A college admissions director states that the age of a typical student currently enrolled has increased from 19 years old. In a random sample of 20 students that are currently enrolled, the mean age is found to be 22.9 years. Assume the distribution of ages is normal with the standard deviation of 1.5 years. Use the significance level of 0.05. Which of the following is the appropriate Decision and Conclusion? Reject the null hypothesis. Sample data did not provide evidence to support that the average age of all students currently enrolled has increased from 19 years old. Reject the null hypothesis. Sample data provided evidence to support that the average age of all students currently enrolled has increased from 19 years old. Do not reject the null hypothesis. Sample data provided evidence to support that the average age of all students currently enrolled has increased from 19 years old. None of these Do not reject the null hypothesis. Sample data did not provide evidence to support that the average age of all students currently enrolled has increased from 19 years old.
Answers
The required 90% confidence interval for population mean age is (22.35,23.45)
Given,
Sample size, n = 20
Sample mean, μ = 22.9 years
Standard deviation, σ = 1.5 years
Significance level, α = 0.05
We have to find the 90% confidence interval;
Here,
x ± z(critical) σ/√n
Substituting the values;
z(critical) at α₀.₀₅ = ±1.64
22.9 ± 1.64 (1.5/√20)
= 22.9 ± 0.55
= (22.35, 23.45)
That is,
(22.35,23.45) is the required 90% confidence interval for population mean age.
Learn more about confidence interval here;
https://brainly.com/question/15871700
#SPJ4
Related Questions
Cameron collects old books, and they convinced their friend Kenji to start collecting as well. Every month, they go to the store together, and they each buy a book. This table shows how many books they each have: Month 1 11 2 22 3 33 4 44 Kenji 1 11 2 22 3 33 4 44 Cameron 12 1212 13 1313 14 1414 15 1515 They both want an equation they can use to find how many books Cameron will have ( � cc) when Kenji has � kk books. Complete their equation. � = c=c, equals
Answers
The linear equation that describe the relationship between the book collection by Cameron, c and Kenji, c each month is represented as c = k - 11.
Linear equations are defined as the equations of degree one. It is represents equation for the straight line. The standard form of linear equation is written as, ax + by + c = 0, where a ≠ 0 and b ≠ 0. We have specify that Cameron collects and his friend Kenji start collecting the old books. The above table figure which contains data of books collected by both in different months. We have to determine the equation many books Cameron will have (c) when Kenji has k books. Let c and k denotes the books collected by Cameron and Kenji respectively. We see there is always increase in old book collection by one in case of both of them (Cameron and Kenji) each month. So, there exits a linear equation. Also, from the table, the Kenji's book collection is always 11 units less from Cameron's book collection. So, the required equation is written by c = k - 11 for each month. Hence, the required equation is equal to c = k - 11.
For more information about linear equation, refer:
https://brainly.com/question/28732353
#SPJ4
Complete question:
The above figure complete the question.
Cameron collects old books, and they convinced their friend Kenji to start collecting as well. Every month, they go to the store together, and they each buy a book. This table shows how many books they each have: They both want an equation they can use to find how many books Cameron will have (c) when Kenji has k books. Complete their equation.
Answer:
c=k+11
Step-by-step explanation:
f(x1, x2) 421 +222 3x² +213 5x11² (√₁+√₂)² 10ln(₁) (x₁+x₂)(x² + x3) min(3r1, 10√2) max{5x1,2r2} MP1(x1, x₂) MP2(X1, X₂) TRS(x1, x₂) Output (2,4)
Answers
The given mathematical expression is evaluated for the input values (2, 4). The result of the expression is calculated using various operations such as addition, multiplication, square root, natural logarithm, minimum, maximum, and function composition.
The expression f(x1, x2) involves several mathematical operations. Let's evaluate each part of the expression step by step:
1. The first term is 421 + 222, which equals 643.
2. The second term is 3x² + 213. Plugging in x1 = 2 and x2 = 4, we get 3(2)² + 213 = 3(4) + 213 = 12 + 213 = 225.
3. The third term is 5x11². Substituting x1 = 2 and x2 = 4, we have 5(2)(11)² = 5(2)(121) = 1210.
4. The fourth term is (√₁+√₂)². Replacing x1 = 2 and x2 = 4, we obtain (√2 + √4)² = (1 + 2)² = 3² = 9.
5. The fifth term is 10ln(₁). Plugging in x1 = 2, we have 10ln(2) = 10 * 0.69314718 ≈ 6.9314718.
6. The sixth term is (x₁+x₂)(x² + x3). Substituting x1 = 2 and x2 = 4, we get (2 + 4)(2² + 4³) = 6(4 + 64) = 6(68) = 408.
7. The seventh term is min(3r1, 10√2). As we don't have the value of r1, we cannot determine the minimum between 3r1 and 10√2.
8. The eighth term is max{5x1,2r2}. Since we don't know the value of r2, we cannot find the maximum between 5x1 and 2r2.
9. Finally, we have MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2), which are not defined or given.
Considering the given expression, the evaluated terms for the input values (2, 4) are as follows:
- 421 + 222 = 643
- 3x² + 213 = 225
- 5x11² = 1210
- (√₁+√₂)² = 9
- 10ln(₁) ≈ 6.9314718
- (x₁+x₂)(x² + x3) = 408
The terms involving min() and max() cannot be calculated without knowing the values of r1 and r2, respectively. Additionally, MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2) are not defined.
To learn more about logarithm click here: brainly.com/question/30226560
#SPJ11
Shelly bought a house five years ago for $150,000 and obtained an 80% loan. Now the home is worth $140,000 and her loan balance has been reduced by $12,000. What is Shelly's current equity?
Answers
Answer:
The current equity is $32,000
Step-by-step explanation:
Here, we are to calculate the current equity of the House
Value of house initially is $150,000
loan borrowed is 80% of this
= 80/100 * 150,000 = $120,000
Now the house value is 140,000 and the loan amount is reduced to 12,000
The outstanding loan amount to pay would be 120,000-12,000 = 108,000
The current equity is thus = Assets - liability = 140,000-108,000 = $32,000
the set of all n-tuples of real numbers that have the form, (x,x,x,...x) with the standard operations on R^n.i have read that n-tuple is a list of elements that are greater than or equal to 0 (non-negative). however, they say its an n-tuple of real numbers. does this mean that the n-tuple (x,x,x,....x) can have negative values (-x,-x,-x...-x)?
Answers
To answer the question, no, the n-tuple (x,x,x,....x) does not necessarily have to consist of non-negative values.
An n-tuple is a sequence of n elements, and in mathematics, it can refer to a sequence of real numbers, complex numbers, or other types of mathematical objects. In the case of the given set of n-tuples, it specifies that the n-tuple consists of real numbers and that all the elements in the tuple have the same value, which is denoted by x.
The definition of the set only specifies that the elements are real numbers and that they are all equal to each other. Therefore, the elements in the tuple can be positive, negative, or zero.
However, if the context of the problem or application requires the elements to be non-negative, then this restriction should be explicitly stated.
For example, if the n-tuple represents a set of quantities that cannot be negative, such as lengths, areas, or volumes, then it is appropriate to specify that the elements are non-negative real numbers.
To learn more about tuple click on,
https://brainly.com/question/29891173
#SPJ4
Opposites and absolute value mean the same thing.
True or false
Answers
Answer:
The absolute value of a number is the distance between the number and zero on a number line. In other words, a number and its opposite have the same absolute value.
Step-by-step explanation:
How many pivot columns must A have if its columns span R5? Why? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The matrix must have pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have only the trivial solution. B. The matrix must have pivot columns. The statements "A has a pivot position in every row" and "the columns of A span R5" are logically equivalent. C. The matrix must have pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would not span R5. D. The columns of a 5x7 matrix cannot span R5 because having more columns than rows makes the columns of the matrix dependent.
Answers
The matrix must have pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would not span R5. Therefore, the correct answer is C.
A pivot column is a column of the matrix that has a non-zero entry in the pivot position and all entries below the pivot are zero. In row echelon form, every row below a pivot column has a zero in the corresponding position. The pivot columns correspond to the linearly independent columns of the original matrix and the number of pivot columns determines the rank of the matrix.
The rank of a matrix is defined as the number of linearly independent columns or rows in the matrix. If the columns of a matrix span Rn, then the rank of the matrix must be equal to n. This means that the matrix must have n linearly independent columns. To ensure that the columns of A span R5, A must have at least 5 pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have a non-trivial solution, meaning that the columns of A would not be linearly independent and would not span R5.
You can learn more about pivot column at
https://brainly.com/question/29786913
#SPJ4
Please help!!!!
Sarah wants to leave a tip of 15%. Her bill before the tip is $23.00. How much should she leave for the tip ? show your work.
Answers
Answer:
$26.45.
Step-by-step explanation:
First, convert the 15% to an actual number that can be used in a calculation. For percents,this is always done by simply dividing the percent (in this case 15%) by 100%.So, the conversational term "15%" becomes 15% / 100% = 0.15 in terms of a real mathematical number.
Second, you need to find out what 15% of your $23.00 meal cost is.This is always done by multiplying 0.15 by $23.00, or
0.15 x $23.00=$3.45.
So, the amount of tip you are going to leave is $3.45.
This makes the total cost of your meal (to write on your charge slip or other payment)
$23.00 + $3.45 = $26.45.
Write cos 29° in terms of sine.
Help pls :(
Answers
Answer:
0.48480962
Step-by-step explanation:
1. Take the sine of 29 ° .
sin ( 29 ° )
2. Evaluate sin ( 29 ° ) .
0.48480962
Question 2 To achieve better software, one viewpoint aims to have the right product. What does having the right product mean?
Answers
Having the right product means that the software being developed meets the needs and requirements of its intended users.
This involves identifying the target audience, understanding their needs, and designing the software in a way that meets those needs. In addition to functionality, having the right product also means ensuring the software is user-friendly, reliable, and efficient. Achieving the right product requires effective communication between developers and stakeholders, as well as ongoing testing and feedback to ensure that the software meets its intended purpose.
Ultimately, having the right product leads to greater user satisfaction, increased productivity, and improved overall performance of the software.
To learn more about Coordinates click here
brainly.com/question/16634867
#SPJ11
100 POINTS !!!!!!
Earlier in this course, you explored Euclidean geometry, which is the study of flat space. This approach follows the teachings of Euclid, in which he describes the relationships between points, lines, and planes without any numerical measurement. You saw evidence of Euclidean geometry inside several proofs and geometric constructions.
In contrast, the focus of this unit is understanding geometry using positions of points in a Cartesian coordinate system. The study of the relationship between algebra and geometry was pioneered by the French mathematician and philosopher René Descartes. In fact, the Cartesian coordinate system is named after him. The study of geometry that uses coordinates in this manner is called analytical geometry.
It’s clear that this course teaches a combination of analytical and Euclidean geometry. Based on your experiences so far, which approach to geometry do you prefer? Why? Which approach is easier to extend beyond two dimensions? What are some situations in which one approach to geometry would prove more beneficial than the other? Describe the situation and why you think analytical or Euclidean geometry is more applicable.
Answers
Answer:
Step-by-step explanation:
Instead of working with the plane, we work with a spear in spiritual geometry, therefore all of the plane's notions are the same as the spear's. Three lines would be required to draw a triangle. We can't adjust the size of these circles to make a triangle bigger. So, in this situation, a line is defined as what I would term a "great circle," meaning it is always the same size as the sphere's radius. As a result, even if we only moved one of them, the angles of the others would shift.
both of the approaches are going fine for me so far. all of the subjects that I've learned have been easy-going and easy to understand. if I had to choose which one was easier for me, I would choose Euclidean. Mostly because it's easier than Analytical as well as it's not hard to solve for the data that was given to me. With Analytical, it's harder to establish a correspondence between geometric curves and algebraic equations.
PLEASE HELP
One number is 2 times as large as another. The sum of their reciprocals is 9/2. Find the two numbers.
Answers
I think this is right!
TRUE OR FALSE: A linear equation has ONE solution when the equation makes a false statement
Answers
Answer:
False
Step-by-step explanation: it can have many
I'm unsure for each process, the options are:
-addition property of equality
- subtraction property of equality
- multiplication property of equality -division property of equality
-simplifying
- distributive
Answers
The process of the equation:
5(3 x+4) = - 10 (Given equation)
15 x + 20 = - 10 (Multiplication property)
15 x + 20-20 = - 10 - 20 (Subtraction property)
15 x = - 30 (Addition property)
\($\frac{15 x}{15}=\frac{-30}{15}$\) (Division property)
x = - 2 (Simplifying )
Complete question attached at the end of the solution:
Given an equation below and evaluate the process:
5(3 x + 4) = - 10
Use the mathematical properties to solve the equation given.
Step 1: Multiplication property of equality to open the bracket
5(3 x+4) = - 10
15 x + 20 = - 10
Step 2: Subtraction property of equality:
15 x + 20 = - 10
Subtract both sides by 20
15 x + 20 - 20 = - 10 - 20
Step 3: Addition property of equality:
Add the numerical values irrespective to signs.
15 x = - 30
Step 4: Division property of equality:
15 x = - 30
Divide both sides by 15
\(\frac{15 x}{15} & =-\frac{30}{15} \\\)
Step 5: Simplifying:
x = - 2
Therefore the correct value of x = - 2
For more questions on mathematical properties
https://brainly.com/question/29301838
#SPJ4
There are 6 blue, 8 green, 5 red, and 10 yellow marbles in a bag. If a
marble is picked from the bag at random, what is the probability that it
will be green or red?
Answers
Answer:
13/29
Step-by-step explanation:
6 + 8 + 5 + 10 = 29
8 + 5 = 13
Jackie orders 7 scones for $12.31. What is the cost of 2 scones?
Answers
Tom work for a company
hi normal rate of pay i £15 per hour
when tom work for longer than 7 hour per day he i paid for each hour he work more than 7 hour
tom rate of overtime pay per hour i 1 1/3
on monday tom work for 11 hour
work out the total amount of money that tom made on monday
Answers
If on Monday Tom work for 11 extra hours the total amount of money that tom made on Monday is £885.
As per the given data, the extra money he earns can be calculated as,
= [(11 - 7) × 15] × 13 + (7 × 15)]
= (4 × 15 × 13) + 105
= 780 + 105
= £885
Therefore, the amount of money is £885.
Time and work are concerned with how long it takes a person or a group of people to finish a task and how well each of them completes it.
Indirect proportion is related to time and work. In both directions, when one quantity rises, the other falls, and vice versa. It takes less time to finish the same amount of work when people work more hours.
To learn more about time and work
https://brainly.com/question/3854047
#SPJ4
James lives in san francisco and works in mountain view. in the morning, he has 333 transportation options (bus, cab, or train) to work, and in the evening he has the same 333 choices for his trip home.
Answers
The probability that James will take the same mode of transportation twice is 1/9.
To find the probability that James will take the same mode of transportation twice, we need to calculate the probability of each individual transportation option and then multiply them together.
In the morning, James has 3 transportation options: bus, cab, or train. Since he randomly chooses his ride, the probability of selecting any particular option is 1 out of 3 (assuming all options are equally likely).
Therefore, the probability of James selecting the same transportation mode in the morning and evening is 1/3.
Hence, the probability that James will take the same mode of transportation twice is 1/3 multiplied by 1/3:
P(same mode of transportation twice) = 1/3 * 1/3 = 1/9.
Therefore, the probability that James will take the same mode of transportation twice is 1/9.
To know more about probability:
https://brainly.com/question/31828911
#SPJ4
16.One night, the temperature decreased at a rate of 0.6 degrees per hour. How many
hours did it take for the temperature to drop 2.7 degrees?
A 4 1/4 hours
B 4 1/2 hours
C 5 1/4 hours
D 4 3/4
Answers
Answer:
B.
2.7÷0.6= 4.5/ 4 1/2
mark as brailiest pls
The confidence associated with an interval estimate is called the:.
Answers
The confidence associated with an interval estimate is called the confidence level.
When making an interval estimate, such as estimating a population parameter based on a sample, it is important to provide an indication of the level of confidence we have in the estimate. The confidence level represents the probability or level of certainty that the true population parameter falls within the calculated interval.
For example, if we calculate a 95% confidence interval for the mean height of a population, it means that we are 95% confident that the true population mean height lies within that interval. This implies that if we were to repeat the sampling and interval estimation process multiple times, approximately 95% of the intervals would contain the true population parameter.
The confidence level is typically expressed as a percentage, such as 90%, 95%, or 99%. A higher confidence level indicates a greater level of certainty in the interval estimate but also results in a wider interval.
In summary, the confidence level associated with an interval estimate represents the level of confidence or probability that the interval contains the true population parameter.
To know more about confidence level click here :
https://brainly.com/question/22851322
#SPJ4
Charlene wants to earn at least $600 this month in commission. What is the minimum amount she needs to sell to earn $600 if she earns a 4.5% commission on everything she sells? Round to the nearest dollar.
Answers
Answer:
She will need to earn a little more than $1333 that week.
Step-by-step explanation:
600/0.45 = 1333.333(repeating) rounded to nearest dollar is 1333
Check by doing 1333 x 0.45 (comes out to be 599.85)
The minimum amount she needs to sell to earn $600 if she earns a 4.5% commission on everything she sells is 1333 dollars that week.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
Given that Charlene wants to earn at least $600 this month in the commission.
600/0.45 = 1333.333 rounded to nearest dollar
= 1333
Therefore, the minimum amount she needs to sell to earn $600 if she earns a 4.5% commission on everything she sells is 1333 dollars.
Learn more about multiplications;
https://brainly.com/question/14059007
#SPJ5
Question is on photo.
Answers
Therefore , the solution of the given problem of triangle comes out to be x = Tan⁻¹(15/8) .
A triangle is what exactly?Because a triangle has two or so more extra parts, it is a polygon. It has a straightforward rectangular shape. Only two of a triangle's three sides—A and B—can differentiate it from a regular triangle. Euclidean geometry produces a single area rather than a cube when boundaries are still not perfectly collinear. Triangles are defined by their three sides and three angles. Angles are formed when a quadrilateral's three sides meet. There are 180 degrees of sides on a triangle.
Here,
Given :
=> AS =15 and AN = 8
So,
We have to find m∠N = x
=> Tanx = 15/8
=> x = Tan⁻¹(15/8)
Therefore , the solution of the given problem of triangle comes out to be x = Tan⁻¹(15/8) .
To know more about triangle visit:
https://brainly.com/question/2773823
#SPJ1
Based on the 2017 season, the Houston Astros have a winning percentage of. 623. Use the binomial model to find the probability that the Astros will when 4 of their next 6 games
Answers
The probability that the Astros will win 4 of their next 6 games is 32.1%
Probability:
In math, probability refers the possible number of occurrence of the particular event.
Given,
Based on the 2017 season, the Houston Astros have a winning percentage of. 623.
Here we need to use the binomial model to find the probability that the Astros will win 4 of their next 6 games.
While we looking into the given question,
The winning percentage of Houston Astros 623.
Total number of games = 6
Here let us consider 50% as the winning percentage of all, then the based on the Astro, then probability of win 4 of their next 6 games is 32.1%.
To know more about Probability here.
https://brainly.com/question/11234923
#SPJ4
the radius of the earth - the distance from surface to core - is 6,370 kilometers. the planet neptune is 24,620 kilometers. if a scale model of the earth is drawn with a radius of 2.5 centimeters, how large would a scale model of neptune have to be drawn? group of answer choices 9848 cm 9.7 cm 2548 cm 0.02548 cm 3.86 cm
Answers
We may build up a proportion and solve for the scale model radius of Neptune using the ratio between the radii of the two planets and the known scale model radius of the Earth. The scale model of Neptune that is produced has a radius of around 9.7 cm.
We may take advantage of the fact that the ratio between the two planets' radii and the ratio between their respective scale model radii is the same. Let's name the Neptune scale model radius "r" Then, we may set up the ratio shown below:
Neptune's radius is equal to the product of Earth's radius and its scale model.
With the provided values, we may simplify and obtain:
24620 km / 6370 km equals 2.5 cm / r
We obtain the following when solving for "r":
r = (24620 km * 2.5 cm) / (6370 km)
r ≈ 9.7 cm
Therefore, a scale model of Neptune would have to be drawn with a radius of approximately 9.7 cm.
Learn more about scale models here:
https://brainly.com/question/17581605
#SPJ4
Pls help I don’t have much time.
Answers
Answer:
Dude dont spend 100 points! This place is scamming people
Step-by-step explanation:
The perimeter of a college basketball court is 96 meters and the length is 14 meters more than the width. What are the dimensions
Answers
Answer:
length = 32m, width= 16m
Step-by-step explanation:
l=2w
2(2w+w)=96
2(3w)=96
6w=96,w= 96/6 = 16m
l=2w=2x16=32m
Answer:
Width is 17, and length is 31
Step-by-step explanation:
The perimeter is all the sides added up.
96 is our perimeter.
We can call the width x, so that the length would be x+14
We have two widths and two lengths, and we can make that into an equation.
2(x)+2(x+14)=96
4x+28=96
4x=68
x=17
So now, we know that the width is 17.
Add 14 to that, and you will get 32.
You can double check this.
17+17=34
31+31=62
34+62=96.
Hope it helped.
Given f(x) = x ^ 2 + 2x and g(x) = x - 1 , find (fg)(x)
A) x^3 + 2x^2
B) x^3 + x^2 + 2x
C) x^3 - x^2 - 2x
D) x^3 + x^2 - 2x
Answers
Heya !! here's your solution :
\( \hookrightarrow \: ( {x}^{2} + 2x) \times (x - 1)\)
\( \hookrightarrow \: \: {x}^{3} - {x}^{2} + 2 {x}^{2} - 2x\)
\( \hookrightarrow \: {x}^{3} + {x}^{2} - 2x\)
therefore , the correct Option is D
The percent of births to toenage mothers that are out-of-wedlock can be approximated by a linear function of the number of years after 1951. The percent was 19 in 1968 and 76 in 2004. Complete parts (a) through (c) (a) What is the slope of the line joining the points (17,19) and (53,76)? The slope of the line is (Simplify your answer. Round to two decimal places as needed.) (b) What is the average rate of change in the percent of teenage out-of-wedlock births over this period? The average rate of change in the percent of teenago out-of-wedlock births over this period is (Simplify your answer. Round to two decimal places as needed.) (c) Use the slope from part (a) and the number of teenage mothers in 2004 to write the equation of the line The equation is p-D (Do not factor. Type an expression using x as the variable.)
Answers
a. The slope of the line is found to be 1.58.
b. The average rate of change is 1.58.
c. the equation of the line is p = 1.58x - 7.86.
How do we calculate?(a)
slope = (change in y) / (change in x)
change in y = 76 - 19 = 57
change in x = 53 - 17 = 36
slope = 57 / 36
slope = 1.58
(b) the average rate of change is 1.58 because average rate of change is equals to the slope
(c)
The points are:
(17, 19) and (53, 76).
p - 19 = 1.58(x - 17)
p - 19 = 1.58x - 26.86
p = 1.58x - 7.86
Learn more about slope at:
https://brainly.com/question/3493733
#SPJ4
(a) a box contains 3 red balls, 2 white balls, and 5 black balls. two balls are drawn at random from the box (with replacement of the first before the second is drawn). what is the probability of getting a red ball on the first draw and a white ball on the second? (enter your probability as a fraction.)
Answers
Answer:2
Step-by-step explanation:i did it
need help please somebody
Answers
Answer:
25.5 u²
Step-by-step explanation:
Find the area of the rectangle, then the area of the triangle. To get the final area, add them together.
Rectangle: 3 x 5 = 15
Triangle: 3 x 7 ÷ 2 = 10.5
Total: 15 + 10.5 = 25.5 u² (you put it in units since you don't know the measure, e.g. cm, m, km...)
What is the slope of the line segment?
у
15
12
9
6
3
0
1 2 3 4 5
0-3
O_1
له |
3
0 1
3
3