Answer:
Hence, the relation R is a reflexive, symmetric and transitive relation.
Given :
A be the set of all lines in the plane and R is a relation on set A.
[tex]R=\{l_1,l_2\in A|l_1 \;\text{is parallel to}\; l_2\}[/tex]
To find :
Which type of relation R on set A.
Explanation :
A relation R on a set A is called reflexive relation if every [tex]a\in A[/tex] then [tex](a,a)\in R[/tex].
So, the relation R is a reflexive relation because a line always parallels to itself.
A relation R on a set A is called Symmetric relation if [tex](a,b)\in R[/tex] then [tex](b,a)\in R[/tex] for all [tex]a,b\in A[/tex].
So, the relation R is a symmetric relation because if a line [tex]l_1[/tex] is parallel to the line [tex]l_2[/tex] the always the line [tex]l_2[/tex] is parallel to the line [tex]l_1[/tex].
A relation R on a set A is called transitive relation if [tex](a,b)\in R[/tex] and [tex](b,c)\in R[/tex] then [tex](a,c)\in R[/tex] for all [tex]a,b,c\in A[/tex].
So, the relation R is a transitive relation because if a line [tex]l_1[/tex] s parallel to the line [tex]l_2[/tex] and the line [tex]l_2[/tex] is parallel to the line [tex]l_3[/tex] then the always line [tex]l_1[/tex] is parallel to the line [tex]l_3[/tex].
Therefore the relation R is a reflexive, symmetric and transitive relation.
(sin30°+cos30°)(sin30°-cos30°)
A sewing class has 185 yards of fabric to make quilts. Each quilt requires 8 yards of fabric. How much fabric will remain after all the quilts are made?
In Buenos Aires, the average daily high temperature temperature in a year is reported to be 18.2^{\circ}\text{C}18.2 ∘ C18, point, 2, degrees, start text, C, end text. Catalina believes that last year was warmer than usual. In order to test her belief, she takes a simple random sample of 202020 days from last year, and records the daily high temperature on each chosen day. She finds that the sample mean temperature is 19.1^{\circ}\text{C}19.1 ∘ C19, point, 1, degrees, start text, C, end text and the sample standard deviation is 7.9^{\circ}\text{C}7.9 ∘ C7, point, 9, degrees, start text, C, end text. Catalina wants to use these sample data to conduct a ttt test on the mean. Assume that all conditions for inference have been met.
Answer:
H 0
:μ=18.2 ∘ C
H a
:μ>18.2 ∘ C
Step-by-step explanation:
Khan............... The null hypothesis has a statement of equality, and the direction of alternative hypothesis (>)(>)left parenthesis, is greater than, right parenthesis matches her belief that last year was warmer.
The three conditions for hypothesis testing are approximately met, and the null hypothesis is that the population mean daily high temperature in Buenos Aires is 18.2∘C.
What is hypothesis testing?Hypothesis Testing is a type of statistical analysis in which you put your assumptions about a population parameter to the test. It is used to estimate the relationship between 2 statistical variables.
here, we have,
The three conditions for hypothesis testing are approximately met based on the information given.
Null hypothesis (H0) is that the population mean daily high temperature in Buenos Aires is 18.2∘C. Alternative hypothesis (Ha) is that the population mean daily high temperature in Buenos Aires is greater.
The test statistic is calculated as (sample mean - population mean) / (sample standard deviation / sqrt(sample size)).
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. It can be calculated using a t-distribution with degrees of freedom equal to the sample size minus one.
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A car travels at the rate of 60 miles per hour and averages 30 miles per gallon of gasoline. Which of the following is the best
approximation of the number of gallons of gasoline that will be used in 8 hours of traveling at 60 miles per hour?
0.06 gallons
16 gallons
3.75 gallons
7.5 gallons
480 gallons
Simplify the algebraic expression -5(6x)
Answer:
-30x
Step-by-step explanation:
The parenthesis is just to multiply, and you can combine like terms. So -5*6=-30, which you multiply with x to get -30x.
Find the zeros
[tex]x^3+8x^2-20x+48[/tex]
Answer:
Graph each side of the equation. The solution is the x-value of the point of intersection.
x≈−10.37392996
Step-by-step explanation:
3x + 5y = 7;( -1 , 2) write an eqautian thats perpidicaluar to the given line that passes through the given point
Answer:
5x -3y + 11 = 0 .
Step-by-step explanation:
Firstly let's find the slope of the line by converting the equation into slope intercept form as ,
=> 3x +5y = 7
=> 5y = 7 - 3x
=> y = (7-3x)/5
=> y = -3/5x + 7/5
On comparing this equation to the slope intercept form y = mx + c ,=> m = -⅗
Now the slope of the line perpendicular to this line will be , say m'
=> m' =- 1/m
=> m' = -1/-⅗
=> m = 5/3
Now the line passes through (-1,2 ) . so on using point slope form , we get ,=> ( x - x1) m = ( y - y1)
=> ( x - (-1)) × 5/3 = y - 2
=> ( x +1)×5 = 3( y -2)
=> 5x + 5 = 3y -6
=> 5x - 3y +5 +6=0
=> 5x -3y +11 = 0
• Hence the equation of line perpendicular to the given line is 5x -3y + 11 = 0 .Find the volume of the cylinder.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi.
please help im tring to pass this class
Volume of a cylinder is the area of the base x the height.
Area of base = pi x r^2 = 3.14 x 2^2 = 12.56
Volume = 12.56 x 8 = 100.48 units^3
Answer:
32 pi units^3
Step-by-step explanation:
The volume of a cylinder is given by
V = Bh where B is the area of the base
The base is a circle
The area of a circle is given by
A = pi r^2
The radius is 2
A = pi (2)^2 = 4pi
The area of the base is 4pi
The height is 8
V = 4pi *8
V = 32 pi units^3
Over what interval(s) is the function decreasing?
A)
-∞ < x < ∞
B)
- ∞ < x < 5
C)
5
D)
never
Answer:
A and BStep-by-step explanation:
C isnt an interval and the function is always decreasing
HELP HELP HELP HELP
What is the equation of the trend line in the scatter plot ?
Answer:
The equation for the trend line is y=2x-10
20 POINT!!
Can someone help me I don’t understand it at all
Answer:
second
Step-by-step explanation:
substitute y=6 and x=1 in the given relations and see if works
y=2x will be 6 = 2*1 false
y=x+5 will be 6 = 1+5 true
because this is true check all the other y and x and if all true is good
7=2+5 true, 8=3+5 true 9= 4+5 true, 10=5+5 true, so second is good
y=2x+1 will be 6=2*1+1 false
y=3x+1 will be 6=3*1+1 false
What is the domain of the following parabola?
1) I can find my volume if the volume of the cylinder is multiplied
by Who am 1?
b. Prism
a. Cone
d. Sphere
c. Pyramid
2) The volume is that of a cylinder that has the same base and
height with me. Who am I?
c. Prism
d. Pyramid
a. Cone
b. Cylinder
3) The volume of the pyramid is of the volume of what figure?
a. Cone
b. Cylinder
C. Prism
d. Pyramid
4) A rectangular prism has 10 cm length, 4 cm width and 5 cm
height. What is the length of the rectangular pyramid?
d. 20 cm
b. 5 cm
c. 10 cm
a. 4 cm
Additional Activities
Directions: Solve the following. Show your solution.
1. Diane has clay in a can. Its radius is 6 cm, while its height is 10
cm. She wanted to transfer some of her clay to her cone-
shaped container. What is the volume of the cone to be filled
and height with the can?
You can find the volume of a sphere by multiplying the volume of a cylinder by 4/3: D. sphere.
How to calculate the volume of a sphere?Mathematically, the volume of a sphere can be calculated by using this formula:
V = 4/3 × πr³
Where:
V is the volume of a sphere.r is the radius of a sphere.Note: The volume of a cylinder is equal to πr² × r.
Thus, 4/3 × πr² × r = 4/3 × πr³ (Volume of a sphere).
How to calculate the volume of a cone?Mathematically, the volume of a cone is calculated by using this formula:
V = 1/3 × πr²h
Note: The volume of a cylinder is equal to πr²h.
Therefore, 1/3 × πr²h (volume of a cone).
How to calculate the volume of a pyramid?Mathematically, the volume of a pyramid is calculated by using this formula:
Volume = 1/3 × base area × height
Volume = 1/3 × πr²h.
In Geometry, the length of a rectangular prism and the height of a rectangle pyramid are the same. Thus, the length of this rectangular pyramid is equal to 10 cm.
How to calculate the volume of Diane's cone?Mathematically, the volume of a cone is calculated by using this formula:
V = 1/3 × πr²h
V = 1/3 × 3.14 × 6² × 10
Volume, V = 376.8 cm³.
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Sylvia bought 8 bags of stickers. Each bag costs $2.79 how much did Sylvia spend
Answer:
Sylvia's total cost=$2.79*8
=$22.32
Step-by-step explanation:
Aaron's bedroom is in the shape of a rectangular prism. The bedroom measures 10 feet by 14 feet by 8 feet. How many cubic feet of space does the room contain?
The formula for the area of a rectangular room is width x length, as shown in the figure below: This is the equation used in our square footage calculator as well.
HELP ME WITH THIS PLEASE. THANK YOU
Answer:
I think it's 2
Step-by-step explanation:
Answer:
1/11 is correct.
Step-by-step explanation:
You can see that the 3 is spun 2 times, but we need to know how many times he spun in total.
2 + 3 + 2 + 4 + 5 + 2 + 1 + 3 = 22
2/22 = 1/11
Have a nice day!
What is the median of this list of grades: 78,55,98,86,92,70,60 ?
Answer:
the median of this list is 78
thirty years later the washington monument was finally completed, and the angle of elevation to the top of the monument from the same marker was 70o. to the nearest foot, how many feet were added to the phase 1 structure of the washington monument?
Answer:
Congress immediately tabled its expected contribution of $200,000 to the Society, effectively halting the appropriation. During its tenure, the Know-Nothing Society added only two courses of masonry, or four feet, to the monument using rejected masonry it found on site, increasing the height of the shaft to 156 feet
Step-by-step explanation:
Use the figure to answer the question. 8 8 What is the area of the shaded region of the circle in terms of a? Enter the answer in the box. The area of the shaded region is f units squared.
Answer:
48pi
Step-by-step explanation:
pi x 8² - pi x 4²
64pi - 16pi
48pi
Find the length of side y.
y=_ft
Answer:
y= 18.582
⨝⨝⨝⨝⨝⨝⨝⨝⨝
Which of the following measures cannot be determined from a box plot?
select all that apply.
A. Interquartile range
B. Mean
C. Mean absolute deviation
D. Median
E. Mode
F.Range
==========================================================
Explanation:
The box plot, aka "box-and-whisker plot", visually represents five things. These things are:
MinimumQ1 = first quartileMedian (sometimes referred to as Q2 or second quartile)Q3 = third quartileMaximumThis list of five items is known as the five number summary.
The min is the tip of the left most whisker, assuming there aren't any small outliers. The max is the opposite side, being the tip of the right most whisker (assuming no large outliers). If there are any outliers, then they'll be shown as "island" dots on their own separated from the main box plot. The left and right edges of the box are Q1 and Q3 respectively. The median is the vertical line inside the box. The vertical line does not have to be at the midpoint of the left and right edges of the box. It simply needs to be somewhere in the box.
--------
Since the box plot lets us know the min and max, we can compute the range because
range = max - min
and we can also calculate the interquartile range (IQR) because
IQR = Q3 - Q1
--------
So to summarize so far, the five number summary is visually represented as the box plot. The range and IQR can be computed using items from the five number summary.
We cannot compute the mean because we would need the actual data set of values, rather than the summary data. The same goes for the mean absolute deviation (MAD) and the mode. Since your teacher is looking for things that cannot be determined from a box plot, we'll go for answers B, C and E.
In other words, we rule out choices A, D, and F because we can compute or determine those values from a box plot.
4. Your best friend's birthday is tomorrow, and you would like to give her an ice cream cone
balloon. The spherical shaped ice cream on top of the cone has a radius of 6 inches. The cone
itself has a diameter of 12 inches and height of 24 inches. How many cubic inches of helium are
nded to fill the entire ice cream cone balloon? Use 3.14 for it.
Answer:
1808.64 IN^3
Step-by-step explanation:
Helium needed = volume of spherical shaped ice cream + volume of cone
Volume of a sphere = 4/3 x pi x r^3
4/3 x 3.14 x 6^3 = 904.32 ft^3
Volume of a cone 1/3 x (nr^2h)
n = 22/7
r = radius = 12/2 = 6
the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.
h = height
1/3 x 3.14 x 6^2 x 24 = 904.32
helium needed = 2 x 904.32 = 1808.64 in^3
(2.8•10^8)(1.9•10^4)
Answer: 5.32 × 10^12
Step-by-step explanation:
This is a question relating to indices. In indices, we add the power given for question relating to multiplication. Hence, this will be:
= (2.8•10^8)(1.9•10^4)
= (2.8 × 1.9) × 10^8+4
= 5.32 × 10^12
Therefore, the answer to the question will be 5.32 × 10^12.
whats 6 divided by 10?
Answer:
1 r 4
Step-by-step explanation:
0 1
6 1 0
− 0
1 0
− 6
4
HELP HELP HELP HELP PLEASE HELP ME
Answer: C is the answer bc it is asking what is more grader
Step-by-step explanation:
What is the surface area of this square pyramid
18 ft
33ft
36 ft
57 ft
The surface area of this square pyramid is 33ft
Surface area of square based pyramidThe formula for calculating the surface area of the ssquare pyramid is expressed as:
TSA = Area of square + 4(area of triange)
TSA = (3*3) + 4(0.5 * 4 * 3)
TSA = 9 + 4(6)
TSA = 9 + 24
TSA = 33 square feet
Hence the surface area of this square pyramid is 33ft
Learn more on surface area of the pyramid here: https://brainly.com/question/16060915
A right triangle has a leg of length 6 and a hypotenuse of length 21 yards. Find the length of the other leg (nearest tenth).
Answer:
20.1
Step-by-step explanation:
a^2+b^2=c^2
6^2+b^2=21^2
36+b^2=441
b^2=441-36
b^2=405
sqrt of b =20.12
The density of a solid bar is 25 pounds per cubic foot. If the bar has a volume of 5.2 cubic feet, what is the weight of the bar?
NO LINKS PLSSSS
Answer:
the weight of the bar is 130 pounds
Answer: realsies
Step-by-step explanation: w manz
An arc that measures 180 degrees is called a
A pretzel company calculated that there is a mean of 73.5 broken pretzels in each production run with a standard deviation of 5.1. If the distribution is approximately normal, find the probability that there will be fewer than 69 broken pretzels in a run.
Answer:
0.1894 = 18.94% probability that there will be fewer than 69 broken pretzels in a run.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
A pretzel company calculated that there is a mean of 73.5 broken pretzels in each production run with a standard deviation of 5.1.
This means that [tex]\mu = 73.5, \sigma = 5.1[/tex]
Find the probability that there will be fewer than 69 broken pretzels in a run.
This is the p-value of Z when X = 69.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{69 - 73.5}{5.1}[/tex]
[tex]Z = -0.88[/tex]
[tex]Z = -0.88[/tex] has a p-value of 0.1894
0.1894 = 18.94% probability that there will be fewer than 69 broken pretzels in a run.