Answer: 1) R = {(a, a), (а,b), (b, a), (b, b), (с, с), (b, с), (с, b)}.
It is clearly not transitive since (a, b) ∈ R and (b, c) ∈ R whilst (a, c) ¢ R. On the other hand, it is reflexive since (x, x) ∈ R for all cases of x: x = a, x = b, and x = c. Likewise, it is symmetric since (а, b) ∈ R and (b, а) ∈ R and (b, с) ∈ R and (c, b) ∈ R.
2) Let S=Z and define R = {(x,y) |x and y have the same parity}
i.e., x and y are either both even or both odd.
The parity relation is an equivalence relation.
a. For any x ∈ Z, x has the same parity as itself, so (x,x) ∈ R.
b. If (x,y) ∈ R, x and y have the same parity, so (y,x) ∈ R.
c. If (x.y) ∈ R, and (y,z) ∈ R, then x and z have the same parity as y, so they have the same parity as each other (if y is odd, both x and z are odd; if y is even, both x and z are even), thus (x,z)∈ R.
3) A reflexive relation is a serial relation but the converse is not true. So, for number 3, a relation that is reflexive but not transitive would also be serial but not transitive, so the relation provided in (1) satisfies this condition.
Step-by-step explanation:
1) By definition,
a) R, a relation in a set X, is reflexive if and only if ∀x∈X, xRx ---> xRx.
That is, x works at the same place of x.
b) R is symmetric if and only if ∀x,y ∈ X, xRy ---> yRx
That is if x works at the same place y, then y works at the same place for x.
c) R is transitive if and only if ∀x,y,z ∈ X, xRy∧yRz ---> xRz
That is, if x works at the same place for y and y works at the same place for z, then x works at the same place for z.
2) An equivalence relation on a set S, is a relation on S which is reflexive, symmetric and transitive.
3) A reflexive relation is a serial relation but the converse is not true. So, for number 3, a relation that is reflexive but not transitive would also be serial and not transitive.
QED!
The terminal ray of angle β , drawn in standard position, passes through the point (−5, 2√7) . What is the value of cos β ? Enter your answer, in simplest radical form, in the box.
Step-by-step explanation:
Draw the triangle formed by the ray.
The hypotenuse of the triangle is:
c² = a² + b²
c² = (-5)² + (2√7)²
c² = 25 + 28
c = √53
Therefore:
cos β = -5 / √53
Or, as a proper fraction:
cos β = -5√53 / 53
The value of cos β is -5√53 / 53
Given that,
The terminal ray of angle β , drawn in standard position, passes through the point (−5, 2√7) . The calculation is:The hypotenuse of the triangle is:
[tex]c62 = a^2 + b^2\\\\c^2 = (-5)^2 + (2\sqrt7)^2\\\\c^2 = 25 + 28\\\\c = \sqrt53[/tex]
Therefore:
cos β = -5 / √53
Or, a proper fraction:
cos β = -5√53 / 53
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Monica wants to tie a ribbon around the trunk of an oak tree that has a circular trunk about 11 inches in diameter. Not counting the ribbon needed to make a bow, how many inches of ribbon are needed just to reach around the tree?
Answer: 34.57 inches.
Step-by-step explanation:
Given : Diameter of tree's trunk = 11 inches
Then, the length of ribbon needed just to reach around the tree = Circumference of trunk.
We know that the circumference of the circle is given by :-
[tex]C=\pi d[/tex] , where d= diameter
Then, Circumference of trunk. = [tex]\pi (11)[/tex]
Put [tex]\pi=\dfrac{22}{7}[/tex] , we get
Circumference of trunk. = [tex]\dfrac{22}{7}\times(11)\approx34.57\text{ inches}[/tex]
Hence , the length of ribbon needed just to reach around the tree = 34.57 inches.
a town wants to install 28 solar panels in an array what are the possible ways the panels could be installed
Answer:
24
Step-by-step explanation:
The box plots show the number of hours of television a group of middle school students and a group of elementary school students watch each week.
Which are true statements when comparing the data in the box plots? Select three choices.
The data for elementary school are more consistent than those for middle school.
More of the data for middle school lie closer to the median than the data for elementary school.
About 50% of elementary school students watch between 4 and 7 hours of television each week.
About one-half of middle school students watch less than 2 hours of television each week.
On average, middle school students watch less television than elementary school students each week.
Answer:
i) The data for elementary school are more consistent than those for
middle school.
iii) About 50% of elementary school students watch between 4 and 7
hours of television each week.
v) On average, middle school students watch less television than
elementary school students each week.
Step-by-step explanation:
The box plots show the number of hours of television a group of middle school students and a group of elementary school students watch each week.
The true statements when comparing the data in the box plots
i) The data for elementary school are more consistent than those for
middle school.
ii) More of the data for middle school lie closer to the median than the data
for elementary school.
iii) About 50% of elementary school students watch between 4 and 7
hours of television each week.
iv) About one-half of middle school students watch less than 2 hours of
television each week.
v) On average, middle school students watch less television than
elementary school students each week.
Answer:
It's 1, 3, 5 Yw
Step-by-step explanation:
I am doing the test and that's what I got
I want to seriously think about students. So 80% of the books donated to the used book sale. They sold 48 books and oil how many books would donated to the used book sale justify your answer.
Solution is in the attachment
A license plate consists of seven symbols on each plate, where the first two symbols are letters of the alphabet and the following five symbols are the digits selected from the set StartSet 0 comma 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8 comma 9 EndSet? How many license plates can be produced if any digit or letter can be repeated on any given license plate?
Final answer:
To find the total number of possible license plates with two letters followed by five digits (with repetition allowed), multiply the number of options for each position: 26 letters and 10 digits result in 67,600,000 different license plates.
Explanation:
The question asks for the total number of license plates that can be produced when the first two symbols are letters from the alphabet and the following five symbols are digits from 0 to 9, with repetition allowed for both letters and digits. To find the number of possible license plates, we use the principle of counting, multiplying the number of choices for each position.
There are 26 possible letters for each of the first two positions (since there are 26 letters in the English alphabet) and 10 possible digits (0-9) for each of the last five positions.
Therefore, the total number of license plates that can be created is calculated as:26 * 26 * 10 * 10 * 10 * 10 * 10. This equals 67,600,000 possible license plates.
This calculation assumes that each symbol (letter or digit) can be repeated, meaning the same letter or digit can be used more than once in the license plate.
What is the median of the following values? 51,22,17,28,98,4,24,83,9,76
Answer:
The answer to your question is 26
Step-by-step explanation:
Median is the middle number of a list order from lowest to highest.
Process
1.- Order the numbers from lowest to highest
4 9 17 22 24 28 51 76 83 98
2.- Look for the middle number, if the total number of items is pair, take the 2 middle number and divide by two.
Middle numbers = 24 and 28
Median = (24 ´+ 28) / 2
Median = 52/2
Median = 26
Answer:
Step-by-step explanation:
First the numbers are arranged in ascending order from the least to the biggest number:
4 9 17 22 24 28 51 76 83 98
The numbers on the 5th and 6th position are in the middle
5th= 24
6th = 28
Since they are two numbers, we add them and divide by 2
= (24 + 28) / 2
= 52 / 2
= 26
Please help asap for the answer
Answer:
Step-by-step explanation:
Triangle ABC is a right angle triangle.
From the given right angle triangle
AC represents the hypotenuse of the right angle triangle.
With ∠A as the reference angle,
AB represents the adjacent side of the right angle triangle.
BC represents the opposite side of the right angle triangle.
To determine the ratio of Tan A , we would apply the tangent trigonometric ratio which is expressed as
Tan θ = opposite side/adjacent side. Therefore,
Tan A = 28/45
PLZ HELP THIS IS TIMED
Which table represents exponential growth? A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 6, 8. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 7, 11. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 6, 10.
Answer:
A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16.
Step-by-step explanation:
Let an exponential growth function is [tex]f(x) = a(b)^{x}[/tex].
Now, [tex]f(1) = a(b)^{1}[/tex], [tex]f(2) = a(b)^{2}[/tex] , [tex]f(3) = a(b)^{3}[/tex] and [tex]f(4) = a(b)^{4}[/tex].
So, the values of the function corresponding to the x-values 1, 2, 3, and 4, are in G.P. and the common ratio of b.
Now, 'a 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16' will be the exponential function as the values are in G.P. with common ratio 2. (Answer)
Answer:
its D
Step-by-step explanation:
just did the assignment
A seven-year medical research study reported that women whose mothers took the drug DES during pregnancy were twice as likely to develop tissue abnormalities that might lead to cancer as were women whose mothers did not take the drug.a. This study involved the comparison of two populations. What were the populations?b. Do you suppose the data were obtained in a survey or an experiment?c. For the population of women whose mothers took the drug DES during pregnancy, a sample of 3980 women showed 63 developed tissue abnormalities that might lead to cancer. Provide a descriptive statistic that could be used to estimate the number of women out of 1000 in this population who have tissue abnormalities.d. For the population of women whose mothers did not take the drug DES during pregnancy, what is the estimate of the number of women out of 1000 who would be expected to have tissue abnormalities?e. Medical studies often use a relatively large sample (in this case, 3980). Why?
Answer:
16 women per 1 000
Step-by-step explanation:
The data was likely to be obtained from a survey. The question states how the information was gathered - most probably from questionnaires.
c. A simple model will be 16 women per 1 000 women. Proportion has been taken into account here.
Let 63 correspond with those that are going to get cancer out of 3980. The women have 63/3980 chance of getting cancer.
For 1 000 women that will be 1000/3980 × (63) = 16
Therefore the probability of a person getting cancer is 16 per 1 000 Ans
e. Large samples are essential to ensure that the results are representative of the actual population. In addition, large samples reduce inherent errors from deviations. Furthermore, useless data can be discarded and the remaining data still represent the actual population size. Lastly, large amounts of data are easy to scale up and use to develop models.
The two populations compared in the study were women whose mothers took the drug DES during pregnancy and those whose mothers did not. The data in the study were obtained through an observational study. A descriptive statistic can be used to estimate the number of women with tissue abnormalities out of 1000 in the population of women whose mothers took the drug DES during pregnancy.
Explanation:a. The two populations in the study were: 1) women whose mothers took the drug DES during pregnancy and 2) women whose mothers did not take the drug.
b. The data in this study were obtained through an observational study, specifically a cohort study. This means that the researchers observed and compared the outcomes between the two groups of women without directly manipulating any variables.
c. A descriptive statistic that could be used to estimate the number of women out of 1000 in the population of women whose mothers took the drug DES during pregnancy and developed tissue abnormalities is:
Number of women with tissue abnormalities in the sample: 63
Descriptive statistic: (63 / 3980) * 1000 = 15.83
Therefore, an estimate is that 15.83 out of 1000 women in this population have tissue abnormalities that might lead to cancer.
d. Since the study only reported that women whose mothers took the drug DES during pregnancy were twice as likely to develop tissue abnormalities, without providing an exact percentage, it is not possible to estimate the number of women without more specific information.
e. Medical studies often use a relatively large sample size, like 3980, to increase the reliability and representativeness of the findings. A larger sample size helps to reduce the chance of biased or random results and increases the generalizability of the findings to the larger population.
A solid rectangular box with height 5 m and square base with side lengths 4 m is built using a lightweight material whose density is 800 kgm3. Constructing this box requires work against gravity.the required work is___________
Final answer:
The work done against gravity in constructing the rectangular box is 3136000 J.
Explanation:
To calculate the work done against gravity in constructing the rectangular box, we need to first calculate the mass of the box. The density of the lightweight material is given as 800 kg/m³. Since the base of the box is a square with side lengths of 4 m and the height is 5 m, the volume of the box is V = (4 m)(4 m)(5 m) = 80 m³.
The mass of the box can be calculated using the formula mass = density × volume. Therefore, the mass of the box is [tex](800 kg/m^3)(80 m^3) = 64000 kg.[/tex]
The work done against gravity is given by the formula work = mass × gravity × height. Assuming the acceleration due to gravity is approximately 9.8 m/s², the work done against gravity is [tex](64000 kg)(9.8 m/s^2)(5 m) = 3136000 J.[/tex]
Points R, T, S, and Q are
a. collinear
b. coplanar
c. neither collinear nor coplanar
d. both collinear and coplanar
The points in the diagram are neither collinear (lying on the same line) nor coplanar (lying on the same plane) as some points are not in alignment or on the same level.
The correct answer is option C.
Collinearity and coplanarity are geometric concepts used to describe the relative positions of points in space. To clarify, collinear points lie on the same straight line, while coplanar points lie on the same flat plane.
In your specific scenario, it is evident that the points under consideration do not satisfy the criteria for either collinearity or coplanarity. Here's an expanded explanation:
Collinearity:
Collinear points are points that can be connected by a single straight line. In simpler terms, if you can draw a straight line that passes through all the points without lifting your pen, those points are collinear. However, based on the provided diagram and description, it is clear that not all the points can be connected in this way. Some points are positioned in such a manner that a single straight line cannot pass through all of them.
Coplanarity:
Coplanar points are points that lie within the same flat plane. If you can imagine a flat surface that contains all the points, those points are coplanar. In the given scenario, it is apparent that the points are not all situated within the same plane. Some points are at different heights or elevations compared to others, indicating that they do not lie within a common flat plane.
In conclusion, the points in the diagram do not meet the conditions for either collinearity or coplanarity. They cannot be connected by a single straight line, nor do they all reside on the same flat plane.
Therefore, from the given options the correct one is C.
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PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠R.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠R = °
Answer:
[tex]m\angle R=69.4^o[/tex]
Step-by-step explanation:
we know that
In the right triangle PQR
[tex]tan(R)=\frac{PQ}{QR}[/tex] ----> by TOA (opposite side divided by adjacent side)
substitute the given values
[tex]tan(R)=\frac{8}{3}[/tex]
using a calculator
[tex]m\angle R=tan^{-1}(\frac{8}{3})=69.4^o[/tex]
Rounded to the nearest whole number, what is the distance, in units, between (−3,2) and (2,−8)?
A
6
B
7
C
11
D
15
Answer:
a
Step-by-step explanation:
The distance between two given coordinate points is 11 units. Therefore, option C is the correct answer.
What is distance formula?The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On 2D plane the distance between two points (x₁, y₁) and (x₂, y₂) is Distance = √[(x₂-x₁)²+(y₂-y₁)²].
The given coordinate points are (-3, 2) and (2, -8).
Substitute (x₁, y₁) =(-3, 2) and (x₂, y₂)= (2, -8) in the distance formula, we get
Distance = √[(2+3)²+(-8-2)²]
= √[5²+(-10)²]
= √125
= 11.18
≈ 11
The distance between two given coordinate points is 11 units. Therefore, option C is the correct answer.
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A consumer takes out a loan for $500 that charges 10% annual interest. What is the total cost of the loan if the consumer pays it back one year from the date of origination?
Answer:the answer is life
Step-by-step explanation:
well life is life that you need
Answer:
$550 i think
Step-by-step explanation:
A corner store bakery sells cake and pies. The cakes are $5 and the pies are $7. In one day the store sells 15 goods and makes a total of $91. How many cakes did they sell?
Answer:
The answer to your question is it sold 7 cakes.
Step-by-step explanation:
Data
cakes = c = $5
pies = p = $7
total pieces = 15
total sell = $91
Process
1.- Write equations to solve this problem
c + p = 15 ------------ l
5c + 7p = 91 ----------- ll
2.- Solve the system of equations by elimination
Multiply equation I by -5
-5c - 5p = -75
5c + 7p = 91
0 + 2p = 16
Solve for p
p = 16/2
p = 8
3.- Substitute p in equation l to find c
c + 8 = 15
solve for c
c = 15 - 8
c = 7
4.- Conclusion
It sold 7 cakes and 8 pies.
Answer: 7 cakes were sold.
Step-by-step explanation:
Let x represent the number of cakes that were sold.
Let y represent the number of cakes that were sold.
The cakes are $5 and the pies are $7. The store makes a total of $91. This means that
5x + 7y = 91- - - - - - -- -1
The store sold a total number of 15 goods. This means that
x + y = 15
Substituting x = 15 - y into equation 1, it becomes
5(15 - y) + 7y = 91
75 - 5y + 7y = 91
- 5y + 7y = 91 - 75
2y = 16
x = 16/2 = 8
x = 15 - y = 15 - 8
x = 7
A Television nanufacture sells 21 of TV model at$299 each, 13 of TV Model B at $549 each and 8 of TV Model C at $619 each. Find tge average price per TV Sold.
Answer:
Step-by-step explanation:
The formula for determining average is expressed as
Average = the total cost of the televisions/ the sum of the televisions
Total number of model A television that was sold is 21
Total cost of 21 televisions = 299 × 21 = $8671
Total number of model B television that was sold is 13
Total cost of 13 televisions = 549 × 13 = $7137
Total number of model C television that was sold is 6
Total cost of 6 televisions = 619 × 6 = $3714
Total number televisions sold is 21 + 13 + 6 = 40
Total cost of the televisions is 8671 + 7137 + 3714 = 19522
Therefore, the average price per TV Sold is
19522/40 = $488.05 per television
Consider the graph of quadrilateral ABCD.
What is the most specific name for quadrilateral ABCD?
square
rectangle
parallelogram
rhombus
Know the properties of each shape:
A square has all sides of equal length plus all corners are right angles
A rectangle has all right angles, but has two pairs of parallel sides
A parallelogram is a quadrilateral that has two pairs of parallel sides
A rhombus is where all sides are equal length, but no right angles at all
So the best choice given the diagram is C: parallelogram
Hope this helped you to understand better.
Find x
1,) -54
2.) 48
3,) 52
4.) 54
Step-by-step explanation:
[tex]m \angle \: WXZ = m \angle \: WYZ \\ ..(angles \: formed \: in \: same \: arc) \\ \therefore \: x \degree = (2x - 54)\degree \\ \therefore \: x = 2x - 54 \\ \therefore \: x - 2x = - 54 \\ \therefore \: - x = - 54 \\ \huge \purple{ \boxed{\therefore \: x = 54}}[/tex]
Answer:
The correct answer is D or 54.
Step-by-step explanation:
x squared equals 9 what is the answer
Answer: x = 3
Step-by-step explanation:
x^2 = 9
x = [tex]\sqrt{9}[/tex]
x = 3
Another way to think about it:
We think what number can be multiplied by itself to get 9.
since 3*3=9, our answer is 3
While at summer camp, Mike asked a random camper from each of the 12 cabins how many siblings he or she had. The results below display the responses. 3, 2, 0, 1, 0, 2, 3, 4, 1, 2, 2, 1 If there are 48 campers altogether, use Mike’s data to infer the mean of the population. What is the mean number of siblings for the population rounded to the nearest unit? 1 sibling 2 siblings 3 siblings 4 siblings
Answer:
Option 2.
Step-by-step explanation:
It is given that Mike asked a random camper from each of the 12 cabins how many siblings he or she had.
The given data set is
3, 2, 0, 1, 0, 2, 3, 4, 1, 2, 2, 1
Sum of observations = 3+2+0+1+0+2+3+4+1+2+2+1=21
Number of observations = 12
Formula for mean:
[tex]Mean=\dfrac{\text{Sum of observations}}{\text{Number of observations}}[/tex]
[tex]Mean=\dfrac{21}{12}[/tex]
[tex]Mean=1.75[/tex]
Round the population to the nearest unit.
[tex]Mean=2[/tex]
We have to use Mike’s data to infer the mean of the population. So, the mean of sample is equal to the mean of population.
The mean number of siblings for the population is 2 siblings.
Therefore, the correct option is 2.
Answer:
the right answer is B
Step-by-step explanation:
Which expression is equivalent to -3x - (x-1) + 3/2(3x +3)?
A. 1/2x + 11/2
B. 1/2x + 7/2
c. 5/2x + 11/2
D. 5/2x + 7/2
Answer:
The answer to your question is letter A
Step-by-step explanation:
Expression
- 3x - (x - 1) + 3/2(3x + 3)
1.- Expand
- 3x - x + 1 + 3/2(3x) + 3/2(3)
2.- Simplify
- 3x - x + 1 + 9/2 x + 9/2
3.- Associate like terms
(-3x - x + 9/2x) + (1 + 9/2)
4.- Simplify like terms
(-4x + 9/2x) + (2 + 9)/2
(-8x + 9x)/2 + 11/2
1/2x + 11/2
Where do I share a photo of my work
Which best describes the three-dimensional figure obtained from rotating the figure around the y-axis?
a cylinder with a radius of 1 unit
a cone with a radius of 1 unit
a cylinder with a radius of 2 units
a cone with a radius of 2 units
Yo sup??
This question can be solved by just imagining the object formed or practically trying it out.
Therefore the correct answer to this question is option 2 ie
a cylinder with a radius of 1 unit.
Hope this helps.
The figure created is a cone with a height of 2 units and a radius of 1 unit.
Which figure will be created?
Notice that we have a triangle, so if we rotate it around the y-axis, we will get a cone.
Because the rotation is around the y-axis, the height of the cone will be equal to the side AB of the triangle, so the height of the cone is 2 units.
And the radius of the cone is equal to BC, then we can see that the radius measures 1 unit.
Then the figure created is a cone with a height of 2 units and a radius of 1 unit.
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What is the difference in area covered by a single 3 inch windshield wiper operating with a central angle of 138 degrees compared to a pair of 5 inch wipers operating together each having a central angle of 114 degrees?
Answer:
38.9 square inches.
Step-by-step explanation:
We are asked to find the difference in area covered by a single 3 inch windshield wiper operating with a central angle of 138 degrees compared to a pair of 5 inch wipers operating together each having a central angle of 114 degrees.
We will use area of sector formula to solve our given problem as:
[tex]\text{Area of sector}=\frac{\theta}{360}\times \pi r^2[/tex], where, r represents radius and theta represents central angle.
Let us find area of sector with central angle 140 degree and radius 3 inch.
[tex]\text{Area of sector}=\frac{138}{360}\times \pi (3)^2[/tex]
[tex]\text{Area of sector}=\frac{138}{360}\times 9\pi[/tex]
[tex]\text{Area of sector}=10.83849[/tex]
Now, we will find area of sector with central angle 114 degree and radius 5 inch and multiply by 2 as:
[tex]\text{Area of sector}=2(\frac{114}{360}\times \pi (5)^2)[/tex]
[tex]\text{Area of sector}=2(\frac{114}{360}\times 25\pi)[/tex]
[tex]\text{Area of sector}=\frac{114}{360}\times 50\pi[/tex]
[tex]\text{Area of sector}=49.74188[/tex]
Let us find difference of area as shown below:
[tex]\text{Difference of areas}=49.74188-10.83849[/tex]
[tex]\text{Difference of areas}=38.90339[/tex]
[tex]\text{Difference of areas}\approx 38.9[/tex]
Therefore, the difference in area covered is approximately 38.9 square inches.
Final answer:
Calculate the areas covered by differently sized and angled windshield wipers to find the difference.
Explanation:
Single 3-inch wiper:
Area covered = (1/2) × r² × (2 × pi × (angle/360))Pair of 5-inch wipers:
Each wiper's area = (1/2) × r² × (2 × pi × (angle/360))Total area covered by the pair = 2 × (area of a single wiper)The difference in area cleaned by the pair of 5-inch wipers compared to the single 3-inch wiper is:
A-diff = A-combined - A-single ≈ 31.50 sq in - 7.07 sq in ≈ 24.43 sq in
Therefore, the pair of 5-inch wipers cleans approximately 24.43 square inches more area than the single 3-inch wiper.
A stack of nested paper cups is 8 inches tall . The 1st cup is 4 inches tall and each of the rest of the cups in the stack adds 1/4 of an inch to the height of the stack. How many cups are in the stack?
Answer:
17
Step-by-step explanation:
For n cups, the height of the stack is ...
4 + (1/4)(n -1)
For a height of 8 inches, we can find n from ...
8 = 4 +(1/4)(n -1)
4 = (1/4)(n -1) . . . . . . subtract 4
16 = n -1 . . . . . . . . . .multiply by 4
17 = n . . . . . . . . . . . .add 1
There are 17 cups in the stack.
The wards decided to use carpet tiles in the family room. The room has an area of 176 square feet and is 5 feet longer than it is wide. Find the dimensions of the family room
Answer:
The dimensions of the room are length is 16 feet and the width is 11 feet.
Step-by-step explanation:
Given:
The wards decided to use carpet tiles in the family room. The room has an area of 176 square feet and is 5 feet longer than it is wide.
Now, to get the dimensions.
Let the width be [tex]x.[/tex]
So, the length = [tex]x+5.[/tex]
Area = 176 square foot.
So, we put formula of area to get the dimensions:
Area = length × width.
[tex]176=(x+5)\times x[/tex]
[tex]176=x^2+5x[/tex]
Subtracting boths sides by 176 we get:
[tex]0=x^2+5x-176\\x^2+5x-176=0[/tex]
On solving the equation:
[tex]x^2+16x-11x-176=0\\x(x+16)-11(x+16)=0\\(x+16)(x-11)=0[/tex]
As,
[tex]x+16[/tex] = 0
[tex]x=-16[/tex]
So, we would not take the negative result.
Thus,
[tex]x-11=0\\x=11[/tex]
So, the width = 11 feet.
Now, to get the length by substituting the value of [tex]x[/tex]:
[tex]x+5\\=11+5\\=16[/tex]
The length = 16 feet.
Therefore, the dimensions of the room are length is 16 feet and the width is 11 feet.
The width is 11 feet, and the length is 5 feet longer, making it 16 feet.
To determine the dimensions of the family room, we start by defining the width of the room as w. According to the problem, the length (l) is 5 feet longer than the width, so we can write this as:
l = w + 5
We also know the area of the room is 176 square feet. The area of a rectangle is calculated by multiplying the width and length:
Area = width × length
Therefore, we get the equation:
w × (w + 5) = 176
Expanding this equation gives us:
w² + 5w = 176
We rearrange this into a standard quadratic equation:
w² + 5w - 176 = 0
Now we solve for w using the quadratic formula, w = (-b ± √(b² - 4ac)) / 2a, where:
a = 1b = 5c = -176This gives us:
w = (-5 ± √(25 + 704)) / 2
w = (-5 ± √729) / 2
w = (-5 ± 27) / 2
Which simplifies to:
w = 11 or w = -16
Since width cannot be negative, we have:
w = 11
Then the length l is:
l = 11 + 5 = 16
Therefore, the dimensions of the family room are 11 feet by 16 feet.
What is the sum of the geometric series? Sigma-Summation Underscript n = 1 Overscript 4 EndScripts (negative 2) (negative 3) Superscript n minus 1
Answer:
Step-by-step explanation:
∑⁴ₙ₌₁ -144 (½)ⁿ⁻¹
This is a finite geometric series with n = 4, a₁ = -144, and r = ½.
S = a₁ (1 − rⁿ) / (1 − r)
S = -144 (1 − (½)⁴) / (1 − ½)
S = -270
If you wanted to find the infinite sum (n = ∞):
S = a₁ / (1 − r)
S = -144 / (1 − ½)
S = -288
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Answer:
The answer is C (40)
Step-by-step explanation:
A class consists of 8 students (four boys and four girls) and one teacher. In how many ways can the students sit in a circle?
Answer: 5040ways
Step-by-step explanation:
This is a circular permutation question. Arrangement of objects in a circular path is (n-1)! where n is the amount of object. Since there are 8 students sitting in a circle excluding their teacher, they can sit in (8-1)! ways i.e 7! ways
7! = 7×6×5×4×3×2×1
7! = 5040ways
This means the students can sit in a circle in 5,040 ways
Final answer:
To find out the number of ways 8 students can sit in a circle, we calculate 7! (7 factorial), as the formula for arrangements in a circle is (n-1)!, resulting in 5040 ways.
Explanation:
The question involves determining the number of ways 8 students can sit in a circle. When arranging n distinct objects in a circle, the number of arrangements is given by (n-1)! .
since one position is fixed to account for the circular arrangement's rotational symmetry. In this case, with 8 students, the calculation is as follows: 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040 ways.
Therefore, the students can sit in a circle in 5040 different ways.
2/ 7 y+3 1/7 y if y= 7/9
Answer:
8/3 = 2 2/3
Step-by-step explanation:
(2/7)y + (3 1/7)y = (3 3/7)y = (24/7)y
For y=7/9, this is ...
(24/7)(7/9) = 24/9 = 8/3
The value of the expression for y=7/9 is 8/3.
Fibonacci follies: suppose you are playing a round of Fibonacci nim with a friend. You start with 15 sticks. You start by removing two sticks; your friend then takes one; you take two; your friend takes one. What should your next move be? Can you make it without breaking the rules of the game? Did you make a mistake at some point? If so, where?
Answer: Yes, made a mistake by taking out 2 in second step.
Step-by-step explanation:
You have started with 15 sticks= 13+2
So you take 2 which is correct.
Now, your friend takes one 13=12+1, so that leaves 12.
Now 12=8+3+1 since this involves smallest number 1 so you should have taken 1 at this point instead you took two here. So it leaves you with 10. Now, your friend takes one from it i.e. 10=9+1 leaving 9 now. Now 9=8+1, you can still take 1 from it and still be in the game. The point is to take out the smallest number involved. in the sum equal to the number that is left behind.
In Fibonacci nim, you cannot take the same number of sticks as your opponent did on the previous turn. Your next move should be to take 2 sticks, as your opponent took 1 on their last turn. You haven't yet made any mistakes in the game.
Explanation:In the game of Fibonacci nim, the only rule is that on each turn a player can take one or two sticks, but not the same amount as their opponent took on the previous turn. Let's track your game:
You start with 15 sticks.You take 2 (13 remaining).Your friend takes 1 (12 remaining).You take 2 (10 remaining).Your friend takes 1 (9 remaining).For the next move, you can take either 1 or 2 sticks, but since your friend took 1 on their last turn, you must take 2 to abide by the rules. So, your next move should be to take 2 sticks.
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