Answer:
Each boy will get 25 marbles.
Step-by-step explanation:
Given:
William has 3 jars of marbles to share equally with his brother the first jar holds 12 marbles the second jar holds 21 marbles the last jar holds 17 marbles.
Now, to write an expression using parentheses to find number of marbles each boy get.
Let the number of marbles each boy get be [tex]x.[/tex]
Total number of boys = 2.
Number of marbles first jar holds = 12.
Second jar holds = 21.
And third jar holds = 17.
As given, William shares marbles equally with his brother.
Now, we write the expression to find the number of marbles each boy get:
[tex]x=\frac{(12+21+17)}{2}[/tex]
[tex]x=\frac{12}{2} +\frac{21}{2} +\frac{17}{2}[/tex]
[tex]x=6+10.5+8.5[/tex]
[tex]x=25.[/tex]
Therefore, each boy will get 25 marbles.
What is data correlation. not anything too in depth just a over all definition
Ridge trail is 3/4 mile long. Valley trail is 7/12 mile long. Crystal brook trail is 2/3 mile long. Write the names of the trails in order from shortest trail to longest trail
Answer:
The answer to your question is below
Step-by-step explanation:
Process
1.- Convert the lengths to the same denominator (12)
Ridge trail 3 /4 mile = 3(3) / 12 = 9/12
Valley trail 7/12 mile = = 7/12
Crystal brook 2/3 mile = 4(2) / 12 = 8/12
2.- Order from shortest to longest
a) Valley trail
b) Crystal brook
c) Ridge trail
Answer:
Ridge trail, Valley trail, Crystal Brook trail
Step-by-step explanation:
3/4 --> 9/12
2/3 --> 8/12
7/12
What are the values of i and j after the following code snippet is run? int i = 10; int j = 20; int count = 0; while (count < 5) { i = i + i; i = i + 1; j = j - 1; j = j - j; count++; } System.out.println("i = " + i + ", j = " + j);
Answer:
i = 351, j = 0
Step-by-step explanation:
The while loop runs 5 times as indicated by the variable, count.
The variable, i, has an initial value of 10. The first line of the loop code doubles the value of i while the second increments it by 1. This is done 5 times. We have
Iteration 1: i = 10 + 10 + 1 = 21
Iteration 1: i = 21 + 21 + 1 = 43
Iteration 1: i = 43 + 43 + 1 = 87
Iteration 1: i = 87 + 87 + 1 = 175
Iteration 1: i = 175 + 175 + 1 = 351
The third line of the loop code decrements j by 1. However, the fourth line sets j = 0 by subtracting it from itself. Hence, j is always 0 at the end of the loop, no matter its initial value or the number of iterations.
Thus, at the end of the code snippet, i = 351 and j = 0.
Write the quadratic function in standard form.
y = -(x + 2)^2
Answer:
Step-by-step explanation:
-(x+2)^2 --> -(x+2)(x+2) --> -(x^2+4x+4) = -x^2-4x-4
Answer:
[tex]x^{2} -4x+4[/tex]
Step-by-step explanation:
[tex]y =-(x+2)^{2}[/tex]
The negative sign multiplies the positive in the bracket
[tex]y=(x-2)^{2}[/tex]
[tex](x-2) X (x-2)[/tex]
[tex]x^{2} -2x-2x+4[/tex]
That gives us
[tex]x^{2} -4x+4[/tex]
WILL MARK BRAINLIEST Suppose MyBook sent out 950 surveys. Which of these numbers of surveys being returned would prevent nonresponse bias?
A.95B.190C.9D.950
Answer:
C) 9
Step-by-step explanation:
The response is very low
Answer: 950, option D
Step-by-step explanation:
Adequate response rate from participants prevents non response bias.
Non-response bias can be said to occur when response rates from participants is below 60%.
Meanwhile, all other options are less than or equals 20% respond rate, while 950 implies 100% response rate.
A line segment that passes through the center and has endpoints on the circumference is called
Answer:
Diameter
Step-by-step explanation:
Knowing that a diameter is the largest chord as it passes through the center point of a circle, if the definition of the chord is a line segment with it's two endpoints on the circle (here by circle we mean circumference) then a diameter is a line segment that passes through the center and has endpoints on the circumference.
Given f(x) and g(x) = f(x + k), use the graph to determine the value of k.
Two lines labeled f of x and g of x. Line f of x passes through points negative 4, 0 and negative 2, 2. Line g of x passes through points negative 10, 0 and negative 8, 2.
6
−3
−6
3
Answer:
6
Step-by-step explanation:
f(-4) = g(-10) = f(-10+k)
f(-2) = g(-8) = f(-8+k)
-4 = -10+k
k = -4+10
k = 6
If the line f passes through (-4,0) and (-2,2) it means:
f(-4)=0 and f(-2)=2
If the line g passes through (-10,0) and (-8,2) it means:
g(-10)=0 and g(-8)=2
We can see that
g(-10)=0=f(-4)
g(-10)=0=f(-10+6)
Also,
g(-8)=2=f(-2)
g(-8)=2=f(-8+6)
Therefore, k=6
Alan is writing out the steps using the "shortest Route Algorithm". On the second step, he just circled the route ABD as the shortest route from A to D. What should he cross out next?
Group of answer choices
AB; 2
AC; 4
AD; 6
ABE; 8
Answer:
Cross out Ab
Step-by-step explanation:
Answer: AD; 6
Step-by-step explanation:
using the shortest route algorithm. The next shortest route to AD would be AD; 6.
5. We want to compare two different groups of students, students taking Composition 1 in a tradition lecture format and students taking Composition 1 in a distance learning format. We know that the mean score on the research paper is 85 for both groups. What additional information would be provided by knowing the standard deviation?
Answer:
By knowing the standard deviation, one gets the idea of how the value is scattered or dispersed about the mean.
Step-by-step explanation:
Let us first define standard deviation.
As it is known that the standard deviation is a measure of dispersion which express the spread of observation in terms of the average of deviations of observations from some central values.
Measure of dispersion gives us an idea about homogeneity or heterogeneity of the distribution.
Standard deviation is supposed almost an ideal measure of dispersion except the general nature of extracting the square root.
Thus for the given question, if we want to compare the two different groups of students whose mean score is 85. Here the standard deviation for both the groups interprets an idea about how the individual score for each group scattered or varied about the mean score i.e. 85.
A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses
Answer:
Step-by-step explanation:
Let the speed of cyclist be C and bus be B.
Using the concept of relative speed:-
For incoming bus,speed = B + C
For overtaking bus,speed = B - C
Now,distance travelled b/w 2 incoming bus = (B + C)*4
Now,distance travelled b/w 2 overtaking bus = (B - C)*12
so,
(B + C)*4 = (B - C)*12
or, B=2C
Hence,distance b/w two buses in same direction,d=4*(3/2)B=6 B
Therefore, time gap=d/B=6 minutes
Time interval between consecutive buses is 6 minutes, determined using relative speeds and given overtaking and meeting intervals.
To solve this problem, let's denote the following:
- [tex]\( v_c \)[/tex] is the speed of the cyclist.
- [tex]\( v_b \)[/tex] is the speed of the buses.
- [tex]\( t \)[/tex] is the time interval between consecutive buses.
Step-by-Step Solution:
1. Relative Speed in the Same Direction:
When a bus overtakes the cyclist, it means the bus is catching up to the cyclist from behind. The relative speed of the bus with respect to the cyclist is:
[tex]\[ v_b - v_c \][/tex]
According to the problem, a bus overtakes the cyclist every 12 minutes:
[tex]\[ v_b - v_c = \frac{d}{12} \][/tex]
where [tex]\( d \)[/tex] is the distance between consecutive buses.
2. Relative Speed in the Opposite Direction:
When the cyclist meets an oncoming bus, they are moving towards each other. The relative speed is:
[tex]\[ v_b + v_c \][/tex]
According to the problem, the cyclist meets an oncoming bus every 4 minutes:
[tex]\[ v_b + v_c = \frac{d}{4} \][/tex]
3. Setting Up Equations:
From the given information, we have two equations:
[tex]\[ v_b - v_c = \frac{d}{12} \][/tex]
[tex]\[ v_b + v_c = \frac{d}{4} \][/tex]
4. Solving for [tex]\( d \)[/tex] and [tex]\( t \)[/tex] :
Let's add these two equations to eliminate [tex]\( v_c \)[/tex]:
[tex]\[ (v_b - v_c) + (v_b + v_c) = \frac{d}{12} + \frac{d}{4} \][/tex]
[tex]\[ 2v_b = \frac{d}{12} + \frac{d}{4} \][/tex]
[tex]\[ 2v_b = \frac{d}{12} + \frac{3d}{12} \][/tex]
[tex]\[ 2v_b = \frac{4d}{12} \][/tex]
[tex]\[ 2v_b = \frac{d}{3} \][/tex]
Multiply both sides by 3:
[tex]\[ 6v_b = d \][/tex]
Now, substitute [tex]\( d = 6v_b \)[/tex] back into either equation, let's use [tex]\( v_b + v_c = \frac{d}{4} \)[/tex]:
[tex]\[ v_b + v_c = \frac{6v_b}{4} \][/tex]
[tex]\[ v_b + v_c = 1.5v_b \][/tex]
[tex]\[ v_c = 0.5v_b \][/tex]
5. Finding the Time Interval [tex]\( t \)[/tex]:
We already established that the distance between consecutive buses is [tex]\( d = 6v_b \)[/tex].
The time interval [tex]\( t \)[/tex] between consecutive buses can be found using the speed of the buses:
[tex]\[ t = \frac{d}{v_b} \][/tex]
[tex]\[ t = \frac{6v_b}{v_b} \][/tex]
[tex]\[ t = 6 \text{ minutes} \][/tex]
So, the time interval between consecutive buses is 6 minutes.
Kayla rented a boat. There was a one-time charge of $100 plus an hourly rate of $45. Her total cost for the day was $370. Which equation, when solved for x, gives the number of hours she rented the boat? A) 45x + 100 = 370 B) 45x − 100 = 370 C) 45x + 370 = 100 D) 45x − 370 = 100
The answer is 'A' twinks!!
The equation that represents her total cost for the day is
A) 45x + 100 = 370
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Given, Kayla rented a boat.
There was a one-time charge of $100 plus an hourly rate of $45.
Assuming no. of hours to be x and total cost to be c(x).
∴ c(x) = 45x + 100.
Her total cost for the day was $370.
370 = 45x + 100.
learn more about equations here :
https://brainly.com/question/10413253
#SPJ5
Which statement is true about the box plots? Both the ranges and the interquartile ranges for the data sets are the same. Neither the ranges nor the interquartile ranges for the data sets are the same. The interquartile ranges for the box plots are the same
Answer:
Neither the ranges nor the interquartile ranges for the data sets are the same.
Step-by-step explanation:
In a visual display, the boxplot presents five sample statistics: the minimum, the lower quartile, the median, the upper quartile and the maximum, and the box length gives an indication of the sample variability and the line across the box shows where the sample is centred, with an end at each quartile. The length of the box is thus the interquartile range of the sample and, whether the sample is symmetric or skewed, either to the right or left, the "shape" of the sample, and by implication, the shape of the population from which it was drawn, considering appropriate analyses of the data.
The question is incomplete! The complete question along with answer and explanation is provided below.
Question:
Which statement is true about the box plots? (attached in the image)
A Both the ranges and the interquartile ranges for the data sets are the same.
B. Neither the ranges nor the interquartile ranges for the data sets are the same.
C. The interquartile ranges for the box plots are the same, but their ranges are different.
D. The ranges for the box plots are the same, but their interquartile ranges are different.
Answer:
D. The range of both box-pots is same (9) but the interquartile range of box-plots is different (6 and 5)
Step-by-step explanation:
To answer this question, first we have to understand what a box plot is!
A box plot is a type of graph which shows 5 statistical characteristics of a data set.
1. Maximum and 2. Minimum values of data
3. Upper Interquartile and 4. Lower interquartile of data
5. Median of the data
Now lets analyze the attached box-plot so that we can conclude what is true about them and what is not!
We have two box-plots for two teacher's classes Marc and Sue and they show the number of incorrect questions in exam.
For Sue's class: (on the bottom)
As you can see the maximum and minimum values are
Maximum = 12 and Minimum = 3
So the Range becomes = 12 - 3 = 9
The upper quartile Q3 is 10 and lower quartile Q1 is 5
So the Interquartile Range becomes = 10 - 5 = 5
This Interquartile Range represents the 25 to 75 percentile of the data
There is little vertical line skewed to the right represents the Median = 9
So to summarize Sue's class
Range = 9
Interquartile Range = 5
Median = 9
For Marc's class: (on the top)
As you can see the maximum and minimum values are
Maximum = 10 and Minimum = 1
So the Range becomes = 10 - 1 = 9
The upper quartile Q3 is 9 and lower quartile Q1 is 3
So the Interquartile Range becomes = 9 - 3 = 6
This Interquartile Range represents the 25 to 75 percentile of the data
There is little vertical line skewed to the left represents the Median = 5
So to summarize Marc's class
Range = 9
Interquartile Range = 6
Median = 5
Conclusion:
The range of both box-pots is same (9) but the interquartile range of box-plots is different (6 and 5).
Therefore, we can confidently conclude that option D is the correct answer.
A political polling organization wishes to select a smaller focus group from a group of 7 Republicans, 10 Democrats, and 2 Independents. In how many ways can the group be chosen if: (a) it will consist of 1 Republican and 4 Democrats?(b) it will consist of 2 Republicans, 2 Democrats, and 3 Independents?
Final answer:
To determine the number of ways a smaller focus group can be chosen, we use combinations to calculate the possible selections for each political affiliation separately and then multiply these numbers. For part (a), there are 1470 ways to select 1 Republican and 4 Democrats. For part (b), there are 945 ways to choose 2 Republicans, 2 Democrats, and 1 Independent.
Explanation:
To find out how many ways a smaller focus group can be chosen from a larger group, we use combinations, which is a part of probability and combinatorics in mathematics.
Part (a): 1 Republican and 4 Democrats
To select 1 Republican out of 7, we calculate this as 7 choose 1, denoted as 7C1.
To select 4 Democrats out of 10, we calculate 10 choose 4, denoted as 10C4.
The total number of ways to choose the group is the product of these two combinations:
7C1 × 10C4 = 7 × (10 × 9 × 8 × 7) / (4 × 3 × 2 × 1) = 7 × 210 = 1470 ways
Part (b): 2 Republicans, 2 Democrats, and 1 Independent
Choosing 2 Republicans from 7, we have 7C2.
For the Democrats, 10C2. Since there are only 2 Independents, they are both selected, so no need to choose:
7C2 × 10C2 × 2C2 = (7 × 6) / (2 × 1) × (10 × 9) / (2 × 1) × 1 = 21 × 45 × 1 = 945 ways
In 2000 the population of a country reached 1 billion, and in 2025 it is projected to be 1.2 billion. (a) Find values for C and a so that P(x)equalsCa Superscript x minus 2000 models the population of a country in year x. (b) Estimate the country's population in 2010. (c) Use P to determine the year when the country's population might reach 1.4 billion. (a) Cequals nothing (Type an integer or decimal rounded to five decimal places as needed.)
Answer:
(a) The value of C is 1.
(b) In 2010, the population would be 1.07555 billions.
(c) In 2047, the population would be 1.4 billions.
Step-by-step explanation:
(a) Here, the given function that shows the population(in billions) of the country in year x,
[tex]P(x)=Ca^{x-2000}[/tex]
So, the population in 2000,
[tex]P(2000)=Ca^{2000-2000}[/tex]
[tex]=Ca^{0}[/tex]
[tex]=C[/tex]
According to the question,
[tex]P(2000)=1[/tex]
[tex]\implies C=1[/tex]
(b) Similarly,
The population in 2025,
[tex]P(2025)=Ca^{2025-2000}[/tex]
[tex]=Ca^{25}[/tex]
[tex]=a^{25}[/tex] (∵ C = 1)
Again according to the question,
[tex]P(2025)=1.2[/tex]
[tex]a^{25}=1.2[/tex]
Taking ln both sides,
[tex]\ln a^{25}=\ln 1.2[/tex]
[tex]25\ln a = \ln 1.2[/tex]
[tex]\ln a = \frac{\ln 1.2}{25}\approx 0.00729[/tex]
[tex]a=e^{0.00729}=1.00731[/tex]
Thus, the function that shows the population in year x,
[tex]P(x)=(1.00731)^{x-2000}[/tex] ...... (1)
The population in 2010,
[tex]P(2010)=(1.00731)^{2010-2000}=(1.00731)^{10}=1.07555[/tex]
Hence, the population in 2010 would be 1.07555 billions.
(c) If population P(x) = 1.4 billion,
Then, from equation (1),
[tex]1.4=(1.00731)^{x-2000}[/tex]
[tex]\ln 1.4=(x-2000)\ln 1.00731[/tex]
[tex]0.33647 = (x-2000)0.00728[/tex]
[tex]0.33647 = 0.00728x-14.56682[/tex]
[tex]0.33647 + 14.56682 = 0.00728x[/tex]
[tex]14.90329 = 0.00728x[/tex]
[tex]\implies x=\frac{14.90329}{0.00728}\approx 2047[/tex]
Therefore, the country's population might reach 1.4 billion in 2047.
An article reported that the mean annual adult consumption of wine was 3.85 gallons and that the standard deviation was 6.07 gallons. Would you use the empirical rule to approximate the proportion of adults who consume more than 9.92 gallons (i.E., the proportion of adults whose consumption value exceeds the mean by more than 1 standard deviation)? Explain your reasoning. (Round your numerical answer to three decimal places.)
To approximate the proportion of adults consuming more than 9.92 gallons of wine annually, we can use the empirical rule.
Explanation:To approximate the proportion of adults who consume more than 9.92 gallons, we can use the empirical rule. The empirical rule states that approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations. Since we want to find the proportion of adults consuming more than 9.92 gallons, which is more than 1 standard deviation above the mean, we can estimate that it would be approximately 32% based on the empirical rule.
Learn more about Empirical Rule here:https://brainly.com/question/35669892
#SPJ3
please look at this multiple choice, thanks!
Step-by-step explanation:
[tex] \frac{y - y1}{x - x1} = \frac{y2 - y1}{x2 - x1} [/tex]
[tex] \frac{y - 0}{x - ( - 1)} = \frac{3 - 0}{1 - ( - 1)} [/tex]
[tex] \frac{y}{x + 1} = \frac{3}{1 + 1} [/tex]
[tex] \frac{y}{x + 1} = \frac{3}{2} [/tex]
[tex]y = \frac{3}{2} (x + 1)[/tex]
[tex]y = \frac{3}{2} x + \frac{3}{2} [/tex]
option B
Researchers are interested in learning more about the age of young adults who watch the television show Parks and Recreation. By interviewing people at a shopping mall, they can identify people who watch this show.
The mean age of these young adults at the mall who watch Parks and Recreation is an example of which of the following?
a. Parameter
b. Statistic
c. Population
d. Sample
Answer:
Option B) Statistic
Step-by-step explanation:
Parameter and Statistic
A parameter is a quantitative value that describes a population.A population is a collection of all possible observation for an event.A statistic is a quantitative variable that describes a sample.A sample is a part of population and is always smaller than the population.For the given research:
Population:
All young adults who watch the television show Parks and Recreation
Sample:
All young adults at the mall who watch the television show Parks and Recreation
Thus, the he mean age of these young adults at the mall who watch Parks and Recreation is a statistic as it describes a sample of the whole population.
Thus, the correct answer is :
Option B) Statistic
Find the perimeter of the polygon if B = D
Perimeter of the polygon is 92 cm
Solution:
The reference image for the solution is attached below.
AX = 10.5 cm, BY = 11.5 cm and CZ = 12.5 cm
AW and AX are tangents to the circle from external point A.
BX and BY are tangents to the circle from external point B.
CY and CZ are tangents to the circle from external point C.
DZ and DW are tangents to the circle from external point D.
Two tangents drawn from an external point to a circle are equal in length.
AW = AX, BX = BY, CY = CZ and DZ = DW
⇒ AW = AX
AW = 10.5 cm
⇒ BX = BY
BX = 11.5 cm
⇒ CY = CZ
CY = 12.5 cm
Given ∠B ≅ ∠D
If two angles are congruent, then the corresponding sides are congruent.
BX = BY = DZ = DW
DZ = DW = 11.5 CM
Perimeter = AW + AX + BX + BY + CY + CZ + DZ + DW
= 10.5 + 10.5 + 11.5 + 11.5 + 12.5 + 12.5 + 11.5 + 11.5
= 92
Perimeter of the polygon is 92 cm.
I WILL GIVE A CROWN JUST NEED HELP ASAP
Answer:
C option is correct 219.
Step-by-step explanation:
Total fans = 365
Fans who bought popcorn = 3/5
No. of Fans who bought popcorn = 365 x 3/5
= 219
Answer:
Step-by-step explanation:
Rachel gets her midterm grades and finds that she has a 2.4 in OB. She expected a better grade point average to date. Rachel is _________ her performance.
Answer:
Answer is; Evaluating
Step-by-step explanation:
Student self-assessment involves students evaluating their own work and learning progress.
Through self-assessment evaluation, students can:
* See where their knowledge is weak
* See where to focus their attention in learning.
* Set realistic goals
* Revise their work
* Track their own progress.
In Rachel's case, after writing her midterm exams, she already set her goal grade. So when she got her midterm grades, she needed to evaluate her work to find out her performance.
Therefore, according to the question, Rachel is EVALUATING her performance.
a. Write the first four terms of the series.
b. Does the series diverge or converge?
c. If the series has a sum, find the sum. Show your work.
Step-by-step explanation:
a. The first four terms are:
-4 (⅓)¹⁻¹ = -4
-4 (⅓)²⁻¹ = -4/3
-4 (⅓)³⁻¹ = -4/9
-4 (⅓)⁴⁻¹ = -4/27
b. This is a geometric series. Since the absolute value of the common ratio is less than 1 (|⅓| < 1), the series converges.
c. The series converges to the sum of:
S = a₁ / (1 − r)
S = -4 / (1 − ⅓)
S = -6
Jocelyn estimates that a piece of wood measures 5.5 cm. If it actually measures 5.62 cm, what is the percent error of Jocelyn's estimate?2.13%2.18%12%46.83%
Answer:
is d
Step-by-step explanation:
Answer:
2.13%
Step-by-step explanation:
Inaccurate measurement = 5.5cm
Actual measurement = 5.62cm
Difference= actual - inaccurate
=> 5.62 - 5.5
Therefore, the measurement Jocelyn obtained is off by 0.12cm (difference)
Note: error = difference
% diff = error÷ actual measurement × 100
= 0.12/5.62 × 100
% diff. = 2.13 (to the nearest decimal place)
PLEASE HELP IM BEING TIMED
Answer:
The 3rd option Summation(4^i-4)
Step-by-step explanation:
Summation(4^i-4)
When i = 1
4^I-4 = 4^1-4 = 4^-3 = 1/64
When i = 2
4^i-4 = 4^2-4 = 4^-2 = 1/16
When i = 3
4^i-4 = 4^3-4 = 4^-1 = 1/4
When i = 4
4^i-4 = 4^4-4 = 4^0 = 1
When i = 5
4^i-4 = 4^5-4 = 4^1 = 4
Answer:
[tex]\sum _{i=1}^54^{i-4}[/tex]
Step-by-step explanation:
[tex]a_{1} \\[/tex] = First term
In this case, our first term is [tex]\frac{1}{64}[/tex]
The ratio of all of the adjacent terms is 4
[tex]a_{1} \\[/tex] = [tex]4^1^-^4[/tex]
[tex]a_{1}=\frac{1}{64}[/tex]
~Hope this helps!~
Use a double integral to find the volume of the solid in the first octant which is enclosed by the surface 3x + 6y + 2z = 12 and the coordinate planes.
Answer:
8 unit^3
Step-by-step explanation:
Given:
- The equation of the plane is:
3x + 6y + 2z = 12
Find:
Use a double integral to find the volume of the solid in the first octant which is enclosed by the plane and the coordinate planes
Solution:
- Express the equation of surface ( plane ) as a subject of any coordinate axis we will use z:
2z = 12 - 3x - 6y
z = 6 - 1.5x - 3y
- The double integral would be set- up as:
[tex]\int\limits^d_c \int\limits^a_b ({6 - 1.5x - 3y}) \, dy.dx[/tex]
- Where, a , b ,c and d are limits of integration.
- To determine the limits we will project the surface to x-y plane or z = 0 plane, the equation we have is:
0 = 6 - 1.5x - 3y
y = 2 - 0.5x
- For limits a and b the integration is with respect to y, so we express the limits of y in terms of x. Where lower limit b = 0, and upper limit a = 2 - 0.5x
- Similarly, the limits c and d is with respect to x are constants we have:
c = 0
0 = 2 - 0.5*d
d = 4
- Then solve the double integral:
[tex]\int\limits^4_0 ({6y - 1.5xy - 1.5y^2}) \,_0 ^2^-^0^.^5^x dx \\\\\int\limits^4_0 ({6(2-0.5x) - 3x + 0.75x^2 - 1.5(2-0.5x)^2}) dx \\\\({-6(2-0.5x)^2 - 1.5x^2 +0.25x^3 + (2-0.5x)^3}) | ^4_0\\\\= ( -6(0) - 1.5(16) + 0.25*(64) + (0) + 6(4) + 0 + 0 - (8) ) \\\\= 8 unit^3[/tex]
Final answer:
To find the volume of the solid in the first octant enclosed by the given surface and the coordinate planes, a double integral is used where z is expressed in terms of x and y, and appropriate limits for x and y are determined.
Explanation:
The volume of the solid in the first octant enclosed by the surface 3x + 6y + 2z = 12 and the coordinate planes can be found using a double integral. First, we need to express z in terms of x and y: z = 6 - (3/2)x - 3y.
The limits for x and y are determined by setting z = 0; thus, x ranges from 0 to 4, and y ranges from 0 to (6-(3/2)x)/3. Hence, the double integral equation is set up as follows:
[tex]\(\int_{0}^{4}\int_{0}^{2-(3/2)x} (6 - \frac{3}{2}x - 3y) dy dx\)[/tex]
Evaluating this double integral will give the volume of the solid.
What would be the results after the following code was executed? int[] x = {23, 55, 83, 19}; int[] y = {36, 78, 12, 24}; for(int a = 0; a < x.length; a++) { x[a] = y[a]; y[a] = x[a]; }
Answer:
x = y = {36, 78, 12, 24}
Step-by-step explanation:
The loop executes 4 times, as indicated by the length of array x.
The first line in the content of the loop assigns every element in array y to array x. Because both arrays now have the same content, the second line of code is quite redundant and is assigning the new values of x to y. Since these new values of x are the old values of y, there is no change in the contents of y. They are just being replaced by themselves.
In other words, the second line is not needed for anything. In fact, if the loop has much more contents, the second makes it work twice as much, reducing efficiency.
The average person in North Carolina will eat about 12,300 pounds of sugar in a 70 or one lifespan about how many pounds of sugar does the average person in North Carolina eat a year
Answer:
The sugar does the average person in North Carolina eat in a year = 175.71 pounds.
Step-by-step explanation:
The person eat sugar in 70 year life span = 12300 pounds
The same person eat sugar in one year = [tex]\frac{12300}{70}[/tex]
= 175.71 pounds
Thus the person eat about 175.71 pounds of sugar in a year.
In a game, a player earns 100 points for each question answered correctly and earns −30 points for each question answered incorrectly. A player answered 14 questions correctly and 6 questions incorrectly. Write a numeric expression to represent the total number of points the player earned. What is the total number of points the player earned?
Answer:
1220
Step-by-step explanation:
Given that in a game, a player earns 100 points for each question answered correctly and earns −30 points for each question answered incorrectly.
Let x be the no of questions correctly answered . Then 20-x would be the question wrongly answered since total number of questions = 14+6 =20
Points gained for correct answer = 100(x) = 100x
Points lost for wrong answer = -30(20-x) = -600+30x
So total points gained when x questions are answered right
= [tex]100x-600+30x\\= 130x-600[/tex]
A player answered 14 questions correctly and 6 questions incorrectly.
Here x =14
Hence we substitute x =14 to get total points earned
Total points earned
[tex]= 130(14)-600\\= 1820-600\\=1220[/tex]
Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28. The probability density function has what value in the interval between 20 and 28?a. 1.000 b. 0c. 0.125 d. 0.050
Answer:
The probability density function is f(x)=0.125.
Step-by-step explanation:
We have he continuous random variable x, which has a uniform distribution over the interval from 20 to 28. We calculate the probability density function has what value in the interval between 20 and 28.
We use the formula:
[tex]\boxed{f(x)=\frac{1}{b-a}}[/tex]
We have a=20 and b=28, we get
[tex]f(x)=\frac{1}{28-20}\\\\f(x)=\frac{1}{8}\\\\f(x)=0.125\\[/tex]
The probability density function is f(x)=0.125.
The value of the probability density function (pdf) in the interval between 20 and 28 is 0.125.
Explanation:The probability density function (pdf) of a continuous uniform distribution is represented by a horizontal line. Since the random variable x has a uniform distribution over the interval from 20 to 28, the pdf will also have a constant value over this interval.
To find the value of the pdf in the interval between 20 and 28, we need to calculate the area under the pdf curve in this interval. Since the pdf is a horizontal line, the area is simply equal to the height multiplied by the width of the interval.
Since the width of the interval is 8 (28 - 20) and the pdf is a uniform distribution, the height is 1/8. Therefore, the value of the pdf in the interval between 20 and 28 is 1/8 or 0.125.
Learn more about Probability density function here:https://brainly.com/question/35625239
#SPJ3
In k-means clustering, k represents the a. number of clusters. b. mean of the cluster. c. number of observations in a cluster. d. number of variables.
Answer:
The correct answer to the question is;
a. number of clusters.
Step-by-step explanation:
Clustering is the process of looking for smaller similar groups of observation within a set of data.
K-means clustering is a vector quantization method used in data mining cluster analysis. The objective of k-means clustering is to a given number of observations into k number of clusters whereby an observation is grouped in a cluster having the closest mean value, hence being representative of tha particular cluster. This is in atempt to make observations in a particular group to be similar.
In k-means clustering, the number of clusters is specified as k.
In k-means clustering, k represents the number of clusters, indicated by answer choice (a). This technique involves partitioning the data into k compact and separate clusters, with the k initial cluster centers often chosen randomly.
Explanation:In k-means clustering, k represents the number of clusters into which the data is to be partitioned. This method involves assigning each data point to the nearest cluster, while keeping the clusters as small as possible. The initial positions of the k clusters are typically chosen at random, and then the mean position of all the points in each cluster is recomputed, and this becomes the new center for the cluster. This process is repeated until the cluster assignments no longer change significantly, meaning the clusters are as compact and as separate as possible. The mean refers to the mean of the data points within each cluster once the clusters have formed. The standard deviation is a measure of the variability of the original distribution of the data. Sample size, denoted as n, is the number of observations in the dataset. Therefore, the answer to the question about what k represents in k-means clustering is (a) the number of clusters.
The king of noble girth said, "you there, victualer, have you procured the food for the upcoming wedding feast?" "No sire," he meekly replied, "I did not know how much of each i was to get." "Listen carefully, and do what i say," growled the king. "one hubdred eighty head fo bird and beast, you are to cook my great feast. 500 feet they have to stand on, the number of each you now must stand on."
The subject of this question is Mathematics. The student needs to determine the number of birds and beasts the victualer needs to get for the upcoming wedding feast.
Explanation:The subject of this question is Mathematics.
The student is being asked to determine how much of each bird and beast the victualer needs to get for the upcoming wedding feast. The king specifies that there should be a total of 180 heads of bird and beast, and the number of feet should be 500. The student needs to calculate the number of each bird and beast that satisfies these conditions.
To solve this problem, we can set up a system of equations. Let x be the number of birds and y be the number of beasts. We have the following two equations:
x + y = 180 (equation 1)
2x + 4y = 500 (equation 2)
We have equation 1 to represent the total number of heads, and equation 2 to represent the total number of feet. We can solve this system of equations to find the values of x and y that satisfy both equations.
In equation 1, we can solve for x in terms of y: x = 180 - y. We can substitute this value of x in equation 2 to get:
2(180 - y) + 4y = 500
Simplifying this equation gives: 360 - 2y + 4y = 500
Combining like terms: 2y = 140
Dividing both sides by 2: y = 70
Substituting this value of y in equation 1 gives: x = 180 - 70 = 110
So, the victualer needs to get 110 birds and 70 beasts for the upcoming wedding feast.
Learn more about Mathematics here:
https://brainly.com/question/41753146
#SPJ11