There are exactly 15 remainders modulo 15 and they are 0,1,2,…,14.
It is given that at least two of them should have the same remainder when divided by 15.
Division algorithm.
Let aa be an integer and d a positive integer. Then there are unique integers q and r with [tex]0\leq r < d[/tex] such that [tex]a=dq+r[/tex]
q is called the quotient and r is called the remainder
q=a div d
r=a mod d
Pigeonhole principle If k is a positive integer and k+1or more objects are placed into k boxes, then there is at least one box containing two or more objects.
Hence, there are exactly 15 remainders modulo 15 and they are 0,1,2,…,14.
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(-1,8) and (8,5). this is a coordinate distance wuestion that i rly need help on
Answer:
3[tex]\sqrt{10}[/tex] ≈ 9.45
Step-by-step explanation:
calculate the distance d between the points using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 1, 8 ) and (x₂, y₂ ) = (8, 5 )
d = [tex]\sqrt{(8-(-1))^2+(5-8)^2}[/tex]
= [tex]\sqrt{(8+1)^2+(-3)^2}[/tex]
= [tex]\sqrt{9^2+9}[/tex]
= [tex]\sqrt{81+9}[/tex]
= [tex]\sqrt{90}[/tex]
= [tex]\sqrt{9(10)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{10}[/tex]
= 3[tex]\sqrt{10}[/tex] ← exact value
≈ 9.49 ( to 2 dec. places )
(x + 1 < 4) ∩ (x - 8 > -7).
The correct answer is x = 2
Inequality(x + 1 < 4) ∩ (x-8>-7)
Make x the subject in each case:
(x<4-1)(x>-7+8)
(x<3)∩(x>1)
If x<3, then x could be 2, 1, -1, etc.
If x>1, then x could be 2, 3, 4, etc.
Thus (x<3)∩(x>1) = 2
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Answer:
x = 2
Step-by-step explanation:
Hello!
We are looking at the intersection of two sets, or common values found between two sets of data.
We can solve for x on each side and find any common values between.
Find the Intersection[tex](x + 1 < 4) \cap(x - 8 > -7)[/tex][tex](x < 3)\cap(x > 1)[/tex][tex](x = 2, 1, 0, -1, -2...)\cap(x = 2, 3, 4, 5, 6...)[/tex][tex]x = 2[/tex]As you can see, the intersection occurs at the common values. The only value that is common between the two sets is 2.
Therefore, the intersection of these sets is 2.
How do you simplify 6 by the power of negative 2 multiplied by 6 by the power of 3
Answer:
Keep in mind the rules.
When we multiply terms with same bases we keep one base and add the exponents.
Step-by-step explanation:
[tex] = {6}^{ - 2} \times {6}^{3} \\ = { 6}^{ - 2 + 3} \\ = {6}^{1} \\ = 6[/tex]Hope this helps.I need to find the restrictions for this equation:
Answer:
Simplify 2x^2-5x-3/x^2-9
The answer is 2x+1 / x+3
Step-by-step explanation:
Simplify the expression.
What is the tangent
ratio of angle C₂ ?
Answer:Tangent ratio of an angle
Step-by-step explanation:
Tangent ratio of an angle the ratio of the length of the opposite side of an angle divided by the length of the adjacent side.
helllppppppppppp please
Answer:
h = 5t
Step-by-step explanation:
So basically, its a slope problem again. You are trying to find the equation that equals hits. So you can cross off t = 5h and t = h + 5. So now, you need to find the most reasonable answer by calculating the slope.
If you try h = t + 5,
Put in 3 - you get 8
Put in 7 - you get 12
But on the table you get 15, 36 respectively.
If you try h = 5t,
Put in 3 - you get 15
Put in 7 - you get 35
Which is much closer to the numbers in the table, therefore it is the answer.
Can someone help me out on this problem
The correlation is a strong negative correlation, because as the weights increases the city MPG decreases
The graph of the table of valuesTo do this, we plot the weights on the x-axis, and the city MPG on the y-axis
See attachment for graph
Type of correlationThe correlation is a strong negative correlation, because as the weights increases the city MPG decreases
The equation of the line of best fitTo do this, we make use of a graphing calculator.
From the graphing calculator, we have the following summary:
Sum of X = 463Sum of Y = 388Mean X = 28.9375Mean Y = 24.25Sum of squares (SSX) = 862.9375Sum of products (SP) = -857.75The line of best fit equation is
y = bx + a
Where
b = SP/SSX = -857.75/862.94 = -0.99399
a = MY - bMX = 24.25 - (-0.99*28.94) = 53.01354
So, we have:
y = -0.99399x + 53.01354
Approximate
y = -0.99x + 53
Hence, the equation of the line of best fit is y = -0.99x + 53
The weight for 30 MPGThis means that y = 30
So, we have:
-0.99x + 53 = 30
Subtract 53 from both sides
-0.99x = -23
Divide by -0.99
x = 23.23
Approximate
x =23
Hence, the predicted weight is 23 pounds
The city MPG for 1500 poundsThis means that x = 1500
So, we have:
y = -0.99 * 1500 + 53
Evaluate
y = -1432
Hence, the city MPG for 1500 pounds is -1432
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A spherical ball is inflated so that it’s radius increases in the ratio 4:3. Find the ratio in which it’s volume is increased
Answer:
64:27
Step-by-step explanation:
If the ratio between the old and new radius is described with the ratio: 4:3, then if the first radius was 3, then the new radius is 4.
Also if you multiply 3 by (4/3) it also equals 4
The volume of a sphere is described as: [tex]\frac{4}{3} \pi r^{3}[/tex]
So let's plug in 3 and 4 and see their ratio.
[tex]\frac{\frac{4}{3}\pi 4^{3} }{ \frac{4}{3}\pi 3^{3} }} = \frac{4^{3} }{3^{3} } = \frac{64}{27}[/tex]
The answer is 64/27 or (4/3)^3
Answer:
by a factor of 64/27 or 64:27
Step-by-step explanation:
Volume of a sphere = 4/3 pi r^3
now increase the radius by 4/3 ( this is 4:3)
new volume = 4/3 pi (4/3 r)^3
= 64/27 * 4/3 pi r^3
so the original volume is increased by 64/27
Identify each of the following as rational or irrational.
Answer:A rational number can be written as a fraction of two integers. √23 is irrational because we do not know what the square root of 23 is in terms of integers in a fraction. 104.42 is rational because it can be expressed as 10442/100 . We can express it as this because.
Step-by-step explanation:
A sum of Rs. 500 is in the form of denominations of Rs. 10 and Rs. 20. If total number of notes are 35, find the number of notes of each denomination.
Answer: 20 of banknotes, denomination of Rs. 10 and 15 of banknotes, denomination of Rs. 20.
Step-by-step explanation:
Let the number of banknotes, denomination of Rs. 10 will be equal to x,
and the number of banknotes, denomination of Rs. 20 will be equal to y.
Hence; [tex]\left \{ {{x+y=35\ \ \ \ } \atop {10*x+20*y=500\ |:10 \ \ }} \right. \ \ \ \ \left \{ {{x+y=35\ \ (1)} \atop {x+2y=50\ \ (2)}} \right. \\[/tex]
From (2) subtract (1):
[tex]y=15\ \ \ \ \ \Rightarrow\\x+15=35\\x=20.[/tex]
What is the constant rate of change of the table below? Please help
Answer:
4 m/s
Step-by-step explanation:
Well the constant rate of change can be defined as the slope or rise/run. This can be calculated using any two points. So I'll use (10, 40) and (20, 80). the seconds increased by 10 (run) and the meters increased by 40 (rise) This gives you the equation 40/10 which simplifies to 4. That is the constant rate of change
vincent ordered pizza for him and his wife for dinner. when they had finished, they realized that 5/8 of the pizza was gone. for lunch the next day, vincent decided to eat 1/4 of what was left. how much was left after lunch?
Answer:
1/8 of the pizza
Step-by-step explanation:
whole pizza=1
5/8 is gone so 1-5/8=8/8-5/8=3/8
3/8-1/4 = 3/8-2/8=1/8
hope this helps
The French army stayed behind in Egypt—and so did the scholars. In late August, shortly after Napoleon's departure, a large, heavy package arrived at the scholars' palace in Cairo. When they opened it, they found it contained a black stone slab covered with writing in three different scripts.
A note from a French army officer accompanied the package. He told the scholars that the stone had been unearthed in an old fort near the town of Rosetta, thirty-five miles north of Alexandria. French soldiers were tearing down a ruined wall in the fort when they came upon the slab.
Which statement accurately describes a cause-and-effect relationship described in this excerpt?
Because Napoleon departs for France, the French army and scholars decide to stay in Egypt.
Because the French army and scholars decide to stay in Egypt, Napoleon decides to depart for France.
Because the French soldiers are tearing down a ruined wall in a fort, they discover the Rosetta Stone.
Because the French soldiers are searching for the Rosetta Stone, they tear down a ruined wall in a fort.
The statement that accurately describes a cause-and-effect relationship described in this excerpt is C. Because the French soldiers are tearing down a ruined wall in a fort, they discover the Rosetta Stone.
What is a cause-and-effect relationship?A cause-and-effect relationship occurs when:
Two events occur at the same time and in the same place.One event immediately precedes the other.The second event appears unlikely to have happened without the first event occurring.Thus, the statement that accurately describes a cause-and-effect relationship described in this excerpt is C. Because the French soldiers are tearing down a ruined wall in a fort, they discover the Rosetta Stone.
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PLEASE HELP URGENT
B Pick the inequality that matches the graph shown. Show all of your work to explain the
choice you selected. (See Ex. 1)
Answer:
B. y > 3x -7
Step-by-step explanation:
We can choose the correct inequality based on the y-intercept and the shading.
Y-interceptThe dashed line crosses the y-axis at approximately y=-7. This is the value of y when x=0. This observation eliminates choices D, E, F.
ShadingThe shading on the graph is seen to be above and to the left of the line. This means the variables in relation to the inequality symbol must be ...
y > ( ) . . . . eliminates choice A
and
x < ( ) or ( ) > x . . . . eliminates choice C, confirms choice B
The inequality that matches the graph is y > 3x -7.
__
Additional comment
For looking at shading, we are interested in the relation of the inequality symbol to a variable term with a positive coefficient. If the coefficient is negative, you can do either of ...
add the opposite of that variable term to both sides of the equationreverse the inequality symbolThat is, if you have -3x < ( ), when considering shading, you can consider the relation x > ( ) with the inequality reversed, or you can consider ( ) < x, which has x on the other side of the inequality. Both of these tell you shading is right of the line, where x-values are greater than those on the line.
An inequality is shown below:
−np − 3 ≥ 7(c − 4)
Which of the following solves for n?
The solution of n is [tex]n \le -\frac 1p(7(c - 4) + 3)[/tex]
How to solve for n?The inequality is given as:
−np − 3 ≥ 7(c − 4)
Add 3 to both sides
−np ≥ 7(c − 4) + 3
Divide through by -p;
This changes the inequality sign.
So, we have:
[tex]n \le -\frac 1p(7(c - 4) + 3)[/tex]
Hence, the solution of n is [tex]n \le -\frac 1p(7(c - 4) + 3)[/tex]
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Suppose $n$ is a positive integer such that $6n$ has exactly 9 positive divisors. How many prime numbers are divisors of $6n$
The number of prime divisors of "6n" is 2 numbers 2 and 3
Given
"n" = 6
thus 6n = 6(6) = 36
The positive divisors are 1, 2, 3, 4, 6, 9, 12, 18 and 36
So, the number of prime divisors of "6n" is 2 numbers 2 and 3.
The prime factors of a positive integer are the top numbers that divide that integer exactly. The technique of finding those numbers is known as integer factorization or prime factorization.
The fundamental theorem of mathematics says that every positive integer has a completely unique prime factorization.
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2. Find four consecutive integers such that six times the sum of the first and third is 12
greater than 9 times the fourth.
Answer:
9
Step-by-step explanation:
a,a+1,a+2,a+3,...
6(a+(a+2))=12+9(a+3)
6(2a+2)=12+9a+27
12a+12=12+9a+27
12a-9a=27
3a=27
a=9
Which number is equal to –906,060? –9.0606 times. 105 –9.06 times. 105 9.06 times. 10–5 9.0606 times. 10–5
Answer:
I don't understand the formatting of the possible answers. Below is a solution.
Step-by-step explanation:
906,060 is the same as 9.0606 x 10^5
The given number is equal to [tex]-9.0606 * 10^5[/tex]
What is Scientific notation ?Scientific notation is a way to write numbers in an abbreviated way, making it easier to work with these numbers.
Why should we use Scientific notation ?The primary reason for converting numbers into scientific notation is to make calculations with unusually large or small numbers less cumbersome. Because zeros are no longer used to set the decimal point, all of the digits in a number in scientific notation are significant.
A widely used floating-point system in which numbers are expressed as products consisting of a number between 1 and 10 multiplied by an appropriate power of 10
Converting –906,060 into scientific notation, we get
-906060/100000
= - 9.06060*10^5
Thus, The given number is equal to -9.06060*10^5
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Solve for t 16−2t=t+9+4t
Answer:
Step-by-step explanation:
16-2t=t+9+4t
7=7t
t=1
You enter a room. 2 dogs, 4 horses, one giraffe, and a duck are laying on a bed. 3 chicken are flying over a chair. How many legs are on the ground?.
Answer: the answer is 28
Step-by-step explanation:
Which explicit formula is equivalent to a1 = 1, an = -6an-1
The explicit formula that is equivalent to aₙ = -6aₙ₋₁ is; aₙ = 1(-6)ⁿ⁻¹
What is the explicit formula?We are given;
a₁ = 1
aₙ = -6aₙ₋₁
Thus, for second term;
a₂ = -6a₁
a₂ = -6
For the third term;
a₃ = -6a₂
a₃ = 36
The resulting sequence is 1, -6, 36,......
The sequence is a geometric sequence with;
a = 1
r = -6
The explicit rule will be aₙ = 1(-6)ⁿ⁻¹
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60 POINTS PLEASEEEEEEEEEEEE
Answer:
A.) Two
Step-by-step explanation:
You can determine the amount of solutions the functions have by counting the number of intersections they have. Since the functions cross each other at two different points, there are two solutions.
-2x
10. What is the least common denominator of 21+2+³=1?
+3
O(x - 1)(x+1)
Ox(x - 1)2(x + 1)
O(x-1)2(x + 1)
Ox(x - 1)(x + 1)
Answer:
O(x-1)2(x + 1)
Step-by-step explanation:
In the parallelogram below, solve for x and y.
I have y but i can’t figure out x
Step-by-step explanation:
how did you get y, when you don't know how to get x ?
the easiest way to solve this is to base on the fact that the opposite angles must be identical.
so,
2x + 32 = 4x - 12
32 = 2x - 12
44 = 2x
x = 22
and the to be sure
-8y - 14 = -5y + 4
-3y = 18
y = -18/3 = -6
or, the sum of 2 consecutive angles must be 180°.
2x + 32 - 5y + 4 = 180
2x - 5y + 36 = 180
2x - 5y = 144
-8y - 14 + 4x - 12 = 180
-8y + 4x = 206
-4y + 2x = 103
-5y + 2x = 144
- -4y + 2x = 103
------------------------
- y 0 = 41
y = -41
-4×-41 + 2x = 103
164 + 2x = 103
2x = -61
x = -30.5
ha, your teacher either set a trap or made a mistake.
these given angles do not belong to a parallelogram.
there is no solution for x and y with these angle expressions to create a parallelogram.
every condition that has to be true creates a different and inconsistent set of solutions (and implausible ones at that creating single angles larger than 200° and even 300°, or smaller than 0°).
Please help ill give whoever answers the best the brainliest answer :)))
Answer:
w(w-5)
Step-by-step explanation:
Given Width of rectangle = w
Length of rectangle is 5 less than width of rectangle = w - 5
Area of Rectangle = Length x Width = w * w-5 = w(w-5)
Answer:
the second answer option
Step-by-step explanation:
the area of a rectangle is
length × width
or
l × w
l = w - 5
so, when we use the second in the first equation, we get
(w - 5)×w
or
w(w - 5)
The interior angle of a regular polygon is twice the exterior angle how many sides has the polygon
Answer:
6 sides
Step-by-step explanation:
the interior angle + the exterior angle = 180°
let x be the exterior angle then 2x is the interior angle and
x + 2x = 180
3x = 180 ( divide both sides by 3 )
x = 60
the exterior angle = 60°
the sum of the exterior angles of a polygon = 360°
since the polygon is regular the the exterior angles are congruent, then
number of sides = 360° ÷ 60° = 6
Thirty-three college freshmen were randomly selected for an on-campus survey at their university. The participants' mean GPA was 2.5, and the standard deviation was 0.5. What is the margin of error, assuming a 95% confidence level
The margin of error is ±0.1706
What is the margin of error?The margin of error is a statistical solution for the amount of random sampling error in the survey results.
What is 95% of a confidence level?The 95% confidence interval means from 100 different samples computing a 95% of confidence for each sample. From this, we get the approximate value 95 of the 100 confidence intervals will contain the true mean value.
We have a sample size of n=33
The critical value of the significance level is [tex]\alpha =0.05\\z_{\frac{\alpha }{2} }=1.96[/tex]
Then our sample mean will be 2.5
then the standard deviation is 0.5
from this, we can assume that this is a normal distribution.
then our margin of error will be
[tex]E=[/tex]±[tex]z_{\frac{\alpha }{2} }\frac{deviation}{\sqrt{n} }[/tex]
⇒[tex]E=[/tex]±[tex](1.96)\frac{0.5}{\sqrt{33} }\\[/tex]
≅±0.1706 is the margin of error.
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The graph shows a vertical translation of y=√x
4
3-
2
1+
-10-8-6-4-2₁- 2
What is the range of the translated function?
O {vly < 0)
O {vly 20}
Oyly is a natural number)
Oyly is a real number)
4
what is the rule for the following geometric sequence? 64, -32,16,-8
The rule is n/(-2)
What is geometric Progression?A geometric progression is a sequence in which any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r.
Given:
64, -32,16,-8
r= 64/-32
r= -2
again, r= -32/16
r= -2
By above we concluded that the common ratio is is -2.
If n is natural numbers for finding geometric progression the rule which defines it n/(-2).
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I need answer quickly
Answer:
√85
Step-by-step explanation:
a² + b² = c²
6² + b² = 11²
36 + b² = 121
b² = 121 - 36
b² = 85
b = √85
Answer:
Hello! The answer is [tex]b = \sqrt{85}[/tex].
Step-by-step explanation:
To solve this question, we have to use the Pythagorean theorem. We are given one of the legs and the hypotenuse. (The hypotenuse is opposite the right angle).
a^2 and b^2 represent our legs while c^2 represents the hypotenuse.
We have to substitute our values in for a^2 and c^2:
6^2 + b^2 = 11^2
This leaves us with 36 + b^2 = 121
To get b^2 by itself, we have to subtract 36 from both sides:
36 + b^2 = 121
-36 -36
This leaves us with b^2 = 85
To get just b, we have to take the square root:
√b^2 = √85
This leaves us with [tex]b = \sqrt{85}[/tex].