution of the average butterfly lifespan, with a mean of 18.8 days and standard deviation of 2 days. We are asked to find the probability that a butterfly will live between 12.04 and 18.38 days. This involves the use of z-scores, which standardize these specific values into terms of standard deviation units from the mean. They are calculated as follows:

Z = (X - μ) / σ

Applying this formula, for X = 12.04, the z-score becomes:

Z = (12.04 - 18.8) / 2 = -3.38

For X = 18.38, the z-score is:

Z = (18.38 - 18.8) / 2 = -0.21

The probability between these Z-scores using a Z-table lookup gives an answer of 0.4164. Therefore, the correct answer is (a) 0.4164.

https://brainly.com/question/34741155

#SPJ11

Answer:

Null hypothesis:[tex]p=0.1[/tex]  

Alternative hypothesis:[tex]p \neq 0.1[/tex]  

[tex]z=\frac{0.087 -0.1}{\sqrt{\frac{0.1(1-0.1)}{367}}}=-0.83[/tex]  

[tex]p_v =2*P(z<-0.83)=0.41[/tex]  

The p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of orders that were not accurate is not significant different from 0.1 or 10% .  

and the accuracy of the test yes is acceptable since the p value obtained is large enough to fail to reject the null hypothesis.

Step-by-step explanation:

Data given and notation n  

n=367 represent the random sample taken

X=32 represent the orders that were not accurate

[tex]\hat p=\frac{32}{367}=0.087[/tex] estimated proportion of orders that were not accurate

[tex]p_o=0.1[/tex] is the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

[tex]p_v{/tex} represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the rate of inaccurate orders is equal to 10%:  

Null hypothesis:[tex]p=0.1[/tex]  

Alternative hypothesis:[tex]p \neq 0.1[/tex]  

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.087 -0.1}{\sqrt{\frac{0.1(1-0.1)}{367}}}=-0.83[/tex]  

Statistical decision  

It's important to refresh the p value method or p value approach . "This methos is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

[tex]p_v =2*P(z<-0.83)=0.41[/tex]  

So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of orders that were not accurate is not significant different from 0.1 or 10% .  

Answer:

a) 0.5198 computers per household

b) 0.01153 computers

Step-by-step explanation:

Given:

number of computers in a home,

q = 0.3458 ln x - 3.045 ;   10,000 ≤ x ≤ 125,000

here x is mean household income

mean income = $30,000

increasing rate, [tex]\frac{dx}{dt}[/tex] = $1,000

Now,

a) computers per household are

since,

mean income of  $30,000 lies in the range of 10,000 ≤ x ≤ 125,000

thus,

q = 0.3458 ln(30,000) - 3.045

or

q = 0.5198 computers per household

b) Rate of increase in computers i.e [tex]\frac{dq}{dt}[/tex]

[tex]\frac{dq}{dt}[/tex] = [tex]\frac{d(0.3458 ln x - 3.045)}{dt}[/tex]

or

[tex]\frac{dq}{dt}=0.3458\times(\frac{1}{x})\frac{dx}{dt} - 0[/tex]

on substituting the values, we get

[tex]\frac{dq}{dt}=0.3458\times(\frac{1}{30,000})\times1,000[/tex]

or

= 0.01153 computers

The computers per household are 0.5187 and the number of computers in a home increasing is 0.01153.

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

In the 1990s the demand for personal computers in the home went up with household income.

For a given community in the 1990s, the average number of computers in a home could be approximated by

q = 0.3458 ln x − 3.045

10,000 ≤ x ≤ 125,000

where x is mean household income.

A certain community had a mean income of $30,000, increasing at a rate of $1,000 per year.

a)  Computer per household will be

Mean income of $30,000 lies in the range of 10,000 ≤ x ≤ 125,000

Then

q = 0.3458 ln (30000) − 3.045

q = 0.5187

b)  The rate of increase in computers will be

[tex]\rm \dfrac{dq}{dt} = \dfrac{d}{dt} 0.3458lnx -3.045\\\\\\\dfrac{dq}{dt} = 0.3458 * \dfrac{1}{x} *\dfrac{dx}{dt}\\\\\\\dfrac{dq}{dt} = 0.3458 * \dfrac{1}{30000} *1000\\\\\\\dfrac{dq}{dt} = 0.01153[/tex]

More about the differentiation link is given below.

https://brainly.com/question/24062595

Answer:the probability that 2 will stick with their tour group is 0.21

Step-by-step explanation:

The survey found that 23% of the respondents stick with their tour group. This means that the probability of success,

p is 23/100 = 0.23

Probability of failure, q = 1 - p = 1 - 0.23

q = 0.77

Number of international travellers sampled, n is 6

Assuming a binomial distribution for the responses, the formula for binomial distribution is

P(x = r) = nCr × q^(n-1) × p^r

To determine the probability that 2 will stick with their tour group, we would determine

P( x= r = 2). It becomes

6C2 × 0.77^(6-1) × 0.23^2

= 15 × 0.77^5 × 0.0529

= 0.21

The probability that exactly 2 out of 6 international travelers will stick with their tour group, given that the probability of an individual sticking with the group is 23%, is approximately 27.81%.

The problem described involves calculating the probability of a specific number of successes in a series of independent trials and is an example of a binomial probability problem. In this case, with the probability that a person sticks with their tour group being 23%, or 0.23, and a sample of 6 international travelers, we want to find the probability that exactly 2 out of these 6 travelers stick with their group. This can be calculated using the binomial probability formula:

P(X = k) = [tex]C(n, k) \times p^k \times (1-p)^{n-k}[/tex]

Where:

P(X = k) is the probability of k successes in n trials

C(n, k) is the combination of n things taken k at a time

p is the probability of success on a single trial

n is the number of trials

k is the number of successes in n trials

For our problem:

P(X = 2) = C(6, 2) x [tex]0.23^2[/tex]x[tex](1-0.23)^{6-2}[/tex]

Calculating the combination, we have C(6, 2) = 6! / (2! x (6-2)!).

Thus:

P(X = 2) = 15 x [tex](0.23^2)[/tex] x [tex](0.77^4)[/tex]

P(X = 2) = 15 x 0.0529 x 0.3515

P(X = 2) = 0.2781

Therefore, the probability that exactly 2 of the 6 international travelers will stick with their tour group is approximately 0.2781, or 27.81%.

Answer:

a) [tex]tc=\pm 1.9601[/tex]

b) [tex]m=1.9601 \frac{26.34}{\sqrt{2322}}=1.0714[/tex]

c) The 95% confidence interval is given by (63.09;65.23)

Step-by-step explanation:

1) Notation and definitions

n=2322 represent the sample size

[tex]\bar X= 64.16[/tex] represent the sample mean

[tex]s=26.34[/tex] represent the sample standard deviation

m represent the margin of error

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".  

2) Calculate the critical value tc

In order to find the critical value is impornta to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. The degrees of freedom are given by:

[tex]df=n-1=2322-1=2321[/tex]

We can find the critical values in excel using the following formulas:

"=T.INV(0.025,2321)" for [tex]t_{\alpha/2}=-1.9601[/tex]

"=T.INV(1-0.025,2321)" for [tex]t_{1-\alpha/2}=1.9601[/tex]

The critical value [tex]tc=\pm 1.9601[/tex]

3) Calculate the margin of error (m)

The margin of error for the sample mean is given by this formula:

[tex]m=t_c \frac{s}{\sqrt{n}}[/tex]

[tex]m=1.9601 \frac{26.34}{\sqrt{2322}}=1.0714[/tex]

4) Calculate the confidence interval

The interval for the mean is given by this formula:

[tex]\bar X \pm t_{c} \frac{s}{\sqrt{n}}[/tex]

And calculating the limits we got:

[tex]64.16 - 1.9601 \frac{26.34}{\sqrt{2322}}=63.09[/tex]

[tex]64.16 + 1.9601 \frac{26.34}{\sqrt{2322}}=65.23[/tex]

The 95% confidence interval is given by (63.09;65.23)

To answer this question, we must calculate the percentage of the total population in each SAT score category that was admitted to the university. We find that 55% of admitted applicants had a Math SAT scores of 700 or more.

First, multiply the overall percentage of applicants by the percentage admitted for each SAT score category. For those with scores of 700 or more, you get 36% * 38% = 13.68%. For those with scores less than 700, it's 18% * 62% = 11.16%. Then, add these results together to get the total percentage of all applicants who were admitted, which is 24.84%.

The next step is to calculate what fraction of this combined admitted students group got a Math SAT of 700 or more. The percentage of admitted students who had a SAT score of 700 or more is the percentage of admitted students in that category divided by the total percentage of all admitted students. So, you get 13.68% ÷ 24.84% = 55.05%. This rounds to 55% when expressed as a percentage, so we can say that 55% of admitted applicants had a Math SAT of 700 or more.

https://brainly.com/question/33594301

#SPJ12

Final answer:

To find the percentage of admitted applicants with a Math SAT of 700 or more, calculate the overall admission rate (AR), and then determine Group A's contribution to this rate. The percentage of admitted applicants with an SAT score of 700 or more is approximately 55% after rounding to the nearest percentage point.

Explanation:

To find the percentage of admitted applicants who had a Math SAT score of 700 or more, we can use the information provided to set up a weighted average problem. Let's denote the applicants with a Math SAT of 700 or more as Group A and those with a Math SAT of less than 700 as Group B.

From the information given:

36% of Group A were admitted.

18% of Group B were admitted.

38% of all applicants are in Group A; hence, 62% are in Group B (100% - 38%).

We want to find the percentage of all admitted students that had a Math SAT of 700 or more. The overall admission rate (AR) can be calculated as follows:

AR = (Percentage of Group A × Admission rate of Group A) + (Percentage of Group B × Admission rate of Group B)

AR = (38% × 36%) + (62% × 18%)

AR = 13.68% + 11.16%

AR = 24.84%

Next, we calculate the contribution of Group A to the overall admission rate:

Contribution from Group A = Percentage of Group A × Admission rate of Group A

Contribution from Group A = 38% × 36%

Contribution from Group A = 13.68%

Now, we find the percentage of the total admissions that were applicants with a Math SAT of 700 or more:

Percentage of admitted applicants with SAT ≥ 700 = (Contribution from Group A ÷ Overall admission rate) × 100

Percentage of admitted applicants with SAT ≥ 700 = (13.68% ÷ 24.84%) × 100

Percentage of admitted applicants with SAT ≥ 700 ≈ 55% (rounded to nearest percentage point)

Answer:

15th term =29/3

16th term = 31/3

Step-by-step explanation:

Given an arithmetic sequence with the first term a1 and the common difference d , the nth (or general) term is given by an=a1+(n−1)d .

First we find the 15th term

n=15

a1=1/3

d=1 - 1/3 = 2/3

Solution

1/3+(15-1)2/3

1/3+28/3

(1+28)/3

29/3

Lets find the 16th term

1/3+(16-1)2/3

1/3+30/3

(1+30)/3

31/3

Answer:

46

Step-by-step explanation:

The order of operations is to multiply before you divide.

2x9= 18

2x14=28

18+28=46

Answer:

46

Step-by-step explanation:

2*9=18

2*14=28

18+28=46

Answer:

a. t-test for the population mean

Step-by-step explanation:

given that the average US woman wears 515 chemicals on an average day from her makeup and toiletries

A random sample from California found that on average the California woman wears 325 chemicals per day with a standard deviation of 90.5.

Note that here we have only sample std deviation and not population.

So better to use t test here.

Sample size is not given so whatever be the sample size here t test would be more appropriate.

Here we are testing for mean.  So the correct answer is

a. t-test for the population mean

Answer:

y = 50

t=0

we find at end of 40 minutes value of salt is y = 242.735

Step-by-step explanation:

explanation has been defined in attachment

Final answer:

The amount of salt in the tank at the end of 40 minutes is 370 pounds.

Explanation:

To find the amount of salt in the tank after 40 minutes, we need to calculate the net change in the amount of salt in the tank during that time. The tank initially contains 200 gallons of brine with 50 pounds of salt, and brine is flowing in and out of the tank at a rate of 4 gallons per minute. Since the salt concentration in the brine entering the tank is 2 pounds per gallon, the amount of salt entering the tank each minute is 4 gallons x 2 pounds = 8 pounds.

Therefore, the net change in the amount of salt in the tank after 40 minutes is 40 minutes x 8 pounds/minute = 320 pounds. Adding this to the initial amount of salt in the tank, we get 50 pounds + 320 pounds = 370 pounds of salt in the tank at the end of 40 minutes.

Answer:

Option C.

Step-by-step explanation:

Given information:

Male-Full stop = 6, Male-Rolling stop = 16, Male-No stop = 4

Female-Full stop = 6, Female-Rolling stop = 15, Female-No stop = 3

Using the given information we get

Total number of males = 6 + 16 + 4 = 26

Total number of males = 6 + 15 + 3 = 24

Probability of No stop is

[tex]p=\dfrac{\text{No-stop}}{Total}[/tex]

[tex]p=\dfrac{4+3}{50}[/tex]

[tex]p=\dfrac{7}{50}[/tex]

We need to find the number of males that would we expect to not stop at all.

Expected number of males = Number of males × Probability

Expected number of males = [tex]26\times \dfrac{7}{50}[/tex]

Expected number of males = [tex]3.64[/tex]

Therefore, the correct option is C.

If gender is independent of type of stop, the expected number of males who would not stop at all is calculated by the formula (Total Males * Total No Stops) / Total Observations, resulting in approximately 3.64.

To determine the expected number of males who would not stop at all at the stop sign, we would use the formula for expected frequency in a contingency table if the two variables are independent. The formula is (row total * column total) / grand total.

From the given data, the total number of males is the sum of male full stops, rolling stops, and no stops (6 + 16 + 4 = 26). The total number of 'no stops,' regardless of gender, is 4 (male) + 3 (female) = 7. The grand total of all observations is 50 (sum of all types of stops for both genders).

So, plug these values into the formula, we get: Expected no stops (male) = (26*7)/50 = 3.64

So, if gender and stop type were not associated, we would expect approximately 3.64 males to not stop at all at the stop sign, almost matching option C from the list provided.

https://brainly.com/question/32669885

#SPJ11

Answer:

  c.  20 baskets per hour

Step-by-step explanation:

In this context, "per" can be considered to mean "divided by." Then to find the unit rate in terms of baskets per hour, we compute ...

  rate = (baskets)/(hours) = (60 baskets)/(3 hours) = (60/3) baskets/hour

  rate = 20 baskets/hour . . . . matches choice C

Answer: There are 2.25×10³⁴ bacteria at the end of 24 hours.

Step-by-step explanation:

Since we have given that

Number of bacteria initially = 1

It triples in number every 20 minutes.

So, [tex]\dfrac{20}{60}=\dfrac{1}{3}[/tex]

So, our equation becomes

[tex]y=y_0e^{\frac{1}{3}k}\\\\3=1e^{\frac{1}{3}k}\\\\\ln 3=\dfrac{1}{3}k\\\\k=\dfrac{1.099}{0.333}=3.3[/tex]

We need to find the number of bacteria that it will contain at the end of 24 hours.

So, it becomes,

[tex]y=1e^{24\times 3.3}\\\\y=e^{79.1}\\\\y=2.25\times 10^{34}[/tex]

Hence, there are 2.25×10³⁴ bacteria at the end of 24 hours.

The colony will contain approximately 3,486,784,401 bacteria at the end of 24 hours.

The bacteria colony starts with 1 bacterium and triples in number every 20 minutes. To determine the number of bacteria at the end of 24 hours, we need to calculate the number of 20-minute intervals in 24 hours. There are 24 hours in a day, so there are 24 intervals of 20 minutes in a day. Therefore, the bacteria would triple in number 24 times. Starting with 1 bacterium, after 24 intervals, the number of bacteria would be:

1 * 3^24 = 1 * 3,486,784,401

So, at the end of 24 hours, the colony would contain approximately 3,486,784,401 bacteria.

https://brainly.com/question/12490064

#SPJ3