(Hard) A composite number n is called a Carmichael number bn−1 ≡ 1 (mod n) for every number b such ... Base case: When n = 2 the formula a + c ≡ b + d (mod m) was already given. ... The sequence goes 1, 3, 7, 15, 31,... guess that it is equal to 2n+1 − 1. ... Prove (now using induction on n) that fm|fmn for all n ≥ 1.
Answer:
That would be n[tex]\geq 1\\[/tex]
Step-by-step explanation:
What is the image of the point (-5,4) after a rotation of 270° counterclockwise
about the origin?
Answer:
A counterclockwise rotation of 270º about the origin is equivalent to a clockwise rotation of 90º about the origin. Given a point (4, 5), the x-value, i.e. 4 and the y-value, i.e. 5 are positive, hence the point is in the 1st quadrant of the xy-plane.
Step-by-step explanation:
what is seven less than the quotient of 16 and 4
Answer:
-3
Step-by-step explanation:
16/4=4, so seven less than that is -3
Find the value of x in the triangle shown below help please!!
Step-by-step explanation:
Hey there!!
It 's so simple.
You remember common property of triangle. (i.e sum of interior angle of a triangle is 180°)
So,
77° + 31° + x = 180°
x + 108° = 180°
x = 180° - 108°
Therefore the measure of angle x is 72°.
Hope it helps....
Explain how solving -7y > 161 is different from solving 7y > -161
Answer:
Sample response:
Both inequalities use the division property to isolate the variable, y. When you divide by a negative number, like –7, you must reverse the direction of the inequality sign. When you divide by a positive number, like 7, the inequality sign stays the same. The solution to the first inequality is y > -23, and the solution to the second inequality is y <>
A submarine that is 245 feet below sea level descends 83 feet and then ascends 103 feet. What is the location of the submarine compared to sea level?
Answer:
225 feet
Step-by-step explanation:
-245 plus -83 then add 103
16x^3
And divide
10x^1
Answer:
8x^3/5
Step-by-step explanation:
Evaluate the exponent
16x^3/10
Factor 2 out of 16x^3
2(8x^3)/10
Cancel the common factors
Factor 2 out of 10
2(8x^3)/2(5)
Cancel the common factor
(8x^3)/5
Rewrite the expression
8x^3/5
I hope this helps! :)
13/11 = x/9 round your answer to the nearest tenth
Answer:
x ≈ 10.6
Step-by-step explanation:
Given
[tex]\frac{13}{11}[/tex] = [tex]\frac{x}{9}[/tex] ( cross- multiply )
11x = 117 ( divide both sides by 11 )
x ≈ 10.6 ( to the nearest tenth )
Which number line shows the points −12/5 and –2.8?
The number line that shows the points −12/5 and –2.8 is Option A.
What is a number line?Integers are arranged at equal intervals along horizontal straight lines called number lines. A number line can be used to represent every number in a series. The endpoints of this line go on forever. Some will have a defined beginning and end. It refers to those as closed number lines. Number lines might be alternatively left empty or blank. A number ladder is a vertical number line.
The given numbers are: −12/5 and –2.8
As we can re-write -12/5 in decimal form= -2.4
Now, we need to mark the number on the number line.
As the number -2.4 lies between -2 and -3 on the left side of zero.
and, -2.4 lies between -the numbers 2.5 and -3.0 on the left side of zero.
Learn more about number line here:
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Explain.
Numbers may only be used once 1-9
Step-by-step explanation:
Ax − B = C
Dy + E = F
Solve for x and y:
x = (B + C) / A
y = (F − E) / D
So the sum of x and y is:
x + y = (B + C) / A + (F − E) / D
For x + y to be as large as possible, A, E and D must be small, and B, C, and F must be large. With some trial and error:
x + y = (9 + 8) / 1 + (7 − 3) / 2
x + y = 17 + 2
x + y = 19
For x + y to be as small as possible, we want the first term to be a small fraction, and the second term to be as negative as possible. So A must be large, B + C must be small, F must be less than E, and D must be small.
x + y = (3 + 4) / 8 + (2 − 9) / 1
x + y = ⅞ − 7
x + y = -6⅛
find the missing value
We can write a ratio:
15/5 = 36/x
Let "x" equal the unknown part of the triangle.
Solution:
15/5 = 36/x
~Cross multiply
15x = 180
~Divide 15 to both sides
x = 12
Best of Luck!
Laura bought 55 shares of stock for $3.50 per share last year. She paid her broker a 1% commission. She sold the stock this week for $2 per share, and paid her broker a $10 flat fee. What were Laura’s net proceeds? Round to the nearest cent. What was her capital gain or loss?
Answer:
cp of 55 shares = 3.50 * 55 = 192.5
commission amount = 1% *192.5 = 1.925
Total invest = 192.5 + 1.925 = 194.425
sp of 1 share = 2
sp of 55 share = 2*55 = 110
Earning from shares = 110
since earning is less than invest, Laura has loss of (194.425 - 110) = 84.425
Laura has a loss of $84.425 for the cost price of $192.5.
What is an expression?Mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Cost price of 55 shares = 3.50 x 55 = 192.5
Commission amount = 1% *192.5 = 1.925
Total invest = 192.5 + 1.925 = 194.425
The selling price of 1 share = 2
The selling price of 55 share = 2*55 = 110
Earning from shares = 110
Since earnings are less than investment, Laura has a loss of (194.425 - 110) = $84.425
Therefore, Laura has a loss of $84.425 for the cost price of $192.5.
To know more about an expression follow
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Jaiden's pen pal from Mexico said that he lives 3.3 kilometers from school. Jaiden knows
that 1 kilometer is approximately 0.62 miles. Which is the closest distance (in miles) that
Jaiden's pen pal lives from school?
Answer:
2 miles
Step-by-step explanation:
3.3 kilometers to miles is 2.0505. I'm not sure if this question want you to round, but if it does, the answer would be 2 miles.
To get your approximate answer, multiply 3.3 (kilometers) by 0.62 (miles).
You get 2.046 if you multiply it by 0.62 like the question says to do.
Find the length of the base of the following pyramid, given the height of the pyramid is 211 meters and the angle of elevation of the base of the
pyramid is 62. Round to the nearest whole number. (4 points)
h = 211 m
62
length of the base
Answer:
224 meters
I took the test, and got it right.
Answer:
224 meters
Step-by-step explanation:
Have a great day!
Use the model to solve for x. A) x = 1 B) x = 3 C) x = 5 D) x =
Answer:
D){?} x = 7Step-by-step explanation:
x + 3•(+1) = 2•x + 4•(-1)
x + 3 = 2x - 4
-3 -3
x = 2x - 7
-2x -2x
- x = -7
÷(-1) ÷(-1)
x = 7
how do you add and subtract decimals??
Answer:
add ans subtract like normal
Step-by-step explanation:
Step-by-step explanation:
To add decimals, follow these steps: Write down the numbers, one under the other, with the decimal points lined up. Put in zeros so the numbers have the same length .Then add, using column addition, remembering to put the decimal point in the answer.
subtraction also in the same way only place the large no up and small down and do subtraction.
I hope this helps....
Taylor makes $8 an hour at the pizza place and she is scheduled to work six hours this afternoon. However, Brandon called and wanted to know if she could go out to the movies. Assuming the movies will cost Taylor $10, what is her opportunity cost of going out to the movies?
Answer:
58
Step-by-step explanation:
im pretty sure its saying like what she is losing by not going to work and how much she is paying for the movie so 8x6 then add the 10
16) Amari ran three-quarter the distance Mary did. Amari ran 12 miles. Write and solve an equation that represents how far Mary
Answer:
Step-by-step explanation:
Amari ran 3/4 distance Mary ran
A = 3/4 M
Amari ran 12 miles
12 = 3/4 M Multiply by 4
12 * 4 = 3*M Combine
48 = 3M Divide by 3
48/3 = M
M = 16
So Mary ran 16 miles.
The human resource department at a certain company wants to conduct a survey regarding worker benefits. The department has an alphabetical list of all 7148 employees at the company and wants to conduct a systematic sample of size 70.
Answer:
The answer is "K= 102"
Step-by-step explanation:
Given:
Number of employees = 7128
sample size =70
k=?
Formula:
[tex]\to K= \frac{\text{Number of employees}}{\text{sample size}} \\\\[/tex]
[tex]= \frac{7148}{70} \\\\= 102.11\ \ \ \ or \ \ \ 102[/tex]
what is 11+15+11+15+11+15+11+15+11+15+11+15+11+15 simplified
Answer:
182
Step-by-step explanation:
You add all of them together and you will get the same answer if you would simplify it i simplified it
find the 55th term of the arithmetic sequence 11,21,31,...
If a car is traveling at 50kph, how long would it take for the car to travel 12.5km?
Answer:
4 km
Step-by-step explanation:
T = time
D = distance
S = speed
the forumla to find the distance is
T * S = D
manipulate the equation for this problem:
D/S = T
Plug-in the known values
D = 12.5 km
S = 50kph
12.5km/50kph
cancel units and simplify
4 km
Which representation shows y as a function of x?
Answer:
A
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
(-4.5)to the power of 0
Answer:
-1
Step-by-step explanation:
The figure below shows part of a stained glass window depicting the rising sun which function can be used to find the area of the region outside of the semicircle but inside the rectangle. (Look at the picture for more details)
We know that the area of a semicircle = 1/2(πr^2)
r = the radius
We also know that the area of a rectangle = xy
x = width
y = length
In our problem,
r = w
x = w
y = w + 5
A(w) = w(w + 5) - 1/2(πw^2)
Let's simplify the right side of the function.
A(w) = w^2 + 5w - 1/2πw^2
2(x + 4) = 3(2x - 2)
HELP!!!
Answer:
7/2 = x
Step-by-step explanation:
2(x + 4) = 3(2x - 2)
Distribute
2x+8 = 6x -6
Subtract 2x from each side
2x-2x+8 = 6x-2x -6
8 = 4x -6
Add 6 to each side
Add 6 to each side
8+6 = 4x-6+6
14 = 4x
14/4 = 4x/4
7/2 = x
Answer:
x= 7/2
Step-by-step explanation:
2x + 8 = 6x - 6
2x - 6x = -6 - 8
- 4x = -14
x = 7/2
Brad drives 527 miles on 17 gallons. How many miles does Brad drive on one gallon? (5 points + Brainiest!)
a
31 miles per gallon
b
527 miles per 17 gallons
c
5.27 miles per gallon
d
1 over 31 miles per gallon
Answer:
d
Step-by-step explanation:
527 / 17 = 31
Create a quadratic function f(x), other than f(x) = x^2, and write it below. Then below the function, state the domain, range, x-intercepts, y-intercept, and f(3).
Answer:
[tex]f(x)=2x^{2}-3[/tex]
[tex]D=(-\infty,\infty)[/tex]
[tex]R=[-3,\infty)[/tex]
x-intercepts: [tex](\frac{\sqrt{6}}{2},0)[/tex] and [tex](-\frac{\sqrt{6}}{2},0)[/tex]
y-intercept: (0,-3)
f(3)=15
Step-by-step explanation:
A quadratic function is any polynomial function whose greatest power is a 2, so [tex]f(x)=2x^{2}-3[/tex] is a nice example of it.
For the domain, as a rule, polynomial functions that have positive whole degrees will be defined for all real numbers, so:
[tex]D=(-\infty,\infty)[/tex]
When talking about quadratic functions, its range will happen from the lowest point (in this case the vertex) to it's highest point (in this case infinity)
In order to find the vertex, we can use the following formula:
[tex]x=-\frac{b}{2a}[/tex]
which is used for quadratic equations in standard form:
[tex]y=ax^{2}+bx+c[/tex]
In this case a=2, b=0 and c=-3, so we get:
[tex]x=-\frac{0}{2(2)}=0[/tex]
Now we know that the range will happen at x=0, so we substitute:
[tex]f(0)=2(0)^{2}-3=-3[/tex]
so the range will be:
[tex]R=[-3,\infty)[/tex]
For the x-intercepts we need to set the given function equal to zero so we get:
[tex]2x^2-3=0[/tex]
and solve for x:
[tex]2x^{2}=3[/tex]
[tex]x^{2}=\frac{3}{2}[/tex]
[tex]x=\pm \sqrt{\frac{3}{2}}[/tex]
which can be rationalized to:
[tex]x=\frac{\sqrt{6}}{2}[/tex] and [tex]x=-\frac{\sqrt{6}}{2}[/tex]
so the x-intercepts are located at:
[tex](\frac{\sqrt{6}}{2},0)[/tex] and [tex](-\frac{\sqrt{6}}{2},0)[/tex]
For the y-intercept, we need to set x=0 so we get:
[tex]f(0)=2(0)^{2}-3[/tex]
[tex]f(0)=-3[/tex]
So the y-intercept is located at:
(0,-3)
and finally, in order to get f(3) we must substitute x for 3 so we get:
[tex]f(3)=2(3)^{2}-3[/tex]
f(3)=15
write the expression (-2). (-2) . 7 . 7 . 7 . 7 . 7 . using exponents
Answer:
[tex]-2^{2}[/tex] * [tex]7^{5}[/tex]
Step-by-step explanation:
-2 is shown two times in the equation, and 7 is shown 5 times. That is why the answer is [tex]-2^{2}[/tex] * [tex]7^{5}[/tex]
Hope this helps!
100000000000 to the 10th power
Answer:
The answer for this question is 1e+110
PLEASEEEE HELP URGENT
Answer:
7.1 cm
Step-by-step explanation:
The diagonal of a cube connects two opposite corners.
You can use the diagonal of a cube in a right triangle in which it is the hypotenuse. The legs of the triangle are a diagonal of a face and an edge.
Let the length of the edge be s.
a^2 + b^2 = c^2
[tex] s^2 + 10^2 = (\sqrt{150})^2 [/tex]
[tex] s^2 + 100 = 150 [/tex]
[tex] s^2 = 50 [/tex]
[tex] s = \sqrt{50} [/tex]
[tex] s = 5\sqrt{2} [/tex]
s = 7.1
Answer: 7.1 cm