Set S should contain 137 number of integers so that at least 35 integers in S have same remainder when divided by 4.
What is pigeonhole principle?According to the pigeonhole principle in mathematics, at least one container must hold more than one item if n things are placed into m containers, where n > m. As an illustration, if one has three gloves (none of which are ambidextrous or reversible), at least two of them must be right-handed or left-handed as there are three items but only two categories of handedness to classify them into. It is possible to establish potentially surprising consequences using this seemingly obvious assertion, a type of counting argument.
Equating pigeonhole principle :Given: Set S = {}, least number of integers having same remainder when divided by 4=35
To find: Number of integers in set S so that at least 35 of the integers in set S have same remainder?As we know, any number when divided by 4 has following remainder = 0, 1, 2, 3.
Least number of integers having same remainder when divided by 4 = 35.
∴ Number of integers in set S = 35×4
= 140
but 3 is to be subtracted from 140 as it is the last different remainder after which the remainders repeat in manner 0, 1, 2 & 3.
∴ Total number of integers in set S = 140-3
= 137
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Write an equation of the line containing the point (2,5) and perpendicular to the line 3x - 2y = 5.
Answer:
y = (-2/3)x + (19/3)
Step-by-step explanation:
3x - 2y = 5
-2y + 3x = 5
-3x -3x
-------------------------
-2y = -3x + 5
-2 -2 -2
---------------------
3 5
y = -------x - -------
2 2
-2
Perpendicular: -------- x
3
-2
(2, 5); m = --------
x₁ y₁ 3
y - y₁ = m(x - x₁)
y - 5 = (-2/3)(x - 2)
y - 5 = (-2/3)x + (4/3)
+5 +5
--------------------------------
y = (-2/3)x + (19/3)
I hope this helps!
Morgan has 98 baseball cards in his collection, which is twelve less than the product of 5 and the number of cards Tyler has.
Answer: Tyler has 22 cards
Step-by-step explanation:
To begin, we know that Morgan has 12 less than 5x Tyler's cards, so...
12+98=110
Now that we had 110, we then read that it is the PRODUCT of 5 and the number that Tyler has, so we will show that algebraically.
110=5x
Now, divide 110 by 5 to find X.
110/5=22
Tyler has 22 cards.
How do I graph the equations x=3 and y=-8
how many ways are there to assign each of $6$ friends to either the chemistry class or the biology class if one of these six, manoj, refuses to be in a class without any of his friends?
There are 62 number of ways in which classes to these students can be assigned. It can be solved by using the fomula of combination.
What is the formula of combination?
Following is the fomula of combination:
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Here, n is the total objects available and r is the number of object need to choose from n objects.
Let six friends are A, B, C, D, E, and manoj.
Consider all 6 friends are in chemistry class. Hence, number of ways in which it can be is,
[tex]^6C_6[/tex]
Consider 5 friends are in chemistry class. Hence, number of ways in which it can be is,
[tex]^6C_5[/tex]
Consider 4 friends are in chemistry class. Hence, number of ways in which it can be is,
[tex]^6C_4[/tex]
Consider 3 friends are in chemistry class. Hence, number of ways in which it can be is,
[tex]^6C_3[/tex]
Consider 2 friends are in chemistry class. Hence, number of ways in which it can be is,
[tex]^6C_2[/tex]
Consider 1 friend is in chemistry class. Hence, number of ways in which it can be is,
[tex]^6C_1[/tex]
Consider no friend is in chemistry class all are in biology class. Hence, number of ways in which it can be is,
[tex]^6C_0[/tex]
Hence, total number of ways in which classes can be assigned to 6 students is,
[tex]^6C_6+^6C_5+^6C_4+^6C_3+^6C_2+^6C_1+^6C_0=64[/tex]
Now, the number of ways in which mnoj is alon. There are two ways. Either he will be in the chemistry class or he will be in the physics class.
Hence, subtract 2 from 64 to get the answer.
[tex]64-2=62[/tex]
Hence, there are 62 number of ways in which classes to these students can be assigned.
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Select a function f whose zeroes are 0,-3,2 and -4
The family of all least polynomials with roots at - 4, - 3, 0, 2 is represented by the polynomial y = a · (x + 4) · (x + 3) · x · (x - 2), where a is the lead coefficient.
What is the function that contains a given set of zeros?
Herein we must determine the family of all least polynomials whose roots must be the real numbers - 4, -3, 0, 2. Polynomials are algebraic expressions, whose factor form is described below:
y = a · Π (x - rₙ), for n = {1, 2, 3, 4, ..., m - 1, m}
Where:
a - Lead coefficient (a real number).rₙ - n-th root of the polynomial.m - Grade of the polynomial.In accordance with all these assumptions and definition, the function is defined below:
y = a · (x + 4) · (x + 3) · x · (x - 2)
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What is the density of a rock if its mass is 39.78 g and its volume is 12.45 cm³?
The density of the rock with a mass of 39.78 g and volume 12.45 cm³ is 3.2 g/cm³.
What is the density of the rock?Density is simply the mass of a unit volume of a material substance.
It is expressed mathematically as;
p = m / v
Where m is mass and v is volume
Given the data in the question;
Mass of the rock m = 39.78 g Volume v = 12.45 cm³Density P = ?Plug the given values into the above formula and solve for p.
p = m / v
p = 39.78g / 12.45 cm³
p = 3.2 g/cm³
Therefore, the density of the rock is approximately 3.2 g/cm³.
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Find the complex roots of the graph to the right.
x = 1+i or x = 1-i are the complex roots of the graph
How to find the complex roots of a graph?
Below are the steps for determining the complex roots of a graph or curve:
1. Draw a vertical line passing through the vertex of the parabola or curve
2. The value of x where the line intersects the x-axis gives the real part of the root
3. Draw a horizontal line of height twice the height of the vertex from the x-axis
4. Draw a vertical line from this point of intersection to intersect the x-axis
5. The distance of this point from the real part of the root gives you the imaginary part of the root
(Check the attached image for the labeling)
From the image attached:
Real part of the root: a = 1
Imaginary part of the root: b = 1
Remember: complex root is of the form x = a±bi
Therefore, the complex roots of the graph are x = 1+i or x = 1-i
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This is an arithmetic sequence.
8, 7.4, 6.8, 6.2, 5.6, …
Which function describes the sequence?
A. f(x) = 0.6x + 8
B. f(x) = 0.6x + 8.6
C. f(x) = −0.6x + 8
D. f(x) = −0.6x + 8.6
The function which describes the arithmetic sequence is f(x) = −0.6x + 8.6.
The correct answer option is option D
Which function describes the sequence?
Given the sequence:
8, 7.4, 6.8, 6.2, 5.6, …
Check all the options
Where,
x = number of term
A. f(x) = 0.6x + 8
When x = 1
f(x) = 0.6x + 8
= 0.6(1) + 8
= 0.6 + 8
= 8.6
B. f(x) = 0.6x + 8.6
When x = 1
= 0.6(1) + 8.6
= 0.6 + 8.6
= 9.2
C. f(x) = −0.6x + 8
When x = 1
= -0.6(1) + 8
= 0.6 + 8
= 8.6
D. f(x) = −0.6x + 8.6
When x = 1
= -0.6(1) + 8.6
= -0.6 + 8.6
= 8
Hence, f(x) = −0.6x + 8.6 is the function which describes the sequence.
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Give the number of lone pairs around the central atom and the molecular geometry of scl2.
SCl2 has a Bent molecular geometry and a tetrahedral shape in nature. SCl2 consists of a single Sulfur atom surrounded by two Chlorine atoms. In its most stable state, Sulfur acts as the central atom and forms two covalent bonds with the Chlorine atoms. It also possesses two lone pairs.
What is molecular geometry?The three-dimensional configuration of the atoms that make up a molecule is known as molecular geometry. In addition to bond lengths, bond angles, torsional angles, and any other geometrical factors that affect each atom's location, it also contains the molecule's overall structure. The arrangement of atoms in a molecule in three dimensions is known as molecular geometry, commonly referred to as the molecular structure. A compound's polarity, reactivity, phase of matter, color, magnetism, and biological activity can all be determined by knowing its molecular structure.
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A line passes through the origin and (5, 3). Identify two additional points on this line.
Answer:
(10,6) and (-5, -3)
Step-by-step explanation:
The slope of the line is given by rise/run between (0,0) and (5,3)
Rise = y2 - y1 = 3 - 0 = 3
Run = x2 - x1 = 5 - 0 = 5
Slope m 3/5
Slope intercept form of a line is
y = mx + b
where m is the slope and b is the y-intercept
Since the line passes through (0,0) the y-intercept is 0
So we get
[tex]y = \dfrac{3}{5}x + 0 \\\\or\\\\y = \dfrac{3}{5}x[/tex]
This means for any x value, the corresponding y value should be 3/5th of that x value
Only the first and third choices have this requirement fulfilled
5. question 5 a data analyst creates a scatter plot in tableau and notices an outlier. what should they do next?
Investigating an outlier that a data analyst has found is the best course of action.
What is a Data analyst?To find the solution to a problem or provide an answer to a question, a data analyst gathers, purifies, and analyzes data sets.
They work in a variety of fields, including as government, business, finance, law enforcement, and science.
Depending on the question you're attempting to answer, data analysis might take on various shapes.
More information on different data analysis types is available here.
In a nutshell, descriptive analysis explains what happened, diagnostic analysis explains why it occurred, predictive analytics offers future projections, and prescriptive analysis generates actionable recommendations for what to do.
Hence, Investigating an outlier that a data analyst has found is the best course of action.
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What is the x & y intercept of the equation?
1/2y + 5x = 7
Answer:
x-intercept: (7/5, 0)
y-intercept: (0, 14)
Step-by-step explanation:
The x intercept is when y is equal to 0.
1/2(0) + 5x = 7
5x = 7
x = 7/5
Put this into point form, where x is 7/5 and y is 0.
(7/5, 0)
The y intercept is when x is equal to 0.
1/2y + 5(0) = 7
1/2y = 7
y = 14
Put this into point form, where x is 0 and y is 14.
(0, 14)
Put the following equation of a line into slope-intercept form, simplifying all fractions.
12x - 20y = -100
Answer:
y = 5 + 3/5x
Step-by-step explanation:
We need to isolate y to get it in slope-intercept form. Let's subtract 12x from both sides, which gives us [tex]-20y=-100-12x[/tex]. Then, we can negate both sides, and then divide by 20, which results in [tex]y = (100+12x)/20[/tex], which we can further simplify to [tex]y=5 + 3/5x[/tex], which gives us our answer.
According to a tudy conducted in one city, 27% of adult in the city have credit card debt of more than $2000. A imple random ample of 400 adult i obtained from the city. Decribe the ampling ditribution of , the ample proportion of adult who have credit card debt of more than $2000. Round to three decimal place when neceary
The sample proportion of persons with credit card debts of further than $2,000 has a distribution that is roughly normal;
μ = 0.27 and σ = 0.022.
Explain the term random sample?A straightforward random sample, where each participant has an equal chance of being selected, selects a tiny, random piece of the total population for the purpose the full data set.According to a research conducted in one town, the percentage of persons living there had credit card debt of at least $2,000:
p = 27% = 0.27.
An adult sample from the entire city was gathered: n = 400 adults.
The following two requirements should be used to determine the whether sample is adequate before obtaining a sampling distribution of the probability value p:
np ≥ 10400 x 0.27 = 108
108 ≥ 10
And,
n(1 - p) ≥ 10400(1 - 0.27) ≥ 10
292 ≥ 10
We know that the as being p is nearly normally distributed the by suing "Central limit theorem."
Mean M; μ = Pstandard deviation σ = √(p(1 - p)/n.Mean of a sample proportion
μ = P = 0.27
The standard deviation's sample proportion P:
σ = √(p(1 - p)/n
σ = √(0.27(1 - 0.27)/400
σ = 0.022
Since the sample proportion of persons with credit card debts of further than $2,000 has a distribution that is roughly normal;
μ = 0.27 and σ = 0.022.
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if m angle 1= 125 what is m angle 2
Answer:
55°
Step-by-step explanation:
Assuming the angle is at 180°
180° - 125° = 55°
light shines from the top of a pole 30 ft high. a ball is dropped from the same height from a point 20 ft away from the light. how fast is the shadow of the ball moving along the ground 1 sec later? (assume the ball falls a distance s
The shadow of the ball moving over the ground at 150 feet per second after 1 second.
How can I determine the shadow of the ball's speed?
Assuming the ball drops the distance indicated by this sentence:
S = 16t²
Additionally, the height (h) of the ball's shadow one second later is provided by
h = 30 - S
The term for the shadow of the ball would then be as follows:
OX/30 = (20 + XQ)/30 = XQ/h
30XQ = 20h + hXQ
20h = 30XQ - hXQ
20h = (30 - h)XQ
XQ = 20h/(30 - h)
Substituting the value of h, we have:
XQ = 20(30 - S)/(30 - 30 - S)
Substituting the value of S, we have:
XQ = 20(30 - 16t²)/(30 - 30 - 16t²)
XQ = 20(30 - 16t²)/16t²
XQ = (600 - 320t²)/16t²
XQ = 600/16t² - 320t²/16t²
XQ = 600/16t² - 20
Differentiating with respect to t, we have:
d(XQ)/dt = 600/16t² - 20
d(XQ)/dt = 600 (-64t/(16t²)²)
d(XQ)/dt = 600 (-64t/256t⁴)
d(XQ)/dt = 600 (-0.5/2t³)
d(XQ)/dt = -300/2t³
Then,
At t = 1, we have:
Speed = 300/2(1)
Speed = 150 ft/s.
That is,
After one second the ball's shadow was travelling over the ground at a speed of 150 feet per second.
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Graph the following equations on graphing paper or your calculator to solve the
system of equations.
Which ordered pair is the best estimate for the solution to the system?
A. (-2, 1)
B. (-2.5, 0)
C. (0, 2)
D. (0, 5)
In linear equation, the solution of equations is ( -2 , 1)
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
y = 2x + 5
y = 1/2x + 2
the solution of equations is ( -2 , 1)
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how many sequences of 0s and 1s of length 19 are there that begin with a 0, end with a 0, contain no two consecutive 0s, and contain no three consecutive 1s? (2019 amc 10 b)
The number of sequence of 0s and 1s of length 19 are there that begin with a 0, end with a 0 are 65 .
In the question ,
After any particular 0, the next 0 in sequence must appear exactly 2 or 3 positions down.
In this case, we start at position 1 and end at position 19,
that is , we move a total of 18 positions down the line.
So , we must add the series of 2s and 3s to get 18.
There are several number of ways to do this:
Case 1: nine 2s - there is only 1 way to arrange them.
Case 2: two 3s and six 2s - there are ⁸C₂ ways = 28 ways
Case 3: four 3s and three 2s - there are ⁷C₄ ways = 35 ways
Case 4: six 3s - there is only 1 way to arrange them.
So , the number of sequences is = 1 + 28 + 35 + 1 = 65 .
Therefore , the total number of sequence is = 65 .
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Solve for x given y = 2
y=x+4
Answer:
x= –2
Step-by-step explanation:
y = 2
just substitute for y
2 = x + 4
2 – 4 = x
–2 = x
or x = –2
check
y=-2+4
y=2
so our answer is correct.
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what is a good rule of thumb for sizing a struct in c/c assuming that the struct is optimally set up?
A good rule of thumb for sizing a struct in c/c assuming that the struct is optimally set up is count all the bytes of the data in the struct.
Rule:
In math rule refers a numerical pattern is a sequence of numbers that has been created based on a formula or rule called a pattern rule
Given,
Here we need to find a good rule of thumb for sizing a struct in c/c assuming that the struct is optimally set up.
According to the rule of thumb, the count all the bytes of the data in the struct.
and then we need to find the nearest power of 2, 4 or 8 based on the largest Data Type in your struct.
So, if the total number of bytes is larger than that power, then the struct will be the next power in size.
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How to work out if 3rackets and 3 balls cost 21.63t?
The cost of a racket and a ball is equal to $3.21 and $4 as per the given data .
As given in the question,
Let us consider cost of a racket is equal to $x
Let us consider cost of a ball is equal to $y.
Equation formed using the given data we have,
3x + 3y = $21.63 ____(1)
3x + 10y = $49.63 ____(2)
Subtract equation (2) from (1) to eliminate x
3x + 10y = $49.63
3x + 3y = $21.63
0x + 7y = $28.00
⇒7y = 28.00
⇒ y = 28 / 7
⇒ y = $4
Substitute the value of y in (1) we get,
3x + 3(4) = 21.63
⇒3x = 21.63 -12
⇒3x = 9.63
⇒ x = $3.21
Therefore, from the given relation the cost of a racket and a ball is equal to $3.21 and $4.00.
The complete question is:
The cost of 3rackets and 3 balls cost $21.63.
The cost of 3rackets and 10 balls is $49.63.
Work out the cost of
a) a ball.
b) a racket
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it as been suggested that 4% of all cars on the freeway are going over 70 mph. if 4 cars are checked what is the probability that at lest 1 is going over 70 mph
It has been suggested that 4% of all cars on the freeway are going 70 mph. If 4 cars are examined, the probability that at least 1 is going 70 miles per hour is 0.151.
A probability is a numerical representation of the likelihood or possibility that a particular event will occur. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Here, it is said that 4% of all vehicles on the roadway are going more than 70 mph.
P(speed excess of 70 mph) = 0.04. Radar is used to determine the speeds of four random cars. Then, n = 4. Then, X = the number of cars going over 70 mph.
Then, the probability that at least one car is going over 70 mph
= P(x = 1, 2, 3, 4)
= 1 - P(x = 0)
= [tex]1 - 4_{C}_{0} (0.04)^{0} (1 - 0.04)^{4-0}[/tex]
= 1 - 0.849
= 0.151
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Help meee! ;( I need to pass
Answer:
250.32 dollars
Step-by-step explanation:
The given loan amount is equal to 8,700 dollars and the number of years is 3 years and the a p r is equal to 2.31 percentage. The formula for monthly payment is a is equal to p into or divided by 12 into 1 plus or divided by 12 points the whole power and whole divided by 1 plus r divided by 12 points.The whole power n minus 1 in this formula, p is the lown amount and r is the well interest rate and n is the number of payments here. We have the number of years is 3, so the number of payments will be 36 points. Then, by this formula we have the monthly payment: a is equal to 8700 into 0.0231, divided by 12 into 0.0231 divided by 12 plus 1. The whole power 36 whole divided by 0.0231, divided by 12 plus 1, the whole power 36 minus 1, and it will be equal to 250.32 dollars. Therefore, the monthly payment is equal to 250.32 dollars.
Ashley, sending to her directly with the number of hours she worked. Suppose that she works seven hours yesterday and earned $84 if she earned 60 today how many hours is she work today?
Answer:
5 hours
Step-by-step explanation:
To figure this out we will do the total she earned yesterday divided by the hours she worked. So, 84/7=12. So know we know how much she earns in an hour, $12. So if she is earn $60 today then we should do 60/12 to figure out how many hours she worked. 60/12=5. So she worked 5 hours.
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a quadratic function can be used to model the height, in feet, of an object above the ground in terms of the time, in seconds, after the object was launched. according to the model, an object was launched into the air from a height of o feet and reached its maximum height of 25 feet 1.25 seconds after it was launched. based on the model, what was the height, in feet. of the object 1.00 seconds after it was launched?
The height of the object after 1.00 seconds launched is 24 feet.
Quadratic FunctionQuadratic function is a function where the maximum power of x variable is 2. Simply you can write quadratic function as:
y = ax^2 + bx + c
y is height in feet and x is time in second.
Known 2 conditions from the question:
The object will reach maximum height of 25 feet after 1.25 second launched from ground.And also, just logic that if the object is launch in 0 second will reach 0 feet.From second condition (0 feet in 0 second), we can substitute 0 both in y and y:
y = ax^2 + bx + c
0 = a(0)^2 + b(0) + c
0 = 0 + 0 + c
0 = c
And this, we know that the constant (c) of the function is 0.
Just substitute c with 0 in previous function.
y = ax^2 + bx + c
y = ax^2 + bx + 0
y = ax^2 + bx
From first condition (25 feet in 1.25 seconds), we can substitute x with 1.25 and y with 25:
y = ax^2 + bx
25 = a(1.25)^2 + b(1.25)
25 = 1.56625a + 1.25b
Maximum/minimum point of quadratic function can be found with dy/dx = 0, dy/dx is differential:
y = ax^2 + bx
dy/dx = 2ax + b
0 = 2ax + b
0 = 2a(1.25) + b
0 = 2.5a + b
-2.5a = b
After we know the ratio a and b, we can substitute b with -2.5a in previous equation:
25 = 1.5625a + 1.25b
25 = 1.5625a + 1.25(-2.5a)
25 = 1.5625a - 3.125a
25 = -1.5625a
15/-1.5635 = a
a = 15/-1.5625
a = 16
We got a = 16. Then we just substitute it in a b ratio equation:
b = -2.5a
b = -2.5(-16)
b = 40
After we know a, b, c, just substitute that three numbers in the function:
y = ax^2 + bx + c
y = -16x^2 + 40x
So, the function can be used in launching of the object is y = -16x^2 + 40x.
Where is the object in 1.00 seconds after launched? Just substitute x with 1.
y = -16x^2 + 40x
y = -16(1)^2 + 40(1)
y = -16 + 40
y = 24 feet
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Multiply the following polynomials. Write the simplified answer in descending order. Use the ^ (shift + 6) to indicate exponents. DO NOT add spaces between any numbers or characters. For example: (x+2)(x+3) = x^2+5x+6.
(m 3n + 8)(m 3n - 5)
The simplified form of (m + 3n + 8)(m + 3n - 8) is m^2 + 3n^2 + 6mn - 64.
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given, (x+2)(x+3) = x^2+5x+6.
∴ (m + 3n + 8)(m + 3n - 8).
= m^2 + 3mn - 8m + 3mn + 3n^2 - 24n + 8m + 24n - 64.
= m^2 + 3n^2 + 6mn - 64.
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A function f (x) is graphed on the coordinate plane. What is the function rule in slope-intercept form? Afunction f (>) is graphed on the coordinate plane What is the function rule in slope-intercept fom? Enter your answer in the box f(r) Basic x2
The required function of the line would be y = 2x + 1.
Coordinate Plane:A coordinate plane is a two-dimensional plane formed by the intersection of two number lines. One of these number lines is a horizontal number line called the x-axis and the other number line is a vertical number line called the y-axis.
The function rule in slope-intercept form:The slope-intercept form is one rule to represent linear function rules. f(x)=mx + b is sometimes used. In any scenario, m and b describe the line's overall features. The slope is denoted by m, while the y-intercept is denoted by b.
According to the given figure,
We clearly see that the coordinates of the y-intercept would be (0, 1).
The value of the x-coordinate is 1 when y-coordinate is 3.
Here the line passes through points (0, 1) and (1, 3).
Let the required linear function would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x₂ -x]
x₁ = 0, y₁ = 1
x₂ = 1, y₂ = 3
⇒ y - y₂ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]
⇒ y - 3 = (3 - 1)/(1 - 0 )[x -1]
⇒ y - 3 = (2)[x -1]
⇒ y - 3 = 2x - 2
⇒ y = 2x - 2 + 3
⇒ y = 2x + 1
Therefore, the required function of the line would be y = 2x + 1 .
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If f(x) = -4x+9
Find f(-6)
Answer:
33
Step-by-step explanation:
-4(-6) + 9
24 + 9
33
A 7-pound bag of potting soil costs $3.92. What is the unit price?
Answer:0.56
Step-by-step explanation:
First multiply $3.92 from 1 pound
Next dived the answer by 7 which will give you 0.56
find the actual distance represented by 1 cm to write the scale of a map with key 2/5 cm =8 km
Answer:
1 cm = 20 km
Step-by-step explanation:
Starting with what we know:
2/5 cm = 8 km
Need to change the left side to a 1. So multiply both sides by 5/2
5/2 × 2/5 = 8 × 5/2
1 cm = 40/2 km
1 cm = 20 km