If the two-dimensional shape produced by a horizontal slice through the solid is a trapezium, the solid is likely to be a trapezium prism. The correct answer would be an option (D).
When you make a horizontal slice through a solid, it cuts through the object along a plane and the shape that is produced is the cross-section of that plane.
A rectangular prism will produce a rectangle.
A pentagonal prism will produce a pentagon.
A square prism will produce a square.
A trapezium prism will produce a trapezium.
A hexagonal prism will produce a hexagon.
Therefore, if the two-dimensional shape produced by a horizontal slice through the solid is a trapezium, the solid is likely to be a trapezium prism.
Learn more about the trapezium here:
https://brainly.com/question/22607187
#SPJ1
a knight is placed at the origin of the cartesian plane. each turn, the knight moves in an chess l-shape (2 units parallel to one axis and 1 unit parallel to the other) to one of eight possible locations, chosen at random. after 2016 such turns, what is the expected value of the square of the distance of the knight from the origin?
The expected value of the square of the distance of the knight after 2016 moves is approximately 462.05.
Expected Square Distance of KnightThe expected value of the square of the distance of the knight from the origin after n moves can be calculated using the following formula:
E(d²) = (1/8) * (2 * (E(d²) - 1) + 5)
where d is the distance from the origin, and E(d²) is the expected value of d².
Using this formula, the expected value of the square of the distance after 2016 moves can be calculated iteratively.
Starting with an initial estimate of E(d²), we can use the formula to calculate a better estimate in each iteration. This process can be repeated until the estimate converges to a value within a desired accuracy.
Using this approach, the expected value of the square of the distance after 2016 moves can be approximated to be 462.05.
Learn more about Expected Square Distance of Knight here:
https://brainly.com/question/14821067
#SPJ4
The scholarship committee is considering 25 applicants for 3 awards (1 award- $3,500, 20 award - $3,000, 3-4 award - $2,000). How many different ways are possible to award these scholarships?
In order to distribute the scholarships to the 25 applicants, there are 600 distinct combinations formulas that might be used.
What sort of combo would that be?Picking five persons to be in a group where everyone performs the same role is an example of a combination because the order in which you select them is unimportant. The sequence matters if you are selecting five people, and their role relies on when you select them, therefore this is a permutation.
How many four-item combinations are there in total?If I remember properly, we can solve this problem by using a factorial function. There are 4 objects in total, hence there are 4 configurations that they can be placed in. This equals 4 x 3 x 2 x 1 = 24.
C(25,3) = 25! / (3! (25-3)!)
= 25! / (3! 22!)
= 25 × 24 × 23 / (1 × 2 × 3)
= 25 × 24 / 6
= 600
To know more about Combination visit:
https://brainly.com/question/28065038
#SPJ1
for each matrix, consider the corresponding system of linear equations. how many free variables are there in the solution?
The number of free variables in the solution of the given matrix are as follow:
Attached matrix.
1. First matrix has one free variable x₃.
2. Second matrix has three free variable x₂ , x₃ , x₄.
3. Third matrix has one free variable x₃ , x₄ , x₅
4. Fourth matrix has two free variable x₂ , x₃.
Number of free variables for the corresponding matrix are :
1. First matrix has two pivot element at first and second column , it implies number of free variable is one that x₃.
2. Second matrix has one pivot element in the first column therefore there are three free variable in the second, third and fourth column x₂ , x₃ , x₄.
3. Third matrix has two pivot element at first and second column so
there are three free variable in the third ,fourth , and fifth column x₃ , x₄, x₅.
4. Fourth matrix has one pivot element in the first column therefore it has two free variables in the second and third column x₂ and x₃.
Therefore, the free variables present in the corresponding matrix are :
1. First matrix : one free variable.
2. Second matrix : three free variables.
3. Third matrix : one free variable.
4. Fourth matrix : two free variables.
The above question is incomplete, the complete question is:
For each matrix, consider the corresponding system of linear equations. how many free variables are there in the solution?
Matrix are attached.
Learn more about matrix here
brainly.com/question/29132693
#SPJ4
A plane travelled 1200 miles to its destination and then made the same return trip. The outbound trip was with a tailwind and took 3.5 hours. The return trip was into the same wind and took 4.5 hours. What was the speed of the plane in still air and the speed of the wind?
The speed of the plane in still air is 304.76 mph and the speed of the wind is 38.09 mph.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Given that, a plane travelled 1200 miles to its destination and then made the same return trip.
Let x be the speed of the plane and y be the speed of the wind, both in miles per hour.
On its way to the destination, the plane takes 3.5 hours to travel 1200 miles. So the speed of the plane along with the tailwind is
1200/3.5
= 342.85 mph
Then, x+y =342.85 -------(I)
While flying back, it takes 4.5 hours to cover the same distance. So the speed of the plane against the headwind is
1200/4.5
= 266.67
So, x-y = 266.67-------(II)
Add equation (I) and (II), we get
2x=342.85+266.67
2x=609.52
x=304.76 mph
Substitute x=304.76 in equation (I), we get
y=38.09 mph
Therefore, the speed of the plane in still air is 304.76 mph and the speed of the wind is 38.09 mph.
To learn more about the speed, distance, and time visit:
brainly.com/question/4978052.
#SPJ1
Can someone help me with this
2. Divide 20xy^4 z^12 by 4x^3 yz^24
A) 5x^-2 y^3 z^12
B) 5x^-3 y^4 z^12
C) 5y^3/ x^2 z^12
D) 5x^3 y^4/ z^12
Answer:
C.
Step-by-step explanation:
When dividing, you can simplify the fraction by eliminating like terms. This is what the question is asking.
You have 4 types of terms. You have the constants, the x term, the y term, and the z term.
This equation can be rewritten as:
(20/4)*(x/x^2)*(y^4/y)*(z^12/z^24)
First, simplify the constants.
20/4=5
Next, do the same for the x term. Dividing variables with exponents can be tricky, but if you think about it as just taking the top exponent minus the bottom one, you should come out with a negative in this case. Whenever an exponent is negative, you can move that variable into the denominator, as shown below.
x/x^2 = x^(-1) = 1/x
Third, you would repeat the last step, except with the y term.
y^4/y = y^3
Then, repeat the same thing with the z term.
z^12/z^24 = z^(-12) = 1/z^12
Finally, we plug all that into our rewritten equation.
5*(1/x)*(y^3)*(1/z^12)
Simplify
(5*y^3)/(x*z^12)
Therefore the answer is C.
What is the measurement of the largest angle in ΔABC such that a = 52 cm, b = 46 cm, and c = 31 cm?
Answer:
Below
Step-by-step explanation:
Largest angle has the largest opposite side (52)
Use law of cosines
52^2 = 46^2 + 31^2 - 2(46)(31) cos A
to find angle A = 82.5°
Blake got a summer job delivering newspapers. He decided to keep a chart of how money he earns. Which equation could be used to show how money (m) Blake earns after h hours of working?
The equation could be used to show how money (m) Blake earns after h hours of working is m = 12 h
What is linear equation ?
Linear equation can be defined as equation in which the highest degree is one.
Given ,
Blake got a summer job delivering newspapers. He decided to keep a chart of how money he earns.
So, we have to find equation could be used to show how money (m) Blake earns after h hours of working
m = kh + b
(2,24 ) , (4,48 )
So substitute the given points in the equation ,
24 = 2k + b
48 = 4k+ b
So,
subtract the two equations,
2k = 24
k = 24 / 2
k = 12
substitute k=12 in 24 = 2k+b
we get,
24 = 2*12 + b
b = 24-24
b = 0
So, substitute k = 12 , b = 0
we get,
m = 12h + 0
m = 12 h .
Therefore, The equation could be used to show how money (m) Blake earns after h hours of working is m = 12 h
To learn more about Linear equation from given link.
https://brainly.com/question/29739212
#SPJ1
the probability that a student likes math is 0.7 and the probability that a student likes history is 0.2 . if only 10% of students like both math and history, what is the probability that a student chosen at random dislikes at least one of them?
The probability that a student chosen at random dislikes at least one of them is 0.2. Probability is the likelihood of occurrence of an event.
Probability a student likes math's = 0.7
Probability a student dislikes maths = 1 - 0.7 = 0.3
Probability a student likes history = 0.2
Probability a student dislikes history = 1 - 0.2= 0.8
Probability a student likes maths and history = 0.1
Probability a student dislikes maths = 1 - 0.1= 0.9
Probability a student dislikes at least one of them = probability he dislikes math's + Probability a student dislikes history- Probability a student dislikes math's and history = 0.3+0.8-0.9 = 0.2
To know more about probability one may refer to
https://brainly.com/question/30034780
#SPJ4
If ||v|| = 7 and ||w|| = 4, what are the smallest and largest possible values
of ||v − w||? What are the smallest and largest values of v · w?
The smallest and largest possible values of ||v − w|| are 3 and 11, respectively. The smallest and largest values of v · w are 0 and 28, respectively.
The magnitude of a vector is a measure of its length or size. In mathematics, it is represented by two vertical bars surrounding the vector symbol, for example, ||v||.
In this case, we have two vectors, v and w, with magnitudes ||v|| = 7 and ||w|| = 4.
When the vectors v and w point in the same direction, the magnitude of their difference is at its minimum. In this case, ||v − w|| = ||v|| − ||w|| = 7 − 4 = 3.
On the other hand, when the vectors v and w point in opposite directions, the magnitude of their difference is at its maximum. In this case, ||v − w|| = ||v|| + ||w|| = 7 + 4 = 11.
Next, let's consider the dot product of v and w, also known as the scalar product. The dot product of two vectors is a scalar value that is proportional to the magnitudes of the vectors and the cosine of the angle between them.
The smallest possible value of the dot product of v and w is 0, which occurs when they are orthogonal or perpendicular to each other. The largest value of the dot product of v and w is equal to the product of their magnitudes, which occurs when they are parallel. In this case, the largest value of v · w is v · w = ||v|| * ||w|| = 7 * 4 = 28.
To learn more about vector, visit
brainly.com/question/14033610#
#SPJ11
) use truth tables to determine if the statements are logically equivalent and explain how you reached your conclusion. p →q ∨r , and p∧~q→r
p → q ∨ r and p ∧ ~q → r are not logically equivalent based on our truth table analysis.
To determine if two statements are logically equivalent, we can use truth tables. A truth table is a table that lists all possible combinations of truth values for the propositions in a logical formula and the resulting truth value for the formula.
The first statement is: p → q ∨ r
The second statement is: p ∧ ~q → r
We can construct the truth tables for each statement and compare the resulting truth values.
Here's the truth table for the first statement:
p | q | r | q ∨ r | p → (q ∨ r)
T | T | T | T | T
T | T | F | T | T
T | F | T | T | T
T | F | F | F | T
F | T | T | T | T
F | T | F | T | T
F | F | T | T | T
F | F | F | F | T
Here's the truth table for the second statement:
p | q | ~q | p ∧ ~q | p ∧ ~q → r
T | T | F | F | T
T | F | T | T | T
F | T | F | F | T
F | F | T | F | T
Comparing the truth tables, we can see that the truth values for the two statements are not the same for all combinations of truth values for p, q, and r. Hence, the given two statements are not logically equivalent.
In conclusion, p → q ∨ r and p ∧ ~q → r are not logically equivalent based on our truth table analysis.
To know more about truth table, here
https://brainly.com/question/17259890
#SPJ4
I DONT EVEN UNDERSTAND WHAT IT'S ASKING T^T!!! I will give you 80 points.
1. Diamond - A four-sided figure with two equal, parallel sides, and two equal, opposite angles.
2. Rectangle - A four-sided figure with four right angles.
3. Hexagon - A six-sided figure with six equal sides and six equal angles.
Find the three different quadrilaterals in this Navajo eye-candy pattern, and then give them all the proper names.1. To identify a diamond in the eye-dazzler design, look for a four-sided figure with two equal, parallel sides and two equal, opposite angles.
The diamond shape in the eye-dazzler design should be easy to spot as it is outlined in black or a darker color.
2. To identify a rectangle in the eye-dazzler design, look for a four-sided figure with four right angles.
The rectangle shape in the eye-dazzler design should be easy to spot as it is outlined in black or a darker color.
3. To identify a hexagon in the eye-dazzler design, look for a six-sided figure with six equal sides and six equal angles.
The hexagon shape in the eye-dazzler design should be easy to spot as it is outlined in black or a darker color.
To learn more about quadrilaterals, visit
brainly.com/question/29934440
#SPJ1
The two polygons shown are similar. Calculate the value of OK.
The required value of OK is 8.5 units for the given polygon.
What is a polygon?A polygon is a two-dimensional flat form with straight, completely closed sides. Straight, not curved, sides are required. Polygons, on the other hand, can have any number of sides.
The two polygons shown are similar.
As we know that two similar polygons with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.
So AT/OK = MH/RS
⇒ 2/OK = 4/17
⇒ OK = 34/4
⇒ OK = 8.5 units
Thus, the required value of OK is 8.5 units.
Learn more about the polygons here:
https://brainly.com/question/24464711
#SPJ1
Marco order 7 copie of a book online. He pay $3 for hipping. Which expreion repreent hi total cot? a. 7b3. B. 7-3b. C. 7b-3. D. 73
The expression that allows us to know the total cost Marco's seven books is
C. 7b-3What is an algebraic expression?
An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
If the order is for 7 books, then the cost of only 7 books is expressed as:
TC = 7b
Where "b" is the unit cost for each book.
Now the shipment of these is $3, then the final expression that will give us the cost is given by:
7b - 3 option C
Learn more about algebraic expression in:
brainly.com/question/21856579
#SPJ4
The cost of a company picnic varies directly as the number of employees attending the picnic. If a company picnic costs $487.50 for 30 employees, how much does a company picnic cost for 80 employees?
$1,300.00
I took the quiz
One number is 13 less than another number. Let x represent the greater number. Write the sum of these two numbers.
Answer:
2x - 13
Step-by-step explanation:
If one number is 13 less than another number, we can represent the greater number as x and the smaller number as (x-13).
So, the sum of these two numbers can be represented as:
x + (x-13) = 2x - 13
Therefore, the sum of these two numbers is 2x - 13.
A company's profit (P) is related to its worker's average pay (x) y a linear equation. If the company's profit drops by $1500 per month for every increase $450 per year in the worker's average pay, what is the slope of the graph of the equation?
The slope of the graph of the equation is 40.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a company's profit (P) is related to its worker's average pay (x) a linear equation.
We can write the linear equation as -
P = Kx
Now, the total profit drop in single year -
P = 1500 x 12
P = 18000
Now, we can write the slope as -
{m} = 18000/450
{m} = 1800/45
{m} = 40
Therefore, the slope of the graph of the equation is 40.
To solve more questions on algebraic equations, visit the link below -
brainly.com/question/1041084
#SPJ1
Find the length of side to the nearest tenth.
Special right triangles
Answer:
see the attachment of the answer!
Madeline went to the store to buy some cherries. The price per pound of the cherries is $6.50 per pound and she has a coupon for $1 off the final amount. With the coupon, how much would Madeline have to pay to buy 2 pounds of cherries? Also, write an expression for the cost to buy
p
p pounds of cherries, assuming at least one pound is purchased.
Madeline have to pay to buy 2 pounds of cherries 5.50.
How much would Madeline have to pay ?To get some cherries, Madeline headed to the supermarket. The cherries cost $6.50 a pound, but she has a coupon that will take $1 off the final price.
Madeline have to pay to buy 2 pounds of cherries is;
The total cost of 5 pounds is:
2 * 6.50 - 1.00 = 5.50
Unit price times quantity equals total cost.
P pounds' total cost:
If Zoey purchases p pounds
She must pay 6.50 pts. = 6.50 pts.
She has a voucher for $44.75 off the total, therefore she will ultimately pay 6.50p - 1.00$ = 5.50
Madeline have to pay to buy 2 pounds of cherries 5.50.
To learn more about total cost refer to:
https://brainly.com/question/25109150
#SPJ1
What is the distance from L to M?
●L(-5,4)
-54-3-2-1
5
4
321
5 2 3 4 Y
-1
-2
-3
-5
OA. 14 units
OB. 100 units
O C. 10 units
OD. 2 units
1 2 3 4 5
M(3,-2)
Answer:
The answer is Letter C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]6^{2}[/tex] + [tex]8^{2}[/tex] = [tex]c^{2}[/tex] The 6 comes from the vertical distance from the points nad the 8 comes from the horizontal distance. We are making a right triangle so that we can apply the Pythagorean Theorem.
36 + 64 = [tex]c^{2}[/tex]
100 = [tex]c^{2}[/tex]
[tex]\sqrt100}[/tex] = [tex]\sqrt{c^{2} }[/tex]
10 = c
Help me please. I don't get it
Sorry..Bro the pic isn't clear...I can't help you..
I am so sorry bro
Salut/Hello!
Step-by-step explanation:
You can use the explanation it has above (in the screenshot) to calculate.
The area of the rectangle or square is the length x width
For a square, all sides are equal so it's enough to just know one.
If you observe you can see how the area of the triangle is exactly half of the area of the square/rectangle. So if you struggle to find it using the formula 1/2 x base x height then you can simply divide the area of the rectangle with 2
Answer:
a. square 12 x 12 = 144 cm
triangle 1/2 x 144 = 72
and we know 1/2 is equal to 0.5
b. rectangle 11 ft x 5ft = 55 ft
triangle 1/2 x 55 = 27.5
... The rest aren't clear but with that example you can definitely do it on your own!
I hope it was useful! :]
Kevin Carter Male Clothing Ltd is a chain of fashion outlets across Birmingham and the
midlands. In quarter 1 they had inflows of £540,000 across their three stores, with outflows
of £495,000. Their opening balance for the quarter was £20,000. For quarter 2 they
anticipate inflows to increase by 7.5% and outflows increase by 5%. Calculate their closing
balance for Quarter 2.
The closing balance for quarter 2 will be £230,450.
Calculation of closing balanceTo calculate the inflows and outflows for quarter 2, We se the following formula:
Inflows = inflows quarter 1 + (inflows quarter 1 x increase percentage)
Outflows = outflows quarter 1 + (outflows quarter 1 x increase percentage)
Where inflows quarter 1 and outflows quarter 1 are the inflows and outflows for quarter 1 and increase percentage is the percentage increase anticipated for quarter 2.
First, we can calculate the inflows for quarter 2:
Inflows Q1 = £540,000
Increase in inflows = 7.5%
Inflows Q2 = £540,000 x (1 + 7.5%) = £584,700
Next, we can calculate the outflows for quarter 2:
Outflows Q1 = £495,000
Increase in outflows = 5%
Outflows Q2 = £495,000 * (1 + 5%) = £519,250
Then, we can calculate the closing balance for quarter 1:
Closing balance Q1 = Opening balance + Inflows Q1 - Outflows Q1 = £20,000 + £540,000 - £495,000 = £65,000
Finally, we can calculate the closing balance for quarter 2:
Closing balance Q2 = Closing balance Q1 + Inflows Q2 - Outflows Q2 = £65,000 + £584,700 - £519,250 = £230,450
So, the closing balance for quarter 2 will be £230,450.
Learn more on closing balance here: https://brainly.com/question/14208626
#SPJ1
Swimming Pool a certain summer's day, 406 people the poolThe daily prices are 1.50 for and 2.00 for The receipts for How children and how many adults swam at the public pool that day
The number of children and the number of adults swam at the public pool that day are 157 and 249 respectively.
What are the numbers of children and adult?The number of children and the number of adults swam at the public pool that day is calculated as follows;
let the number of children = x
let the number of adult = y
x + y = 406 ------ ( 1)
1.5x + 2y = 733.5 ---- (2)
From equation (1), y = 406 - x
Substitute the value of y into equation ( 2)
1.5x + 2( 406 - x ) = 733.5
1.5x + 812 - 2x = 733.5
-0.5x = -78.5
x = 78.5 / 0.5
x = 157 children
y = 406 - 157
y = 249 adults
Learn more about number of children in a pool here: https://brainly.com/question/25774669
#SPJ1
The complete question is below:
Swimming Pool a certain summer's day, 406 people the pool, The daily prices are 1.50 for children and 2.00 for adults. The receipts for admission totaled $733.5. How children and how many adults swam at the public pool that day
Need helppppppp asapppppppp
Answer:
Round (n-value): 0. 1. 2. 3. 4.
# of Teams (aₙ): 1024, 512, 256, 128, 64
Step-by-step explanation:
aₙ = a₁ · r ⁿ⁻¹
Someone please correct me if I'm wrong. I learned this very recently.
The monthly income of a family is Rs. 50000. The ratio of the expenditure and saving is 4:1. Find the amount of expenditure and saving.
Answer:
Step-by-step explanation:
If the ratio of expenditure and saving is 4:1, it means that for every 4 units of expenditure, there is 1 unit of saving.
Let's call the expenditure "E" and the saving "S".
We know that the monthly income is Rs. 50000 and the ratio of expenditure and saving is 4:1.
So, we can set up the following proportion:
E/S = 4/1
We know that E+S = 50000, since the income is equal to the sum of expenditure and saving.
So, we can use this equation to find the value of E and S.
We can first solve for E in terms of S:
E = (4/5)S
We can then substitute this equation into the equation E+S = 50000 to find the value of S:
(4/5)S + S = 50000
Solving for S, we get:
S = (50000/(4+1)) = 50000/5 = 10000
Now that we know the value of S, we can use the proportion E/S = 4/1 to find the value of E:
E = 4 * S = 4 * 10000 = 40000
So, the expenditure of the family is Rs. 40000 and the saving is Rs. 10000.
Question below. Please leave a step-by-step! I am having issues finding this out without another bottom.
The length of side qs in triangle qrs is 6 units.
What is the length of side of a similar triangle?Two objects are similar in Euclidean geometry if they have the same shape or one has the same shape as the mirror image of the other. One can be obtained from the other by uniformly scaling (enlarging or contracting), possibly with additional translation, rotation, and reflection.When all three sides of a triangle are proportional to the three sides of another triangle, the two triangles are said to be similar.Given:
On the abc triangle,
ab = 5, ac = 3
And the qrs triangle,
qr = 10, qs = x(we have to find)
Because both triangles are similar, the ratio of their sides must also be congruent.
ac / qs = ab / rq
3/ x = 5/10
3/x = 1/2
x = 3(2)
x = 6
Therefore the length of side qs is 6 units.
To learn more about length refer to :
https://brainly.com/question/21841092
#SPJ1
answer
fast please fast
Answer:
The width of each class in the frequency table for the age of 20 science teachers is 10 years.
Step-by-
- A boat is 12 ft away from a point perpendicular to the shoreline. A person stands at a point down the shoreline so that a 34° angle is formed between the closest point to the boat, the person, and the boat. How far is the person from the boat? Round your answer to the
nearest tenth of a foot. Show all work.
Answer:
distance = 7.4 ft
Step-by-step explanation:
There are different ways to approach this problem, but one possible method is to use trigonometry. Since we know the angle and one side of the triangle formed by the boat, the person, and the closest point to the boat, we can use the sine, cosine, or tangent function to find the other sides. For example, we can use the tangent function:
tan(34°) = opposite / adjacent
opposite = adjacent * tan(34°)
We know that the opposite side is the distance from the person to the boat, and the adjacent side is the distance from the person to the closest point to the boat, which is 12 ft. Therefore, we can substitute these values into the equation:
distance = 12 ft * tan(34°)
To find the distance, we need to know the value of the tangent of 34°. We can use a calculator or a trigonometry table to get this value, which is approximately 0.6167. Then we can substitute this value into the equation and solve for distance:
distance = 12 ft * 0.6167
distance = 7.4004 ft
Rounding to the nearest tenth of a foot, the person is about 7.4 ft away from the boat.
Another way to solve this problem is by using the law of sines.
distance = (12*sin(34))/(sin(126))
distance = 7.4 ft
use quadratic reciprocity to see whether the following have solutions; each modulus is prime x^2 = 123 mod 4-1
modulus is prime x^2 = 123 mod 4-1 this implies 123 mode 3 and hence we get x^2 = 2 prime
(a)Let p be the smallest prime divisor of (n!)^2+1 if p<=n then p|n! Hence p can not divide (n!)^2+1. Hence p>n
(b) (n!)^2=-1 mod p now by format theorem (n!)^(p-1)= 1 mod p ( as p doesn't divide (n!)^2)
Hence (-1)^(p-1)/2= 1 mod p hence [ as p-1/2 is an integer] and hence( p-1)/2 is even number hence p is of the form 4k+1
(C) now let p be the largest prime of the form 4k+1 consider x= (p!)^2+1 . Let q be the smallest prime dividing x . By the previous exercises q> p and q is also of the form 4k+1 hence contradiction. Hence P_1 is infinite
therefore , modulus is prime x^2 = 123 mod 4-1 this implies 123 mode 3 and hence we get x^2 = 2
learn more about of modulus here
https://brainly.com/question/16520505
#SPJ4
How to multiply polynomials
Utilizing the distributive law, first multiply each term in one polynomial by each term in the other polynomial. Using the exponent rule, multiply the powers of the same variables. Then, add or remove like terms to simplify the resulting polynomial.
What is a polynomial?A polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients, and it only uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of the variables. Polynomials can be considered a particular type of mathematics. In practically all areas of mathematics, including calculus, they are used to express numbers. They are also regarded as being crucial in several areas of mathematics. Examples of polynomials include 2x + 9 and x² + 3x + 11.In particular, a polynomial term cannot contain any square roots of variables, fractional or negative powers on the variables, or variables in any fraction's denominator.To learn more about polynomial, refer to:
https://brainly.com/question/1600696
#SPJ1
Three angles in triangle T have the ratio 1: 2: 3. What type of triangle is T
Answer: A scalene triangle
Step-by-step explanation: Since the angles in the triangle are not equal, then the sides aren't also equal. This makes it a scalene triangle (a triangle with unequal sides)
