For each positive integer K, let S k denotes the increasing arithmetic progression of positive integers whose first term is 1 and whose common difference is K. For example S 3 is the sequence 1,4,7,10,..... For how many values of K, S k contains the term 2004?
Answers
For the positive integer of K, \(S_{k}\) contains the term 2004, the values would be 2.
Series \(S_{k}\) is 1,1+k,1+2k,... and so on
So nth term of the series \(S_{k}\) will be 1+(n−1)k
for some nth term would be 2004
So 1+(n−1)k=2004
= (n−1)k=2003
= n−1= \(\frac{2003}{k}\)
Therefore, k should be factor of 2003 which is a positive integer
So the factors are 1,2003
Thus, there are only two factors for 2003
Hence, there are only 2 values or factors for k
Integers include zero, a positive natural number, and a negative integer denoted by a minus sign. The negative numbers are the inverse additions of the comparable positive numbers. An arithmetic progression or arithmetic sequence (AP) is a succession of numbers with a constant difference between the terms.
An ascending arithmetic progression is a growing sequence of numbers that have a common difference. A declining arithmetic progression is a sequence of numbers with the same common difference that gets less over time.
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Related Questions
A group of seniors decide to spend their spring break away from home, attending at least one major event. The following table summarizes their preferences.
Attend a concert Attend a festival
Stay in state
214
186
Travel out of state 391
59
What percent want to attend a festival, given that they want to travel out of state?
6.94%
13.11%
24.08%
31.72%
Answers
The percentage of those who want to attend a festival given that they want to travel out of state is 24.08%.
What is the percent?
Percentage is the fraction of an amount expressed as a number out of hundred. The sign that represents percentages is %. Percentage is a measure of frequency.
Percentage of those who want to attend a festival given that they want to travel out of state =
(Number of those that are attending the festival and travelling out of state / total number of people that attend the festival) x 100
total number of people that attend the festival = 186 + 59 = 245
(59 / 245) x 100 = 24.08%
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The average annual salary in pennsylvania was $25,000 in 1992. assume that salaries were normally distributed for a certain group of wage earners, and the standard deviation of this group was $3,000. find the probability that for a randomly selected sample of 10 individuals, the mean salary was less than $24,000.
Answers
Answer:
0.6293
Step-by-step explanation:
The \(z\) score for $24000 is \(\frac{24000-25000}{3000} \approx 0.333\).
\(P(z<0.333)=0.6293\)
Carmen has a sign with dimensions 5 ft x 7.5 ft. She wants to reduce it to make a postcard. The postcard sizes are 3.5 in x 5 in., 4 in. x 6 in., and 4.25 in. x 6 in. Which size postcard should she use?
Answers
Answer:
7.5 / 5 = 1.5
5/ 1.5 = 3.33
6 / 1.5 = 4
Only 4in X 6in has the same relative dimensions
Which Line has The Greater Slope
1
2
3
4
Answers
State if the two triangles are congruent. If they are, state the congruence property. If they are not congruent, you do not need to write in the property. 10.Congruent? ___________ If so, what property? ________11.Congruent? ___________ If so, what property? ________
Answers
Answer:
The image for number 10 is shown below as
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
Simplify as far as possible
Please help
x²+3x²-4x²+5x
Answers
Answer:
I think 5x is the answer
stay safe
5x
on monday, jessica told two friends a secret. on tuesday, each of those friends told the secret to two other friends. each time a student heard the secret, he or she told the secret to two other friends the following day. on what day of the week will $1023$ students know the secret?
Answers
It will take 10 days for 1023 students to know the secret.
We can start by using the formula for exponential growth: n = 2^k
where n is the number of students who know the secret and k is the number of days.
On Monday, 1 student knew the secret (Jessica). On Tuesday, 2 students knew the secret. On Wednesday, 2 x 2 = 4 students knew the secret. And so on, each day the number of students who know the secret doubles.
We want to find k when n = 1023, so we can solve for k:
1023 = 2^k
log2 1023 = k
k = 10
So, it takes 10 days for 1023 students to know the secret. Since Monday was the first day, the 10th day is 10 days after Monday, which is a Thursday. Therefore, on Thursday, 1023 students will know the secret.
Therefore, It will take 10 days for 1023 students to know the secret.
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It will take 10 days for 1023 students to know the secret.
We can start by using the formula for exponential growth: n = 2^k
where n is the number of students who know the secret and k is the number of days.
On Monday, 1 student knew the secret (Jessica). On Tuesday, 2 students knew the secret. On Wednesday, 2 x 2 = 4 students knew the secret. And so on, each day the number of students who know the secret doubles.
We want to find k when n = 1023, so we can solve for k:
1023 = 2^k
log2 (1023) = k
k = 10
So, it takes 10 days for 1023 students to know the secret. Since Monday was the first day, the 10th day is 10 days after Monday, which is a Thursday. Therefore, on Thursday, 1023 students will know the secret.
Therefore, It will take 10 days for 1023 students to know the secret.
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The value of a company’s stock is represented by the expression x2 – 2y and the company’s purchases are modeled by 2x 5y. the company’s goal is to maintain a stock value of at least $5,000, while keeping the purchases below $1,000. which system of inequalities represents this scenario? x2 – 2y > 5000 2x 5y < 1000 x2 – 2y > 5000 2x 5y ≤ 1000 x2 – 2y ≥ 5000 2x 5y < 1000 x2 – 2y ≤ 5000 2x 5y ≤ 1000
Answers
Answer:
answer is (c)
May it help you
Option C. The inequality can then be written as x² - 2y ≥ 5000 and 2x + 5y <1000
How to write the inequality
Stock = x² - 2y
Purchase = 2x + 5y
Stock is said to be at least 5000 dollars. We can write this as
x² - 2y ≥ 5000
Then the purchase is said to be below 1000. This is written as 2x + 5y <1000
The inequality can then be written as x² - 2y ≥ 5000 and 2x + 5y <1000
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suppose you have an uneven 6-sided die where the numbers 1-5 are equally likely to occur, and the expected value of the entire die is 4. what is the probability of getting a 6?
Answers
The likelihood of striking a 6 on the this unbalanced die is therefore 1, or 100%.
What does value mean to you?A reasonable transaction result in money, products, or services. 2.: The monetary value of anything. 3.: value, usefulness, or significance in relation to anything else
As the die has only 6 sides, the probability of rolling a 6 is denoted by P(6). Let's use the formula of expected value to find P(6).
The expected value of the die is given by:
E(X) = (1 + 2 + 3 + 4 + 5 + 6)/6 = 21/6 = 3.5
We know that the expected value of the entire die is 4. Therefore, the expected value of the additional bonus for rolling a 6 is:
E(Y) = 4 - E(X) = 4 - 3.5 = 0.5
Since the bonus value can only be obtained by rolling a 6, the probability of getting a 6 is equal to the probability of obtaining the bonus value of 0.5. Hence, we have:
P(6) = P(Y = 0.5) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
Since the numbers 1-5 are equally likely to occur, we have:
P(X = 1) = P(X = 2) = P(X = 3) = P(X = 4) = P(X = 5) = 1/5
Therefore,
P(6) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 5/5 = 1
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Core Algebra
Englis
Solving for an Unknown Using the Distributive Property
180(n-2)
The equation a = represents the angle measuresya, in a regular n-sided polygon. When the equation is
solved for n, n is equal to a fraction with a denominator of a - 180. What is the numerator of the fraction?
Answers
Answer:
-360
Step-by-step explanation:
I got it right
the sum of two consecutive even integers is 122. what are the integers?
Answers
Answer:
If the numbers were the same, they'd both be 61
So, try 60 and 62.
x + x+2 = 122
2x = 120
x = 60
Hope that helps!
Answer:
60 and 62
Step-by-step explanation:
To find the answer we need to set up our problem.
For the two consecutive even integers we can call them x and x+2, as adding 2 to x will give us the next even number.
Then we form our equation:
x+x+2=122
Since we have two x we can combine them into a single term
2x+2=122
We then subtract 2 from both sides
2x=120
Divide by 2
x=60
Find the second number by inserting it into
x+2
60+2=62
A smart phone is bought at ₹ 46000. Its value depreciated at the rate of 12% per annum. Find its value after one year.
please answer fast please :)
Answers
Answer:
40480
Step-by-step explanation:
find 12% of 46000 and subtract it by 46000
brainliest pls
Answer:
40480
Step-by-step explanation
take 12% of the cost
46000*.12=5520
subtract answer from original number
46000-5520=40480
Question 1(Multiple Choice Worth 4 points) (02.05 LC) A surgeon performed two types of surgeries to treat large kidney stones and small kidney stones. Treatment A on large stones was successful 73% of the time, but on small stones it was successful 93% of the time. Treatment B was successful on large stones 69% of the time, but on small stones it was successful 87% of the time. The overall report stated treatment B was more successful. What may make this claim possible? Sampling error Cause-and-effect relationship Convenience error Confounding Simpson's Paradox
Answers
The correct option is Simpson's Paradox because the concept of the other options don't depict the paradox displayed in the question.
Simpson's paradox
it is simply a phenomenon in probability and statistics, whereby a trend appears in several different groups of data but will disappear or reverse when these groups are combined.
This result is often encountered in many areas of statistics and is very problematic especially when frequency data is given causal interpretations. The paradox can be resolved when causal relations are appropriately addressed in the statistical modeling.
It concluded that treatment B was more successful than treatment A without considering the conditions under which both treatments were carried out neither did it consider the severity of cases of patients involved in the treatment.
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The area and perimeter is needed
Answers
Answer:
Perimeter = 30 + 4\(\pi\) ≈42.56 cm
Area = 88 - 8\(\pi\) ≈ 62.88 cm^2
Step-by-step explanation:
area of rectangle = 11* 8 = 88
Perimeter of rectangle = 38
perimeter of circle = 2\(\pi\)4 = 8\(\pi \\\)
area of circle = \(\pi 4^{2}\) = 16 \(\pi\)
Answer:
Step-by-step explanation:
Area of shaded region = Area of rectangle - area of semi circle
Rectangle:
length = 11 cm
Width = diameter of circle = 4 + 4 = 8 cm
Area 1 = length * width
= 11 * 8
= 88 sq. cm
Circle:
radius = r = 4 cm
Area of semicircle = \(\dfrac{1}{2}\pi r^{2}\\\)
\(=\dfrac{1}{2}*3.14*4*4\\\\= 25.12 \ cm^{2}\)
Circumference of semicircle = \(\dfrac{2\pi r}{2}=\pi r\)
= 3.14 * 4
= 12.56 cm
Area of the shaded region = 88 - 25.12 = 62.88 = 63 square cm
Perimeter of shaded region = 11 + 8 + 11 + circumference of semicircle
= 11 + 8 + 11 + 12.56
= 42.56
= 43 cm
Hannah runs down the street to catch her bus. she runs for a total of 12 seconds. on the sidewalk, she runs 16 feet per second. when she crosses the street, she runs 3 feet per second. hannah runs a total distance of 127 feet.
Answers
If hannah runs a total distance of 127 feet, Hannah spent 7 seconds running on the sidewalk.
Let's use s to represent the number of seconds that Hannah spent running on the sidewalk. We know that she runs at a speed of 16 feet per second on the sidewalk, and that the total distance she ran was 127 feet. We also know that she ran at a speed of 3 feet per second when crossing the street.
We can set up an equation that relates the distances Hannah ran on the sidewalk and crossing the street to the total distance she ran:
Distance on sidewalk + Distance crossing street = Total distance
16s + 3(12 - s) = 127
Simplifying this equation:
16s + 36 - 3s = 127
13s = 91
s = 7
In summary, we used the given information and variables to set up an equation and solve for the unknown variable (the number of seconds Hannah spent running on the sidewalk) by simplifying and isolating it on one side of the equation.
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Complete question is:
Hannah runs down the street to catch her bus. she runs for a total of 12 seconds. on the sidewalk, she runs 16 feet per second. when she crosses the street, she runs 3 feet per second. hannah runs a total distance of 127 feet. How many seconds did Hannah spend running on the sidewalk? Enter your answer in the box.
Which value is not part of the five-number summary for the following data set?
35, 23, 24, 30, 28, 23, 27, 33, 27, 34, 30, 30
A. 29
B. 23
C. 31.5
D. 24
Answers
Answer:
D. 24
Step-by-step explanation:
The 5-number summary of a data set includes ...
minimum1st quartilemedian (2nd quartile)3rd quartilemaximumSummary valuesWhen the data are written in increasing order, they are ...
23 23 24 27 27 28 30 30 30 33 34 35
The minimum is the first value on the list, 23.
The first quartile is the average of the two middle values in the lower half of the data set: (24+27)/2 = 25.5.
The median is the average of the two middle values: (28+30)/2 = 29.
The third quartile is the average of the two middle values in the upper half of the data set: (30+33)/2 = 31.5.
The maximum is the last value on the list: 35.
Answer choicesA. 29 is the median
B. 23 is the minimum
C. 31.5 is the 3rd quartile
D. 24 is not part of the 5-number summary
a function f is given, and the indicated transformations are applied to its graph (in the given order). write the equation for the final transformed graph. f(x)
Answers
The equation for the final transformed graph is h(x) = - (x + 6)²
To find the equation for the final transformed graph after applying the given transformations to the function f(x) = x², we will apply each transformation step by step.
1. Shift 6 units to the left:
To shift the graph 6 units to the left, we subtract 6 from the original function:
g(x) = f(x + 6) = (x + 6)²
2. Reflect in the x-axis:
To reflect the graph in the x-axis, we take the negative of the function:
h(x) = -g(x) = - (x + 6)²
Therefore, the equation for the final transformed graph is h(x) = - (x + 6)².
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The given question is given, the complete question is below
A function f is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph.
f(x) = x²; shift 6 units to the left and reflect in the x-axis
A group of 8 friends each buy 1 ticket and 1 small popcorn
at the movie theater. Each ticket costs $7.50. The group of
friends spends a total of $83.60.
Enter the cost of 1 small popcorn.
Answers
Answer:
$2.95
Step-by-step explanation:
8x+8y=83.60
8 is the amount of friends/amount of tickets/amount of small popcorn
x is the cost 1 ticket
y is the cost 1 small popcorn
We know that the price of a ticket is 7.50 so we replace "x" with 7.50
8(7.5)+8y=83.60
Simplify
60+8y=83.60
Now subtract 60 from both sides
8y=23.60
Now divided both sides by 8
y=2.95
the cost of 1 small popcorn is $2.95
PLs help i really need it will give brainliest and thanks and 5 stars
Answers
Answer:
(5-2t)<-4
Step-by-step explanation:
The midnight temprature is 5 °C and the temprature is decreasing at the rate of 2°C per hour . If T is the hours past midnight then after t hours the temprature will be ( 5t-2t) . If the temprature is colder than -4°C right now , then your inequality can be written like 5t-2t<-4
You want to start a business selling shoes. The shoes cost $30 to
a
make as well as a $50 delivery fee from the company. You are
planning to sell the shoes for $45 each.
QUESTIONS:
Write a function that represents the cost to make the shoes.
Write a function that represents the revenue from selling the shoes.
Write a function that represents the profit from selling the shoes.
How many shoes will you have to sell to make profit?
Answers
Answer:
A shoe company will make a new type of shoe. The fixed cost for the production will be $24,000. The variable cost will be $32 per pair of shoes. The shoes ...
5 pages
Step-by-step explanation:
confused on how to solve this,,
The volume of a shipping container in the
shape of a rectangular prism can be represented by the
polynomial 6x3 + 11x² + 4x, where the height is x.
a. Find the length and width of the container.
b. Find the ratio of the three dimensions of the
container when x = 2.
C. Will the ratio of the three dimensions be the same
for all values of x?
Answers
After carrying out the calculations on the volume of the container, we found the following values:
a. Length = 3x + 4 / Width = 2x + 1 / Height = xb. Length: Width: Height = 10: 5: 2 = 2: 1: 0.4c. No, the ratio of the three dimensions will not be the same for all values of x. How to calculate each data?For the letter a, we can find the length and width of the container by factoring the given polynomial. So let's factor X:
6x³ + 11x² + 4x = x(6x² + 11x + 4)Next, let's factor the quadratic expression inside the parentheses:
6x² + 11x + 4 = (2x + 1)(3x + 4)The polynomial can be written as:
6x³ + 11x² + 4x = x(2x + 1)(3x + 4)Thus, the dimensions of the container are:
Length = 3x + 4 Width = 2x + 1 Height = xFor the letter b, p to find the ratio of the three dimensions when x = 2, we simply substitute x = 2 into the expressions we found for length, width and height:
Length = 3(2) + 4 = 10 Width = 2(2) + 1 = 5 Height = 2So the ratio between the dimensions is:
Length: Width: Height = 10: 5: 2 = 2: 1: 0.4Therefore, after the calculations, we find the answer for the letter c, since the ratio of the three dimensions will not be the same for all values of x. As x varies, the expressions for length, width, and height also vary, leading to different dimension ratios.
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A student wonders if people of similar heights tend to date each other. She measures herself, her dormitory roommate, and the women in the adjoining rooms, then she measures the next man whom each woman dates. Here are the data (heights in inches): Women: 64 65 65 66 66 70 Men: 68 68 69 70 72 74 Determine whether each of the following statements is true (T) orfalse (F). (a) If we had measured the heights of the men and women in centimeters (1 inch= 2.54 cm), the correlation coefficient would have been 2.54 times larger. (b) There is a strong negative association between the heights of men and women because women are always smaller than the men they date. (c) There is a positive association between the heights of men and women.
Answers
Answer:
(a) False
(b) False
(c) True
Step-by-step explanation:
(a) If we had measured the heights of the men and women in centimeters (1 inch= 2.54 cm), the correlation coefficient would have been 2.54 times larger.
No, since changing the units of measurement does not change the correlation coefficient
(b) There is a strong negative association between the heights of men and women because women are always smaller than the men they date.
Negative association means that as one variable increases, the other decreases, Here, we see that as the heights of the men increase, the height of the women do not reliably decrease, hence there is no strong negative asscoiation
(c) There is a positive association between the heights of men and women.
We see from the values given that as the heights of men increase, so do the heights of women and vise versa, so there is a positive association between the heights of men and women
Which expression can be used to find 80% of 120?
80% of 120
20%
20%
20%
20%
20%
(0.8) (24)
(0.2) (120)
(0.8) (120)
(0.2) (24)
Answers
Answer:
96
Step-by-step explanation:
80÷100×120
96 ,, , ,; , ,
Answer:
(0.8) (120)
Step-by-step explanation:
\(80\% \: of \: 120\\\\ = \frac{80}{100} \times 120 \\ \\ = (0.8)(120)\\\\=96\)
Evaluate: 2x + 5x - 11 = -46
Answers
Answer:
x=-5
Step-by-step explanation:
Combine like terms: 7x-11=-46
Add 11 to -46: -35
Divide: 7x/-35
ANSWER: x=-5
Asmall island ist am from the nearest point on the straight shine of a large if a woman on the island cartow a boat 3 kmh and can walk where should the boot belanded in order to arrive at a town 12 km down the shore from Pintere? The boat should be aded down the shore from (Type an exacta)
Answers
To determine the landing point, we need to balance the time it takes to row the boat with the time it takes to walk.
The woman's rowing speed is 3 km/h, and her walking speed is denoted as w km/h. Let d be the distance from the island to the landing point, and x be the distance she needs to walk from the landing point to reach the town. The total time for rowing (d/3) should be equal to the total time for walking [(12 - x)/w] in order to arrive at the town.
By rearranging the equation, we find that the landing point should be 12 km minus the distance covered by walking (d * w) divided by 3.
The exact value of x depends on the specific distances involved and the woman's walking speed, which are not provided in the given information.
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g(x) = -3x + 1
g(10) =
Answers
6. what are the two most generic and widely used valuation multiples?
Answers
The two most generic and widely used valuation multiples in finance and investment analysis are the price-to-earnings (P/E) ratio and the enterprise value-to-earnings before interest, taxes, depreciation, and amortization (EV/EBITDA) multiple.
1. Price-to-Earnings (P/E) Ratio: The P/E ratio is calculated by dividing the market price per share of a company's stock by its earnings per share (EPS). It provides a measure of how much investors are willing to pay for each dollar of earnings generated by the company.
A high P/E ratio suggests that investors have high expectations for future growth and are willing to pay a premium for the stock. On the other hand, a low P/E ratio may indicate that the stock is undervalued or that investors have low expectations for future growth.
2. Enterprise Value-to-EBITDA (EV/EBITDA) Multiple: The EV/EBITDA multiple is calculated by dividing the enterprise value (EV) of a company by its earnings before interest, taxes, depreciation, and amortization (EBITDA).
The EV is the total market value of a company's equity and debt, minus its cash and cash equivalents. EBITDA represents the company's operating earnings before accounting for interest, taxes, depreciation, and amortization.
The EV/EBITDA multiple is commonly used in evaluating the valuation of companies, especially in the context of mergers and acquisitions. It provides a measure of a company's overall value relative to its earnings, without being affected by capital structure or tax considerations.
Both the P/E ratio and EV/EBITDA multiple are widely used because they are relatively easy to calculate and understand. However, it's important to note that these multiples have limitations and should be used in conjunction with other valuation methods and qualitative analysis to make informed investment decisions.
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So grateful if you help
Answers
Answer:
Question 3
a) 7/6 = 1 1/6
b) 8/3 = 2 2/3
c) 7/2 = 3 1/2
d) 3/2 = 1 1/2
e) 17/6 = 2 5/6
f) 10/3 = 3 1/3
Question 4
a) 4 x 8 = 32
b) 27/8 = 3 3/8
c) (32-27)/8 = 5/8
Step-by-step explanation:
Question 3
a) 7/6 = 1 1/6
b) 8/3 = 2 2/3
c) 7/2 = 3 1/2
d) 3/2 = 1 1/2
e) 17/6 = 2 5/6
f) 10/3 = 3 1/3
Question 4
a) 4 x 8 = 32
b) 27/8 = 3 3/8
c) (32-27)/8 = 5/8
Part-a) 7/6:
=> 1/6 + 6/6=> 1/6 + 1 = 1 1/6Part-b) 8/3:
=> 2/3 + 3/3 + 3/3=> 2/3 + 1 + 1=> 2/3 + 2=> 2 2/3Part-c) 7/2:
=> 1/2 + 2/2 + 2/2 + 2/2=> 1/2 + 1 + 1 + 1 => 1/2 + 3=> 3 1/2Part-d) 3/2:
=> 1/2 + 2/2=> 1/2 + 1=> 1 1/2Part-e) 17/6:
=> 5/6 + 6/6 + 6/6=> 5/6 + 1 + 1=> 5/6 + 2=> 2 5/6Part-f) 10/3:
=> 1/3 + 3/3 + 3/3 + 3/3=> 1/3 + 1 + 1 + 1=> 1/3 + 3=> 3 1/3Solution (Question 4):Note that:
1 pizza = 8 slicesTotal pizzas ordered: 4 pizzasPart-a) How many slices of pizzas were there altogether?
Use the equation (1 pizza = 8 slices) to find out how many slices were there.
=> 1 pizza = 8 slices=> 4 pizzas = 8 x 4 slices=> 4 pizzas = 32 slices32 slices of pizza were in total.
Part-b) How many pizzas were eaten? Express your answer as a mixed number.
Divide 27 by 8 to find out how many pizzas were eaten.
27/8 = 3 3/8 pizza3 3/8 of pizza were eaten.
Part-c) How many pizzas were left over? Express your answer as a fraction.
Subtract the pizza eaten from the pizza ordered to find out how many pizzas were left.
4 - 3 3/8=> 4 - 27/8=> 32/8 - 27/8=> 5/85/8 of pizza were left over.
Russell is helping set up for a school picnic. He has 35 small paper plates and 44 large ones. In all, how many paper plates does he have?
Answers
Answer:
44+35=79
...............
Which of the following statements about t distribution are true? (Select all that apply.)
a) It assumes the population data is normally distributed.
b) It is used to construct confidence intervals for the population mean when population standard deviation is unknown.
c) It has less area in the tails than does the standard normal distribution.
d) It approaches the standard normal distribution as the sample size decreases.
e) It approaches the standard normal distribution as the sample size increases.
f) It assumes the population data is not normally distributed.
Answers
The correct statements are b), c), and d).
The correct statements about the t-distribution are:
b) It is used to construct confidence intervals for the population mean when the population standard deviation is unknown. The t-distribution is specifically used when the population standard deviation is unknown and the sample size is small.
c) It has less area in the tails than does the standard normal distribution. The t-distribution has fatter tails compared to the standard normal distribution, meaning it has more area in the tails.
d) It approaches the standard normal distribution as the sample size decreases. As the sample size increases, the t-distribution approaches the standard normal distribution. For large sample sizes (typically considered above 30), the t-distribution is very similar to the standard normal distribution.
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