A department store wants to know what fraction of its customers in a certain market have store credit cards, and what their average balance might be. Of the 120 customers surveyed, 30 had store credit cards. Amongst those customers, the average balance was $600, with a sample standard deviation of $80. Find the 98% confidence interval for the average credit card balance. ( , ) Round your answers to two decimal places.

Answer:

x = 42

Step-by-step explanation:

The two angles are complementary so the add to 90 degrees.

x+48 = 90

Subtract 48 from each side

x+48-48=90-48

x = 42

Answer:

The angle x°=42.

Step-by-step explanation:

∠PQS equals 90° because it's a right angle (denoted with the square on the bottom).

∠PQS = ∠PQR + ∠RQS

So, ∠RQS = ∠PQS - ∠PQR where ∠PQR = 48°

Plug in the Values:

∠RQS = 90° - 48° = 42°

Given:

The given parent function is [tex]f(x)=x^2[/tex]

We need to determine the equation of the new translated (shifted) function g(x).

Vertical stretch:

The general rule to shift the graph f(x), to shift c units upward is [tex]g(x)=f(x)+c[/tex]

From the graph, it is obvious that the graph f(x) is shifted 1 unit upwards.

Thus, applying the above rule, we get;

[tex]g(x)=x^2+1[/tex]

Horizontal stretch:

The general rule to shift the graph f(x) to shift c units to the left is [tex]g(x)=f(x+c)[/tex]

From, the graph, it is obvious that the graph f(x) is shifted 2 units to the left.

Thus, applying the above rule, we have;

[tex]g(x)=(x+2)^2[/tex]

Equation of the new function g(x):

From the figure, it is obvious that the graph g(x) is shifted 1 unit upwards and 2 units to the left.

Thus, we have;

[tex]g(x)=(x+2)^2+1[/tex]

Therefore, the equation of the new function g(x) is [tex]g(x)=(x+2)^2+1[/tex]

Answer:

61 degrees

Step-by-step explanation:

87+32=119

180 (total degrees for triangle)-119=67 degrees

The answer is 15.66

Answer:

15.66

Step-by-step explanation:

[tex]18\% \: of \: 87 \\ \\ = \frac{18}{100} \times 87 \\ \\ = 0.18 \times 87 \\ \\ = 15.66 \\ [/tex]

Answer:

y=6

Step-by-step explanation:

3=9-y

y+3=9

y=6

Answer:

y=6

Step-by-step explanation:

3=9-y

3-9 = -y

-6 = -y

y=6

Answer:

Tyler ran 2030 meters. Jennifer ran 2386. Together they ran 4416 meters.

Step-by-step explanation:

Turn the km to m then add them together to get Tyler's distance. From Tyler's distance add what Jennifer ran more of to Tyler's to get Jennifer's distance. Then add together what they ran to get the total amount of meters they ran.

Answer:586

Step-by-step explanation:

Answer and explanation:

Here is code:

credit = int(input("Enter credits : "))

if credit < 7:

print("You are a Freshman")

elif credit >= 7 and credit < 16:

print("You are a Sophomore")

elif credit >= 16 and credit < 26:

print("You are a Junior")

elif credit >= 26:

print("You are a Senior")

Output: check image

To calculate a student's class standing, use conditional statements to determine the appropriate class based on the number of credits earned.

To write a program that calculates a student's class standing based on the number of credits earned, you can use conditional statements. Here's a step-by-step explanation:

Take the input of the number of credits earned from the user.

Use conditional statements (if, else if) to check the number of credits and assign the appropriate class standing.

If the number of credits is less than 7, then the student is a Freshman. If it is at least 7 and less than 16, then the student is a Sophomore.

If it is at least 16 and less than 26, then the student is a Junior. Otherwise, the student is a Senior.

Display the class standing to the user.

Here's an example pseudocode:

credits = input('Enter the number of credits earned: ')

if credits < 7:

   print('Class Standing: Freshman')

elif credits < 16:

   print('Class Standing: Sophomore')

elif credits < 26:

   print('Class Standing: Junior')

else:

   print('Class Standing: Senior')

Learn more about Calculating class standing here:

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Answer:

Step-by-step explanation:

From the information given we know that

[tex]p \equiv 0 \,\,\,\, \text{mod(3)}\\p \equiv 1 \,\,\,\, \text{mod(5)}\\p \equiv 2 \,\,\,\, \text{mod(7)}\\[/tex]

And we know as well that

[tex]p \equiv x \,\,\,\, \text{mod(11)}\\p \equiv x \,\,\,\, \text{mod(13)}[/tex]

Remember what that the Chinese reminder theorem states.

Theorem:

Let  p,q be coprimes, then the system of equations

[tex]x \equiv a \,\,\,\, mod(p)\\x \equiv b \,\,\,\, mod(q)[/tex]

has a unique solution [tex]mod(pq)[/tex].

Now, if you read the proof of the theorem you will notice that  if

[tex]q_1 = q^{-1} \,\, mod(p) , p_1 = p^{-1} \,\,mod(q)[/tex]

the the solution looks like this.

[tex]x = aqq_1 + bpp_1[/tex]

Now. you can easily generalize what I just stated for multiple equations and you will see that if you apply the theorem for this case it is straightforward that

[tex]p \equiv 0*35*[35^{-1}]_3+1*21*[21^{-1}]_5+2*15[15^{-1}]_7 \,\,\,\,\,\,\,\, mod(3*5*7)\\p \equiv 1*21*1+2*15*1 \,\,\,\,\,\,\,\,mod(105) \\p \equiv 1*21*1+2*15*1 \,\,\,\,\,\,\,\, \\p \equiv 51[/tex]

Therefore, Alice is in room 51.

(b)

Using the Chinese reminder theorem you need less than 2 erasures. The process is very similar.

Answer:

Step-by-step explanation:

From the information given we know that

And we know as well that

Remember what that the Chinese reminder theorem states.

Theorem:

Let  p,q be coprimes, then the system of equations

has a unique solution .

Now, if you read the proof of the theorem you will notice that  if

the the solution looks like this.

Now. you can easily generalize what I just stated for multiple equations and you will see that if you apply the theorem for this case it is straightforward that

Therefore, Alice is in room 51.

(b)

Using the Chinese reminder theorem you need less than 2 erasures. The process is very similar.

Step-by-step explanation:

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

On the planet of Mercury, 4-year-olds average 3.2 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.7 hours and the amount of time spent alone is normally distributed. We randomly survey one Mercurian 4-year-old living in a rural area. We are interested in the amount of time X the child spends alone per day.

a. In words, define the random variable X

b. What is X ~N(,)

c. Find the probability that the child spends less than 2 hours per day unsupervised.

d. What percent of the children spend over 12 hours per day unsupervised?

Given Information:  

Mean = μ = 3.2 hours  

Standard deviation = σ = 1.7 hours  

Required Information:  

a. In words, define the random variable X

b. X ~N(,) = ?

c. P(X < 2) = ?

d. P(X > 12) = ?

Answer:  

a) X is the number of hours in a day that a 4-year-old child spends being unsupervised.

b) X ~N(μ,σ) = X ~N(3.2, 1.7)

c) P(X < 2) = 23.88%

d) P(X > 12) = 0%

Explanation:  

a)

Let X is the number of hours in a day that a 4-year-old child spends being unsupervised.

b)

X ~N(μ,σ) = X ~N(3.2, 1.7)

Where 3.2 is the average number of hours that 4-year-old child spends being unsupervised and 1.7 is the standard deviation.

c)

We want to find out the probability that a child spends less than 2 hours per day unsupervised.

P(X < 2) = P(Z < (x - μ)/σ)

P(X < 2) = P(Z < (2 - 3.2)/1.7)

P(X < 2) = P(Z < (- 1.2)/1.7)

P(X < 2) = P(Z < -0.71)

The z-score corresponding to -0.71 is 0.2388

P(X < 2) = 0.2388

P(X < 2) = 23.88%

Therefore, the probability that a child spends less than 2 hours per day unsupervised is 23.88%

d)

We want to find out the probability that a child spends over 12 hours per day unsupervised.

P(X > 12) = 1 - P(X < 12 )

P(X > 12) = 1 - P(X < (x - μ)/σ)

P(X > 12) = 1 - P(X < (12 - 3.2)/1.7)

P(X > 12) = 1 - P(X < 8.8/1.7)

P(X > 12) = 1 - P(X < 5.18)

The z-score corresponding to 5.18 is 1

P(X > 12) = 1 - 1

P(X > 12) = 0

Therefore, the probability that a child spends over 12 hours per day unsupervised is 0%

The question discusses unsupervised hours of Mercurian children and it's a statistics problem involving normal distribution where the average unsupervised time is 3.2 hours with a standard deviation of 1.7 hours.

This question is related to statistics, specifically about normal distribution. The mean unsupervised time for 4-year-olds on Mercury is 3.2 hours, with a standard deviation of 1.7 hours. If we randomly survey a 4-year-old Mercurian child living in a rural area, the time they likely spend alone, denoted as X, will range according to this distribution.

Normal distributions can be defined by two parameters: the mean (μ) and the standard deviation (σ). In this case, μ = 3.2 hours and σ = 1.7 hours. Therefore, we can say that the time X spent by this sampled child alone is normally distributed with these parameters.

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Answer:

Account B

Step-by-step explanation:

Answer:

41.25$

Step-by-step explanation:

Answer:

41.25

Step-by-step explanation:

55/4=13.75

So 13.75 is 25% of 55

So then you would do 55-13.75

Because that is 25% off

The final answer would be $41.25 for the sale price.

Answer:

43.62% probability that it will take more than an additional 34 minutes

Step-by-step explanation:

To solve this question, we need to understand the exponential distribution and the conditional probability formula.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

Conditional probability formula:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Taking more than 24 minutes.

Event B: Taking ore than 24+34 = 58 minutes.

P(A)

More than 24, use the exponential distribution.

Mean of 41, so [tex]m = 41, \mu = \frac{1}{41} = 0.0244[/tex]

[tex]P(A) = P(X > 24) = e^{-0.0244*24} = 0.5568[/tex]

Intersection:

More than 24 and more than 58, the intersection is more than 58. So

[tex]P(A \cap B) = P(X > 58) = e^{-0.0244*58} = 0.2429[/tex]

Then:

[tex]P(B|A) = \frac{0.2429}{0.5568} = 0.4362[/tex]

43.62% probability that it will take more than an additional 34 minutes

Final answer:

The standard deviation used to calculate the test statistic for the one-sample z-test, when investigating the proportion of people in Norway with A positive blood type against the U.S. proportion, is 0.0392.

Explanation:

To calculate the standard deviation used to calculate the test statistic for a one-sample z-test in this scenario, where we are testing whether the proportion of people in Norway with a blood type of A positive is different from that in the United States, we use the formula for the standard deviation of a proportion, which is  [tex]\(\sqrt{\frac{p(1-p)}{n}}\)[/tex], where p is the proportion in the population (0.36 in this case, representing 36%), and n is the sample size (150 in this case).

Plugging in the values: [tex]\(\sqrt{\frac{0.36(1-0.36)}{150}}\) = \(\sqrt{\frac{0.36(0.64)}{150}}\) = \(\sqrt{\frac{0.2304}{150}}\) = \(\sqrt{0.001536}\) = 0.0392.[/tex]

So, the standard deviation used to calculate the test statistic for this hypothesis test is 0.0392.

The standard deviation used to calculate the test statistic for the one-sample z-test is approximately 0.0379.

To determine the standard deviation for the one-sample z-test, we use the formula for the standard deviation of a sample proportion, which is given by:

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

 Given that the population proportion p of people with A positive blood type in the United States is 0.36, and the sample size n from Norway is 150, we can plug these values into the formula:

[tex]\[ \sigma_{\hat{p}} = \sqrt{\frac{0.36(1-0.36)}{150}} \][/tex]

[tex]\[ \sigma_{\hat{p}} = \sqrt{\frac{0.36 \times 0.64}{150}} \][/tex]

[tex]\[ \sigma_{\hat{p}} \approx 0.0379 \][/tex]

Therefore, the standard deviation used in the calculation of the test statistic for the one-sample z-test is approximately 0.0379.

Answer:

False

Step-by-step explanation:

Substitute 22 in for b

16 < b - 8

16 < 22 - 8

16 < 14

False, 14 is not greater than 16

The solution:

16 < b - 8

Add 8 to both sides

24 < b

Answer:

-2,4

Step-by-step explanation:

i just did it

Answer:

-2,4

Step-by-step explanation:

i just did it on ed 2020

Step-by-step explanation:

Given, the face of a clock is divided into 12 equal parts.

Angle of each part = [tex]\frac{360}{12}[/tex] = 30°

(i) When one hand points at 2 and the other points at 4, this is can be divided into two parts, 2 to 3 and 3 to 4.

The angle formed = 2 (30) = 60°

Option (i) is correct

(ii) The circumference of the clock is ,

Circumference of circle = 2πr,

where r is the radius = 6 and π = 3.14.

Substituting the values in the formula, we get

Circumference of circle = 37.68.

Option (ii) is wrong.

(iii) With one hand at 5 and the other at 10, this is 5 parts

The angle formed= 30(5) = 150°.  

The arc length =[tex]\frac{150}{360}[/tex](37.68) = 15.7

Option (iii) is correct

(iv) When one hand points at 1 and the other points at 9, this is 4 parts,

30(4) = 120°.  T

Option (iv) is wrong

(v) The length of the minor arc from 11 to 2, this is 3 parts

3(30) = 90°  

minor arc from 7 to 10 is 3(30) = 90°  

Option (v) is correct

Answer: options 1,3,5

Answer:

V = 18.75

Method: First find the area of the pyramid on top, then find the area of the rectangular prism below.

V of the pyramid = 3.75 ft³

V of the rectangular prism = 15 ft³

3.75 + 15 = 18.75

Hope this helped!!  :)

First, find the volume of the pyramid on top:

(2.5 * 3 * 1.5) / 3 = 3.25

Then, find the volume of the rectangular prism:

2.5 * 3 * 2 = 15

Add the two volumes together:

3.25 + 15 = 18.25

To explain: you found the volume of each separate part and added it together.

Answer:

a) The null hypothesis is represented as

H₀: p ≥ 0.08

The alternative hypothesis is represented as

Hₐ: p < 0.08

b) A type I error for this question would be that

we conclude that the proportion of defective products is less than 8% when in reality, the proportion of defective products, is more than or equal to 8%.

c) At most, the number of defective products in the sample for you to agree to use the new product = 7

d) If minimum of 5000 pieces are purchased, 90% confidence interval for minimum number of flawed pieces will be (103, 497)

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 is usually stating the opposite of the theory is being tested. It usually maintains that random chance is responsible for the outcome or results of any experimental study/hypothesis testing. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis takes the other side of the hypothesis; that there is indeed a significant difference between two proportions being compared. It usually confirms the the theory being tested by the experimental setup. It usually maintains that other than random chance, there are significant factors affecting the outcome or results of the experimental study/hypothesis testing. It usually contains the signs ≠, < and > depending on the directions of the test

For this question, we want to prove that less than 8% of the products we subsequently purchase will be defective.

So, the null hypothesis will be that there is not enough evidence in the sample to say that less than 8% of the products we subsequently purchase will be defective. That is, the proportion of the sample that are defective is more than or equal to 8%.

And the alternative hypothesis is that there is enough evidence in the sample to say that less than 8% of the products we subsequently purchase will be defective.

Mathematically,

The null hypothesis is represented as

H₀: p ≥ 0.08

The alternative hypothesis is represented as

Hₐ: p < 0.08

b) A type I error involves rejecting the null hypothesis and accepting the alternative hypothesis when in reality, the null hypothesis is true. It involves saying that there is enough evidence in the sample to say that less than 8% of the products we subsequently purchase will be defective when in reality, there isn't enough evidence to arrive at this conclusion.

That is, the proportion of defective products in reality, is more than or equal to 8% and we have concluded that the proportion is less than 8%.

c) Out of the 100 samples provided by the manufacturer, at most how many can be defective for you to agree to use the new product?

The engineer agrees to use the new product when less than 8% of the products we subsequently purchase will be defective.

8% of the product = 0.08 × 100 = 8.

Meaning that the engineer agrees to subsequently purchase the product if less than 8 out of 100 are defective.

So, the maximum number of defective product in the sample that will still let the engineer purchase the products will be 7.

(d) For better or worse, your boss convinces you to go through with the deal. Turns out the minimum order is 5000 pieces. Assuming you purchase that many pieces of the new product, and that you found 6 defective pieces out of the 100, generate a 90% two-sided confidence interval for the number of pieces that will be flawed.

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion = 0.495

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 90% confidence interval for sample size of 100 using the t-tables since information on the population standard deviation.

Degree of freedom = n - 1 = 100 - 1 = 99

Significance level = (100-90)/2 = 5% = 0.05

Critical value = t(0.05, 99) = 1.660

Standard error of the mean = σₓ = √[p(1-p)/n]

p = 0.06

n = sample size = 100

σₓ = (0.06/√100) = 0.006

σₓ = √[0.06(0.94)/100] = 0.0237486842 = 0.02375

90% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.06 ± (1.660 × 0.02375)

CI = 0.06 ± 0.039425

90% CI = (0.020575, 0.099425)

90% Confidence interval = (0.0206, 0.0994)

If minimum of 5000 pieces are purchased, 90% confidence interval for minimum number of flawed pieces will be

5000 × (0.0206, 0.0994) = (103, 497)

Hope this Helps!!!

(a) The null hypothesis [tex]\(H_0\)[/tex] is that the proportion of defective products is 8% or less (b)  A Type I error occurs when the null hypothesis is true (the actual proportion of defective products is 8% or less), but we incorrectly reject it (c) at most 12 defective products can be found in the sample for the deal to proceed. (d) the 90% two-sided confidence interval for the number of defective pieces in the order of 5000 is from 105 to 496.

(a) The null hypothesis [tex]\(H_0\)[/tex] is that the proportion of defective products is 8% or less. The alternative hypothesis [tex]\(H_1\)[/tex] is that the proportion of defective products is greater than 8%. Mathematically, this can be expressed as:

[tex]\(H_0: p \leq 0.08\) \(H_1: p > 0.08\)[/tex]

(b) A Type I error occurs when the null hypothesis is true (the actual proportion of defective products is 8% or less), but we incorrectly reject it, concluding that the proportion of defective products is greater than 8%. This would mean unnecessarily turning down a good deal and potentially incurring additional costs to find another supplier.

(c) To ensure a 90% confidence level with a maximum defective rate of 8%, we can use the binomial distribution to find the maximum number of defective products allowed in the sample of 100. The formula for a binomial confidence interval is given by:

[tex]\(n \cdot p \pm Z_{\alpha/2} \sqrt{n \cdot p \cdot (1 - p)}\)[/tex]

where [tex]\(n\)[/tex] is the sample size, [tex]\(p\)[/tex] is the defect rate, and [tex]\(Z_{\alpha/2}\)[/tex] is the Z-score corresponding to the desired confidence level. For a 90% confidence level, [tex]\(Z_{\alpha/2} = 1.645\)[/tex]. Plugging in the values:

[tex]\(100 \cdot 0.08 \pm 1.645 \sqrt{100 \cdot 0.08 \cdot (1 - 0.08)}\)[/tex]

[tex]\(8 \pm 1.645 \sqrt{100 \cdot 0.08 \cdot 0.92}\)[/tex]

[tex]\(8 \pm 1.645 \sqrt{7.36}\)[/tex]

[tex]\(8 \pm 1.645 \cdot 2.713\)[/tex]

[tex]\(8 \pm 4.46\)[/tex]

The interval is from [tex]\(8 - 4.46\) to \(8 + 4.46\)[/tex], which gives us a range from approximately 3.54 to 12.46. Since we cannot have a fraction of a defective product, we round down to 3. Therefore, at most 12 defective products can be found in the sample for the deal to proceed.

(d) To generate a 90% two-sided confidence interval for the number of defective pieces out of 5000, given that 6 defective pieces were found out of 100, we first calculate the sample proportion of defective products:

[tex]\(\hat{p} = \frac{6}{100} = 0.06\)[/tex]

The formula for the confidence interval is:

[tex]\(\hat{p} \pm Z_{\alpha/2} \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}\)[/tex]

where [tex]\(n\)[/tex] is the sample size (100 in this case), and [tex]\(Z_{\alpha/2}\)[/tex] is the Z-score for a 90% confidence level (1.645). Plugging in the values:

[tex]\(0.06 \pm 1.645 \sqrt{\frac{0.06(1 - 0.06)}{100}}\)[/tex]

[tex]\(0.06 \pm 1.645 \sqrt{\frac{0.06 \cdot 0.94}{100}}\)[/tex]

[tex]\(0.06 \pm 1.645 \sqrt{\frac{0.0564}{100}}\)[/tex]

[tex]\(0.06 \pm 1.645 \cdot \sqrt{0.000564}\)[/tex]

[tex]\(0.06 \pm 1.645 \cdot 0.0237\)[/tex]

[tex]\(0.06 \pm 0.0391\)[/tex]

The interval is from [tex]\(0.06 - 0.0391\) to \(0.06 + 0.0391\)[/tex], which gives us a range from approximately 0.0209 to 0.0991. To find the number of defective pieces in the order of 5000, we multiply these proportions by 5000:

Lower bound: [tex]\(0.0209 \cdot 5000 = 104.5\)[/tex](round to 105)

Upper bound: [tex]\(0.0991 \cdot 5000 = 495.5\)[/tex] (round to 496)

Therefore, the 90% two-sided confidence interval for the number of defective pieces in the order of 5000 is from 105 to 496.

Answer:

17,19,23

that the prime number

Answer:

A prime number is a number whose only factors are one and itself

Prime numbers between 15 and 25:

17, 19, 23

Final answer:

The incorrect statement about the normal distribution is that its distribution function generally has a bell shape when graphed. This shape relates to the probability density function, not the cumulative distribution function, which actually has an S-shaped curve.

Explanation:

When we discuss the properties of a normal distribution, we are dealing with a continuous probability distribution that is widely used across many fields. The statement in question is identifying characteristics of the cumulative distribution function (CDF) of a normal distribution. The correct attributes of this function are that it ranges from 0 to 1, it increases as the quantity increases, and it returns the probability that the outcome from the normal distribution is a certain quantity or lower. However, the statement that the distribution function generally has a bell shape when graphed is incorrect regarding the CDF. The bell shape is a characteristic of the probability density function (PDF) and not the CDF, which increases from 0 to 1 in an S-shaped curve.

The standard normal distribution, which is a special case of the normal distribution with a mean (μ) of zero and a standard deviation (σ) of one, is used for a variety of applications in psychology, business, engineering, and other fields. Understanding the properties of the normal distribution — particularly the standard normal distribution — is crucial for interpreting data and using statistical methods.

It is also important to note that the integral of the normal distribution across its entirety (from ∞ to ∞) is equal to one. This area under the curve represents the total probability of all outcomes and justifies why the CDF ranges from 0 at the minimum to 1 at the maximum end of the distribution.

Answer:

Among 4.1 and 4.009 The greater one is 4.1

Hope it will help.

Answer:

I don't know you're options but the answer could be 30.

Answer:

The answer is B

Step-by-step explanation:

the question states that they are similar, so B is automatically an option. It's 8 times because the radius and height are being doubled. Logically there are more factors to be A and E.

B. The two cans are similar figures, and the volume of the new can is 8 times the volume of the old can.

Answer:

f(2x+1)sin(9[tex]F(2x+1)sin(90.9292)\pi[/tex]- 4.3784)

Step-by-step explanation:

The number of bald eagles is 26.

Answer:

The scale factor is 1/2

Step-by-step explanation:

we know that

A dilation is a non rigid transformation that produces similar figures

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z ---> the scale factor

x ---> the area after dilation

y ---> the original area

[tex]z^2=\frac{x}{y}[/tex]

we have

[tex]x=25\ cm^2\\y=100\ cm^2[/tex]

substitute

[tex]z^2=\frac{25}{100}[/tex]

[tex]z^2=\frac{1}{4}[/tex]

[tex]z=\frac{1}{2}[/tex]

1+3+5+7+...+999 =

= 1+2+3+4+...+500

     +1+2+3+...+499

= 2·(1+2+3+...+499) + 500

= 2·(499·500)/2 + 500

= 499·500 + 500

= 500·(499 + 1)

= 500·500

= 250.000

To find the sum of the series 1 + 3 + 5 + 7 + ... + 999, we recognize this is the sum of the first 500 odd numbers. Using the property that the sum of the first n odd numbers is n², we find the sum to be 500², which is 250000.

Summation of Odd Numbers:

To find the sum of the series 1 + 3 + 5 + 7 + ... + 999 using Gauss's method, we first recognize that this sequence is a series of the first 500 odd numbers.

An interesting property to note is that the sum of the first n odd numbers is n².

For example:

→ 1 = 1 (which is 1¹)

→ 1 + 3 = 4 (which is 2²)

→ 1 + 3 + 5 = 9 (which is 3³)

And so on...

In general, the [tex]n_{th[/tex] odd number can be expressed as 2n - 1.

For 999, to find its position in the series, note that 999 is the 500th odd number (since 2*500 - 1 = 999).

Thus, the sum of the first 500 odd numbers is:

→ Sum = 500²

           = 250000

→ So, the sum of the series 1 + 3 + 5 + 7 + ... + 999 is 250000.

Answer:

47.5% of lightbulb replacement requests numbering between 63 and 83

Step-by-step explanation:

The Empirical Rule(68-95-99.7 rule) states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 63

Standard deviation = 10

What is the approximate percentage of lightbulb replacement requests numbering between 63 and 83

63 is the mean

83 = 63 + 2*20

So 83 is two standard deviations above the mean.

The normal distribution is symmetric, so 50% of the measures are above the mean and 50% below the mean.

Of those above the mean, 95% are within 2 standard deviations of the mean.

So

0.5*95% = 47.5%

47.5% of lightbulb replacement requests numbering between 63 and 83

Answer:

  C.  all real numbers except 3/4

Step-by-step explanation:

f(x) and g(x) are both defined for all real numbers. However, the ratio f/g will be undefined where g(x) = 0. That occurs when ...

  4x -3 = 0

  4x = 3 . . . . . add 3

  x = 3/4 . . . . . divide by 4

The value of x = 3/4 makes f/g undefined, so must be excluded from the domain.