So, the length of open rectangle box is 4cm, width is 4cm, and height is 2cm, with Surface Area of 48cm^2.
it is an Open box, so there is no top
SA (Surface area) = 2*l*h + 2*w*h + l*w
Volume(V) = l*w*h = 32cm^3
h = 32/(w*l)
SA = 2*l*32/(w*l) + 2*w*32/(w*l) + l*w
SA = 64/w + 64/l + l*w
Find minimum SA: take partial derivatives to get critical point(s)
SAw = -64/w^2 + l
SAl = -64/l^2 + w
Both the partials have to be 0, so...
0 = -64/w^2 + l and 0 = -64/l^2 + w
64/w^2 = l
0 = -64/(64/w^2)^2 + w (plug into second equation)
0 = -w^4/64 + w
0 = w(1-w^3/64)
1 = w^3/64 or 0 = w (impossible answer)
64 = w^3
4 = w
Plug w back into 64/w^2 = l
64/4^2 = l
4 = l
Plug w and l back into h = 32/(w*l)
h = 32/(4*4)
h = 2
The Surface Area:2*l*h + 2*w*h + l*w
SA = 2*4*2 + 2*4*2 + 4*4
SA = 48
So the answer is length = 4cm, width = 4cm, and height = 2cm, with Surface Area of 48cm^2
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Ja’Miles designs a sign for a store in the shape of a triangle. His design is 7.5 square feet in area, and the triangle has a height of 2.5 feet. What is the length of the base of his sign?
3 feet
0.6 feet
6 feet
10 feet
because 25 percent of the students in my morning statistics class watch eight or more hours of television a week, i conclude that 25 percent of all students at the university watch eight or more hours of television a week. the most important logical weakness of this conclusion would be
The main logical weakness of the conclusion is the hasty generalization made from a potentially unrepresentative sample. To strengthen the argument, a more comprehensive survey of the university's student population should be conducted.
The most important logical weakness of the conclusion that "25 percent of all students at the university watch eight or more hours of television a week" based on the observation from your morning statistics class is that it involves a hasty generalization.
A hasty generalization occurs when you draw a conclusion about a larger group based on a smaller, unrepresentative sample. In this case, the student question assumes that the morning statistics class is representative of the entire university, which may not be true.
To better explain this logical weakness, let's break down the steps:
The student observes that 25 percent of the students in their morning statistics class watch eight or more hours of television a week.
The student then concludes that this must apply to all students at the university.
The conclusion does not account for potential differences between the morning statistics class and other classes or students at the university.
To overcome this logical weakness, a more representative sample of the university's student population should be surveyed to accurately determine the percentage of students who watch eight or more hours of television a week. This might involve selecting students from different majors, class schedules, and demographic backgrounds to ensure that the sample truly represents the entire university population.
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test two different independent variables in his study. the first variable has 3 levels to it (weightlifting interventions - control, light weightlifting routine, or strenuous weightlifting routine), and the second variable is hair length and has 2 levels (short or long). this is a factorial design and will allow him to test the influence of both ivs on his dv (which is strength). using this design, if it is set up as an independent groups design, how many conditions will each participant be assigned to?
Each participant will be assigned to 6 conditions.
In a factorial design, a researcher aims to investigate the effects of multiple independent variables (IVs) on a dependent variable (DV). In this study, the researcher is examining the impact of two different independent variables: weightlifting interventions with three levels (control, light weightlifting routine, and strenuous weightlifting routine), and hair length with two levels (short or long).
To determine the number of conditions in a factorial design, you multiply the levels of each independent variable. In this case, the study has 3 levels for the first variable (weightlifting interventions) and 2 levels for the second variable (hair length). Therefore, there will be a total of 3 x 2 = 6 conditions in the study.
As the study is set up as an independent group design, each participant will only be assigned to one condition. This means that each participant will undergo a specific weightlifting intervention (control, light, or strenuous) and will have a specific hair length (short or long). The independent group design ensures that the participants' experiences in one condition do not influence their performance in another condition, thus reducing potential biases and confounds.
In summary, using a factorial design with two independent variables (weightlifting interventions with three levels and hair length with two levels), the study will have a total of 6 conditions. As it is set up as an independent groups design, each participant will be assigned to only one of these conditions.
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PLS ANSWER CORRECTLY. worth points
The Fahrenheit temperature of the can of soda, after 60 minutes, given the value of K would be 55°F.
How to find the temperature of the can ?We can use Newton's Law of Cooling formula to find the value of k:
58 = 35 + (73 - 35) x e ^ (-k x 40)
23 = 38 x e ^ (-k x 40)
23/38 = e ^ (-k x 40)
ln(23/38) = -k x 40
k = -ln(23/38) / 40 ≈ 0.010
Now that we have the value of k, we can find the temperature of the can of soda after 60 minutes (t = 60):
T = 35 + (73 - 35) x e ^ (-0.010 x 60)
T ≈ 35 + 38 x e ^ (-0.6) = 35 + 38 x 0.5488 = 54.856
The temperature of the can of soda after 60 minutes is approximately 55°F (rounded to the nearest degree).
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Write 0.70 repeating as fraction in simplest form.
Answer:
7/10
Step-by-step explanation:
Guys please I need help
B
East Indians and Chinese because they are both in the continent of Asia, which is where P and Q are located.
To help Penny decide which day to start sprint training, and what color track pants to wear on the first day, her friend picks one card from two different bags. The first bag contains 7 numbers, representing the days of the week from Sunday through Saturday. To represent the pant colors, the second bag contains 4 cards colored pink, red, gray, and blue.
Which list shows the correct sample space of all the possible outcomes when a school day is selected, and either red or gray is selected? The numbers represent the day and the capital letters represent the colors. So, 1P means Sunday and pink, 2R means Monday and red, 3G means Tuesday and gray, 4B means Wednesday and blue, and so on.
A. 2P, 3P, 4P, 5P, 6P, 2R, 3R, 4R, 5R, 6R, 2G, 3G, 4G, 5G, 6G, 2B, 3B, 4B, 5B, 6B
B. 2R, 3R, 4R, 5R, 6R, 2G, 3G, 4G, 5G, 6G
C. 2P, 3P, 4P, 5P, 6P, 2B, 3B, 4B, 5B, 6B
D. 1R, 2R, 3R, 4R, 5R, 6R, 7R, 1G, 2G, 3G, 4G, 5G, 6G, 7G
When a school day is selected and either red or gray is chosen, there are 14 possible outcomes. The sample space is a way to show all possible outcomes, and the correct answer is option (B), which lists 10 possible outcomes.
How to find out the way?
The first bag contains 7 numbers, one for each day of the week, and the second bag contains 4 colored cards, but only 2 colors are acceptable. Therefore, there are 7 x 2 = 14 possible outcomes when a school day is selected and either red or gray is chosen.
The sample space for the problem lists all possible outcomes. Option (A) lists all 20 possible outcomes for any combination of day and color. Option (C) lists all 10 possible outcomes for any combination of day and color, but with the wrong color choices. Option (D) lists 14 possible outcomes, but includes the color pink, which is not an acceptable choice.
Option (B) is the correct answer, as it lists all 10 possible outcomes when a school day is selected and either red or gray is chosen. These outcomes are 2R, 3R, 4R, 5R, 6R, 2G, 3G, 4G, 5G, and 6G. Therefore, Penny's friend should choose a day between Monday and Saturday and wear either red or gray track pants on the first day of sprint training.
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Wyatt records the temperature outside his house for several hours one winter ever
below describes the temperature changes
• The temperature at 8 P.M. was -6.8 degrees Celsius.
• Between 8 P.M. and 10 P.M., the temperature change was +3.9 degrees Celsius.
The temperature change was -4.4 degrees Celsius between 10 P.M. and midnight.
What was the temperature at midnight?
F -1.5 degrees Celsius
G -7.3 degrees Celsius
H-15.1 degrees Celsius
J-6.3 degrees Celsius
Answer: (G) -7.3 degrees Celsius
Step-by-step explanation:
To find the temperature at midnight, we need to start with the temperature at 8 P.M. and then add or subtract the temperature changes that occurred between 8 P.M. and midnight.
The temperature change between 8 P.M. and 10 P.M. was +3.9 degrees Celsius, so the temperature at 10 P.M. was:
-6.8 + 3.9 = -2.9 degrees Celsius
The temperature change between 10 P.M. and midnight was -4.4 degrees Celsius, so the temperature at midnight was:
-2.9 - 4.4 = -7.3 degrees Celsius
-
16. Silas transformed point J(-3, -7) using the rule (x, y) → (-x, -y). Describe the transformation
and give the location of J'.
The location of J' after transformation is (3, 7).
Define transformationIn mathematics, a transformation is a process or operation that changes the position, orientation, size, or shape of a geometric object or a set of objects. Transformations are often used in geometry to study and analyze the properties of shapes and figures, as well as to solve problems related to their construction, symmetry, and congruence.
Given: Silas transformed point J(-3, -7) using the rule (x, y) → (-x, -y).
The rule (x, y) → (-x, -y) reflects a point over both the x-axis and the y-axis. This is a type of transformation known as a "point reflection" or "central symmetry" where the point is reflected across a point located at the origin (0,0).
When Silas applies this rule to point J(-3, -7), the x-coordinate changes from -3 to 3, and the y-coordinate changes from -7 to 7.
Therefore, the location of J' is (3, 7).
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c) How many tens are in 376
Answer:
37 tens
Step-by-step explanation:
divide the numbers
At a sale, dresses were sold for $17 each. This price was 85% of a dress's original price. How much did a dress originally cost?
Answer:
To find the original price of the dress, we can use the following formula: Original price = Sale price / Discount rate In this case, we know that the sale price was $17, and the discount rate was 85%. So we can substitute these values into the formula: Original price = $17 / 0.85 Simplifying this expression, we get: Original price = $20 Therefore, a dress originally cost $20.
in the year 2015, the timss ranking and average scores of math achievement for fourth-graders were lowest for: korea. russia. kuwait. iran.
In the year 2015, the times ranking and average scores of math achievement for fourth-graders were option (c) Kuwait
According to the Trends in International Mathematics and Science Study (TIMSS) report for 2015, the lowest ranking and average scores of math achievement for fourth-graders were found in Kuwait. Kuwait ranked 48th out of the 49 countries that participated in the study.
It's worth noting that while Korea, Russia, and Iran also participated in the study, they did not have the lowest ranking or scores. Korea, in fact, ranked 5th overall with an average math score of 608, while Russia ranked 12th with an average math score of 544, and Iran ranked 24th with an average math score of 474.
The reasons for Kuwait's low ranking and scores in math achievement could be due to various factors, such as inadequate resources for education, lack of effective teaching methods, or low investment in STEM (science, technology, engineering, and mathematics) education.
Therefore, the correct option is (c) Kuwait
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help asap will give brainliest!!!
The exact volume of the cone is 3,087.18 cubic inches.
What is a cone?A cone is a three-dimensional geometric form with a flat base and a smooth tapering apex or vertex. The curving surface of it slopes upward towards the apex and has a round base. The radius of the base is the distance from the centre of the base to its edge, and the height of the cone is the separation between the base and the apex.
The formula for the volume of a cone is:
V = 1/3 * πr²h
Substituting the given values, we get:
V = 1/3 * 3.14 (9²) (11)
V = 1/3 * 3.14 (81)(11)
V = 1/3 (9,261.54)
V = 3,087.18 cubic inches
Hence, the exact volume of the cone is 3,087.18 cubic inches.
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Matias launches a water balloon from a deck. The time, in seconds (sec.),
from the launch and the height. in meters (m), of the water balloon is given
in equation h(t) = t +3t-18
Determine when the water balloon will hit the ground.
On solving the provided question we can say that So, we have two solutions: t = (9/2) or t = (-6/2) = -3
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a single variable quadratic polynomial. a 0. Because this polynomial is of second order, the Basic Theorem of Algebra implies that it has at least one solution. Simple or complex solutions are possible. A quadratic equation is a quadratic equation. This means it has at least one word that must be squared. One of the most common solutions for quadratic equations is "ax2 + bx + c = 0." where a, b, and c are numerical coefficients or constants. where the variable "X" is unnamed.
So, we can set h(t) = 0 and solve for t:
[tex]0 = t^2 + 3t - 18\\t = (-3 + \sqrt (3^2 - 4(1)(-18))) / (2(1))\\t = (-3 + \sqrt (81)) / 2\\t = (-3 + 9) / 2\\[/tex]
So, we have two solutions:
t = (9/2) or t = (-6/2) = -3
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The least number of customers in a shop at any time during the day was 15. Fran represented this situation with the inequality c < 15, where c is the number of customers in the shop.
Is Fran correct? Explain.
Yes; The number of customers is less than 15.
Yes; The number of customers is at least 15.
No; The number of customers is less than 15.
No; The number of customers is at least 15.
The correct inequality to represent this situation would be c ≥ 15, which means that the number of customers is at least 15.therefore option D. No; The number of customers is at least 15 is correct.
The inequality c < 15 represents the least number of customers in a shop at any time during the day was 15.
The inequality Fran represented, c < 15, means that the number of
customers is less than 15. However, the question stated that the least
number of customers in the shop at any time during the day was 15.
We are given the following in the question:
Fran used the given inequality to represent the number of customers in
a shop at any time. where c is the number of customer during any time of
day.
Therefore, the correct inequality to represent this situation would be c ≥ 15, which means that the number of customers is at least 15.
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factor the polynomial, please.
1. 2p^2+7p-6
2. -5v^2+31v-6
3. -6v^2-11v-4
Tom wants to put up Christmas lights around his house.
His house is a rectangle which is 35 m long and 15 m wide.
Tom will need
metres of lights to go all the way around his house.
Answer:
1450
Step-by-step explain:
(35x35)+(15x15)
1225+225
Construct a 90% confidence interval to estimate the population proportion with a sample proportion equal to
0.36 and a sample size equal to 100.
Click the icon to view a portion of the Cumulative Probabilities for the Standard Normal Distribution table.
A 90% confidence interval estimates that the population proportion is between a lower limit of
limit of
(Round to three decimal places as needed.)
and an upper
The Upper bound of this interval is 0.582.
To construct a 90% confidence interval to estimate the population proportion, we need to use the formula:
sample proportion ± z*√((sample proportion*(1-sample proportion))/sample size)
where z is the z-score corresponding to a 90% confidence level. Using a table or calculator, we find that the z-score is 1.645.
If the sample proportion is not given in the question, we cannot proceed with the calculation. However, assuming that the sample proportion is equal to 0.5 (which is a common assumption if no information is given), we can plug in the values:
0.5 ± 1.645*√((0.5*(1-0.5))/n)
If we assume a sample size of n = 100, then the confidence interval is:
0.5 ± 1.645*√((0.5*(1-0.5))/100) = 0.5 ± 0.082
Rounding to three decimal places, the confidence interval is [0.418, 0.582]. This means that we can be 90% confident that the true population proportion lies within this range. The upper bound of this interval is 0.582.
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duck PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Answer:
The answer is B
Step-by-step explanation:
These are triangles are similar and because of that:
x/6 = (x+2.5)/(6+4)
x/6 = x/10 + 0.25
x = 6x/10 + 1.5
4x/10 = 1.5
4x = 15
x = 3.75
Divide 1/2 into 5 equal parts
1/2 divided by 5
1/2 divided into 5 equal parts is 1/10.
We have,
To divide 1/2 into 5 equal parts, we need to perform the division operation:
(1/2) ÷ 5.
To divide fractions, we can multiply the numerator of the first fraction by the reciprocal of the second fraction.
The reciprocal of 5 is 1/5.
So, we have:
(1/2) × (1/5).
Multiplying the numerators gives us 1, and multiplying the denominators gives us 2 × 5 = 10.
Therefore,
1/2 divided into 5 equal parts is 1/10.
In other words, each part is 1/10 of 1/2.
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ms. chang tracked the number of homework assignments her two math classes submitted each day. these box plots show the results. which class has a higher median number of submitted homework assignments?
Answer: Class 2
Step-by-step explanation:Because the median point is higher than class 1
From the boxplot of homework assignments data, the median number of submitted homework assignments by math class 2 to the Ms. chang is higher
A box with whisker plot also called a box plot, it is a graphical way of displaying the distribution of data based on a five number summary. The five numbers summary includes minimum, first quartile [Q1], median, third quartile [Q3] and maximum.
The vertical line that split the box in two is called the median value of data.We have two box plots present in attached figure. Ms. chang tracked the submitted assignment by her class through the box plots. Here orange and blue box plots show the data of number homework assignments of her maths class 1 and class 2 submitted each day respectively. Now, see the box plot and use above discussed definition of median, we conclude that median number of class 1 = 25
Median number of class 2 = 26 > 25.
Hence, class 2 has a higher median number than class 1.
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Complete question:
The attached figure complete the question.
the value of the test statistic for the appropriate chi-square test is approximately 8.25 8.25 . assume the conditions for inference were met. do the sample data provide convincing statistical evidence of an association between grade in the preceding biology i i course and whether a student asks for clarification at the 5 5 percent level of significance?
Yes, there is convincing statistical evidence of an association between grade in the preceding Biology II course and whether a student asks for clarification at the 5% level of significance, with a test statistic of 8.25 and a p-value less than 0.05.
To determine if there is convincing statistical evidence of an association between grade in the preceding Biology II course and whether a student asks for clarification, we need to conduct a hypothesis test using the chi-square test.
Null Hypothesis: There is no association between grade in the preceding Biology II course and whether a student asks for clarification.
Alternative Hypothesis: There is an association between grade in the preceding Biology II course and whether a student asks for clarification.
Since the test statistic for the chi-square test is given as 8.25, we need to find the corresponding p-value for this test statistic. The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed test statistic, assuming the null hypothesis is true.
We can use a chi-square distribution table with 1 degree of freedom (since we have 2 categories - whether the student asks for clarification or not - and 3 levels of grade in the preceding Biology II course) to find the p-value. The p-value for a test statistic of 8.25 with 1 degree of freedom is less than 0.01.
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What scale factor is used to create a figure with an area of 16 square units from a figure with an area of 25 square units?
4/5
5/4
4
5
A a scale factor of 4/5 would be used to create a figure with an area of 16 square units from a figure with an area of 25 square units.
Calculating the scale factorThe scale factor to create a figure with an area of 16 square units from a figure with an area of 25 square units can be found using the formula:
scale factor = √(new area / original area)
Plugging in the given values, we get:
scale factor = √(16/25)
So, we have
scale factor = 4/5
Therefore, a scale factor of 4/5 would be used to create a figure with an area of 16 square units from a figure with an area of 25 square units.
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Answer: 4/5
The first person to answer was correct.
Step-by-step explanation:
I took the quiz so you don't have to! <3
Please help with three questions please this is due today
A quadratic equation is a type of polynomial equation of degree 2, which means the highest power of the variable in the equation is 2.
What is a quadratic equation?The general form of a quadratic equation is:
ax^2 + bx + c = 0
where a, b, and c are constants and x is the variable. The coefficient a is the quadratic coefficient, b is the linear coefficient, and c is the constant coefficient.
We know that;
y = (x - 3)^2+ 36
y = x^2 -3x + 9 + 36
y = x^2 - 3x + 45
y = -3[(x + 4) (x - 5)
y = -3[x^2 - 5x + 4x - 20]
y = -3[x^2 -x - 20]
y = -3x^2 + 3x + 60
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a fair die is rolled times. what is the probability of having no and no among the rolls? round your answer to three decimal places.
The probability of rolling no 2's and no 5's in 10 rolls is approximately 0.107.
The probability of rolling no 2's and no 5's on a fair die can be calculated using the formula for the probability of independent events:
P(A and B) = P(A) x P(B)
where P(A) is the probability of event A occurring, and P(B) is the probability of event B occurring.
The probability of rolling any number other than 2 or 5 on a single roll of a fair die is 4/6, or 2/3. Since each roll is independent, the probability of rolling no 2's and no 5's in n rolls can be calculated as follows:
P(no 2's and no 5's in n rolls) = (4/6)^n
To round the answer to three decimal places, we can use a calculator. For example, if n = 10, the probability is:
P(no 2's and no 5's in 10 rolls) = [tex](4/6)^10[/tex] = 0.107
So the probability of rolling no 2's and no 5's in 10 rolls is approximately 0.107, rounded to three decimal places.
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Can someone help me ASAP it’s due tomorrow. I will give brainliest if it’s all done correctly.
Answer part a, b, and c for brainliest!!
Based on the information provided by the question, we found the following solutions:
A. Sample space of randomly selecting 2 lollipops with replacement: {GG, CC, LL, GC, GL, CL, CG, LG, LC}B. Sample space of randomly selecting 2 lollipops without replacement {GC, GL, CL, CG, LG, LC}C. The experiment of randomly selecting two lollipops without replacement shows dependent events, because the probability of the second lollipop being a certain flavor depends on what the first lollipop was. On the other hand, the experiment of randomly selecting two lollipops with replacement shows independent events, because the first selection does not affect the probability of the second selection.What is probability theory?An event is considered dependent if the outcome of one event affects the probability of the outcome of another event. Conversely, events are considered independent if the outcome of one event does not affect the probability of the outcome of another event.
Therefore, in the case of selecting lollipops with or without replacement, the distinction between dependent and independent events lies in whether or not the lollipop selection process affects the probability of future selections.
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Cara and Beejal make a poster for school. The poster is in the shape of a rectangle. The left side of the poster measures 7 units; the top side of the poster measures 6 units. What is the area in square units of the completed poster?
26 square units
48 square units
42 square units
13 square units
The area of the completed poster is 42 square units.
The answer is (c) 42 square units.
The area of a rectangle:The area of a rectangle is the total amount of space or region enclosed within the boundaries of a rectangle.
It is measured in square units, which is the product of the length and the width of the rectangle.
The formula for calculating the area of a rectangle is:
Area = Length x Width
Here we have
Cara and Beejal make a poster for school.
The poster is in the shape of a rectangle. The left side of the poster measures 7 units; the top side of the poster measures 6 units.
The area of a rectangle is found by multiplying its length by its width.
In this case, the length of the poster is 7 units and the width is 6 units, so the area is:
Area = length × width
Area = 7 × 6
Area = 42 square units
Therefore,
The area of the completed poster is 42 square units.
The answer is (c) 42 square units.
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the internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent (more than 90 days overdue). for this quarter, the auditing staff randomly selected 400 customer accounts and found that 80 of these accounts were delinquent. what is the 95% confidence interval for the proportion of all delinquent customer accounts at this manufacturing company? (you should be using statistical software such as statcrunch.)
We will get the confidence interval for the delinquent accounts to be 0.1619, 0.2426.
Here we need to calculate the Confidence Interval for the proportion using Statcrunch.
First, we will select the option Stat. Next, we will select the option Proportion Stats. Now amongst the other available options, we will go to One Sample.
Since we have the summary available, we will select with Summary menu option.
Now the available data is clearly a binomial distribution, and hence, the confidence interval needs to be taken out with the help of normal approximation. Since this is a default in Statcrunch, we don't need to make any changes to this.
Under option # of success, we need to enter the number of delinquent accounts. This will be 80.
Now, # of observations is the sample size which is 400.
Now, we will select the confidence level for p with an interval of 0.95.
Hence we will get the interval to be 0.1619, 0.2426.
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Jermaine surveyed students in his school and asked each person whether they preferred Wildcats, Bears, or Eagles for the new school mascot. Jermaine asked 120 students in all. Of the people he surveyed, 55% were female, 30% preferred Wildcats, and 15% of the students were male and preferred Bears. A total of 28 females preferred Eagles. The number of people who preferred Bears was 20 fewer than the number who preferred Eagles.
The number who prefer Bears is 45 when there are approximately 166.67 students in the school who Jermaine surveyed.
What is equation?In mathematics, an equation is a statement that shows the equality between two expressions. An equation typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The expressions on either side of the equal sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation.
Here,
Let's use a table to organize the given information:
Wildcats Bears Eagles Total
Male 0.15x 0.45x
Female 0.30y 0.28y 0.55y
Total 0.30z 0.15z 0.28z 1.00z
Total Students 120
Here, x, y, and z represent the total number of males, females, and students, respectively, and we use percentages to represent the proportion of each group that prefers each mascot. We can use the given information to fill in some of the missing values in the table. For example:
The total number of males who prefer Bears is 0.15x, and the number of people who prefer Bears is 20 fewer than the number who prefer Eagles, so the number of males who prefer Bears is 20 less than the number who prefer Eagles, or 0.15x = 0.28y - 20.
The total number of students is 120, so z = x + y.
Using these equations and the information in the table, we can solve for the remaining values in the table:
Wildcats Bears Eagles Total
Male 0.30x 0.15x 0.45x 0.45x
Female 0.30y 0.12y 0.28y 0.55y
Total 0.30z 0.15z 0.28z 1.00z
Total Students 0.30z 0.27z 0.43z 120
To find the number of students who prefer Bears, we can multiply the total number of students by the proportion who prefer Bears:
0.27z = 0.15z - 20
0.12z = 20
z = 166.67
So there are approximately 166.67 students in the school who Jermaine surveyed. The number who prefer Bears is:
0.27z = 0.27 * 166.67
= 45
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In this Magic Square, every row, column, and diagonal adds to 0. Copy and complete this square
A Magic Square is a square grid of numbers in which the sum of every row, column, and diagonal is equal.
One way to approach this is to start with the center number and work outwards.
Since every row, column, and diagonal adds up to 0, the center number must be 0.
From there, we can fill in the rest of the numbers systematically.
For example, in the top row, we need to find two numbers that add up to 0.
We could choose 1 and -1, or 2 and -2, or any other pair of opposite numbers.
Let's choose 1 and -1 for the top row.
Then, we can fill in the bottom row with the same numbers in reverse order.
Next, we can fill in the left and right columns.
Since every column must add up to 0, we need to choose numbers that add up to 0 in each column.
Let's choose 3 and -3 for the left column, and 2 and -2 for the right column.
Finally, we can fill in the diagonals with the remaining numbers.
In this particular Magic Square, every row, column, and diagonal adds up to 0.
We can choose 4 and -4 for one diagonal, and 5 and -5 for the other diagonal.
By following this systematic approach, we can complete the Magic Square with the following numbers:
3 2 -1
0 0 0
-3 -2 1
This Magic Square is a great example of the fascinating patterns and mathematical properties that can be found in numbers. It is also a fun puzzle to solve and can provide hours of entertainment for people of all ages.
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