Answer:
A. It is an equivalence relation on R
B. In fact, the set [0,1) is a set of representatives
Step-by-step explanation:
A. The definition of an equivalence relation demands 3 things:
The relation being reflexive (∀a∈R, a∼a)The relation being symmetric (∀a,b∈R, a∼b⇒b∼a)The relation being transitive (∀a,b,c∈R, a∼b^b∼c⇒a∼c)And the relation ∼ fills every condition.
∼ is Reflexive:
Let a ∈ R
it´s known that a-a=0 and because 0 is an integer
a∼a, ∀a ∈ R.
∼ is Reflexive by definition
∼ is Symmetric:
Let a,b ∈ R and suppose a∼b
a∼b ⇒ a-b=k, k ∈ Z
b-a=-k, -k ∈ Z
b∼a, ∀a,b ∈ R
∼ is Symmetric by definition
∼ is Transitive:
Let a,b,c ∈ R and suppose a∼b and b∼c
a-b=k and b-c=l, with k,l ∈ Z
(a-b)+(b-c)=k+l
a-c=k+l with k+l ∈ Z
a∼c, ∀a,b,c ∈ R
∼ is Transitive by definition
We´ve shown that ∼ is an equivalence relation on R.
B. Now we have to show that there´s a bijection from [0,1) to the set of all equivalence classes (C) in the relation ∼.
Let F: [0,1) ⇒ C a function that goes as follows: F(x)=[x] where [x] is the class of x.
Now we have to prove that this function F is injective (∀x,y∈[0,1), F(x)=F(y) ⇒ x=y) and surjective (∀b∈C, Exist x such that F(x)=b):
F is injective:
let x,y ∈ [0,1) and suppose F(x)=F(y)
[x]=[y]
x ∈ [y]
x-y=k, k ∈ Z
x=k+y
because x,y ∈ [0,1), then k must be 0. If it isn´t, then x ∉ [0,1) and then we would have a contradiction
x=y, ∀x,y ∈ [0,1)
F is injective by definition
F is surjective:
Let b ∈ R, let´s find x such as x ∈ [0,1) and F(x)=[b]
Let c=║b║, in other words the whole part of b (c ∈ Z)
Set r as b-c (let r be the decimal part of b)
r=b-c and r ∈ [0,1)
Let´s show that r∼b
r=b-c ⇒ c=b-r and because c ∈ Z
r∼b
[r]=[b]
F(r)=[b]
∼ is surjective
Then F maps [0,1) into C, i.e [0,1) is a set of representatives for the set of the equivalence classes.
The price of a certain computer stock t days after it is issued for sale is p(t)=100+20t−6t^2 dollars. The price of the stock initially rises, but eventually begins to fall. During what period of time does the stock price rise?
0 < t < ____?
If you owned the stock, after how many days would you sell it? ____ days
Answer:
0 < t < [tex]\frac{5}{3}[/tex]
After 1.67 days the stocks would be sold out.
Step-by-step explanation:
The price of a certain computer stock after t days is modeled by
p(t) = 100 + 20t - 6t²
Now we will take the derivative of the given function and equate it to zero to find the critical points,
p'(t) = 20 - 12t = 0
t = [tex]\frac{20}{12}[/tex]
t = [tex]\frac{5}{3}[/tex] days
Therefore, there are two intervals in which the given function is defined
(0, [tex]\frac{5}{3}[/tex]) and ([tex]\frac{5}{3}[/tex], ∞)
For the interval (0, [tex]\frac{5}{3}[/tex]),
p'(1) = 20 - 12(1) = 20
For the interval ([tex]\frac{5}{3}[/tex], ∞),
p'(2) = 20 - 12(2) = -4
Positive value of p'(t) in the interval (0, [tex]\frac{5}{3}[/tex]) indicates that the function is increasing.
0 < t < [tex]\frac{5}{3}[/tex]
Since at the point t = 1.67 days curve is showing the maximum, so the stocks should be sold after 1.67 days.
The price of the computer stock rises for the first 5/3 days after it is issued. Ideally, if you owned the stock, you should sell it after 5/3 days to maximize your profit.
Explanation:The price of the stock becomes maximum when the rate of change of the price is 0. To find when that is, we need to take the derivative of the price function, which is p'(t) = 20 - 12t, and set it equal to 0. Solving for t, we get t = 20/12 = 5/3. So, the price of the stock rises for t in (0, 5/3) days. Therefore, if you owned the stock, you should sell it after 5/3 days to maximize your profit.
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Find the slope of each line defined below and compare their values.
Answer: slope=-1, slope is -1/6, line a has a greater slope
Step-by-step explanation:
slope of line a is "m" in y=mx+b form
so slope=-1
slope for line b
first find two point, slope is change in y divided by change in x
1 down for every 6 units forward, so slope is -1/6
line a has a greater slope
The experimental probability of rain in a certain town is 20 percent. In the next 45 days, how many days can one expect it to rain?
Answer:
9 days
Step-by-step explanation:
Experimental probability is the number of times an event occurs divided by the total number of trials of the event.
We know the experimental probability, based on past data, that rain will fall 20% chance.
So, one can expect, that in the next 45 days, rain will fall 20% of the days, according to our experimental probability.
First, we find decimal equivalent of 20%. We divide by 100:
20% = 20/100 = 0.2
Now we multiply this with the number of days:
0.2 * 45 = 9
Thus,
One can expect it to rain 9 days
For an object in damped harmonic motion with initial amplitude a, period 2π/ω, and damping constant c, find an equation that models the displacement y at time t for the following.
(a)
y = 0 at time t = 0
y= ?
(b)
y = a at time t = 0
y= ?
Answer:
see below
Step-by-step explanation:
We presume the damping constant is the opposite of the multiplier of time in the exponential term. Then the equations are ...
(a) y = a·e^(-ct)·sin(ωt)
(b) y = a·e^(-ct)·cos(ωt)
__
These are the standard equations for simple harmonic motion assuming there is no driving function.
a = initial amplitude*
c = damping constant**
ω = frequency of oscillation in radians per second
t = time in seconds
_____
* Of course, when y(0) = 0, the motion never actually reaches this amplitude because it is subject to decay before it can.
__
** In electrical engineering, damping is often specified in terms of a time constant, the time it takes for amplitude to decay to 1/e (≈36.8%) of the original amplitude. If that time is represented by τ, then the exponential factor is e^(-t/τ).
In a damped harmonic motion, the equation for displacement y at time t would be y = ae-ct/2mcos(ωt+φ). At t = 0, if y = 0, the phase constant φ is π/2; if y = a, then φ = 0.
Explanation:In the context of damped harmonic motion, the displacement y at time t of an object with damping constant c, period 2π/ω, and initial amplitude a generally would follow the equation: y = ae-ct/2mcos(ωt+φ) , where m is the mass of the object and φ is the phase constant.
(a) If y = 0 at time t = 0, then the phase constant φ is π/2.
(b) If y= a at time t= 0, then φ=0 because all the displacement is in the stretch or compression, not the oscillation.
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Rewrite the equation −5x2+3x+5y2+5y−3z2+4z+12=0 −5x2+3x+5y2+5y−3z2+4z+12=0 in cylindrical and spherical coordinates. NOTE: write any greek letters using similar standard characters - i.e., for θθ use t, for rhorho use r, for ϕϕ use f, etc.
Answer:
Cylindrical:
5r^2(sin(t)^2 - cos(t)^2) +r(3cos(t) + 5sin(t)) - 3z^2 + 4z + 12 = 0
Spherical:
5r^2sin(t)^2 (sin(f)^2 - cos(f)^2) - 3r^2 cos(t)^2 + r sin(t) (3cos(f) + 5sin(f)) + 4r cos(t) +12 = 0
Step-by-step explanation:
In cylindrical coordinates:
x = r cos(t)
y = r sin(t)
z = z
Let us reorganize the original equation
−5x^2+3x+5y^2+5y−3z^2+4z+12=0
5 (y^2-x^2) + 3x + 5y - 3z^2 + 4z + 12 = 0
Now, we can replace x and y:
5 (r^2 sin(t)^2 - r^2 cos(t)^2) + 3rcos(t) + 5r sin(t) - 3z^2 + 4z + 12 = 0
5r^2(sin(t)^2 - cos(t)^2) +r(3cos(t) + 5sin(t)) - 3z^2 + 4z + 12 = 0
In spherical coordinates:
x = r sin(t) cos(f)
y = r sin(t) sin(f)
z = r cos(t)
Let us reorganize the equation:
5 (y^2-x^2) - 3z^2 + 3x + 5y + 4z + 12 = 0
5r^2sin(t)^2 (sin(f)^2 - cos(f)^2) - 3r^2 cos(t)^2 + r sin(t) (3cos(f) + 5sin(f)) + 4r cos(t) +12 = 0
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What series of transformations would carry trapezoid ABCD onto itself?
(x + 0, y − 4), 90° clockwise rotation, reflection over the y-axis
(x + 0, y − 4), 180° rotation, reflection over the y-axis
(x + 6, y + 0), 90° clockwise rotation, reflection over the x‐axis
(x + 6, y + 0), 180° rotation, reflection over the x‐axis
Answer:
(x + 6, y + 0), 180° rotation, reflection over the x‐axis
Step-by-step explanation:
The answer can be found out simply , a trapezoid has its horizontal sides usually parallel meanwhile the vertical sides are not parallel.
The horizontal parallel sides are on the x-axis.
Reflection over y- axis would leave the trapezoid in a vertical position such that the trapezoid ABCD won't be carried on the transformed trapezoid as shown in figure.
So option 1 and 2 are removed.
Now, a 90 degree rotation would leave the trapezoid in a vertical position again so its not suitable again.
In,The final option (x + 6, y + 0), 180° rotation, reflection over the x‐axis, x+6 would allow the parallel sides to increase in value hence the trapezoid would increase in size,
180 degree rotation would leave the trapezoid in an opposite position and reflection over x-axis would bring it below the Original trapezoid. Hence, transformed trapezoid A`B`C`D` would carry original trapezoid ABCD onto itself
Montel bought a spool of string for making kites. It contained 10 3/20 meters of string. He used 6 9/10 meters of string for kites. How many meters of string does Montel have left?
Answer: he has 65/20 meters of string left
Step-by-step explanation:
Montel bought a spool of string for making kites. It contained 10 3/20 meters of string. Let us first convert this length of string to improper fraction, it becomes 203/20 meters
He used 6 9/10 meters of string for kites. Changing 6 9/10 to improper fraction, it becomes 69/10 meters
To determine how many meters of string that Montel have left, we will subtract the length of string used from the total length of string. It becomes
203/20 - 69/10 = 203 - 138/20 = 65/20 meters of string left
A parabola opens upward and has no vertical stretch. The complex roots of the quadratic function are 6 + 4i and 6 – 4i. Determine the function rule.
Answer:
Step-by-step explanation:
Describing the function rule means that you are going to write the equation of the parabola using that roots. If x = 6 + 4i, then the factor for that is
(x - 6 - 4i).
If x = 6 - 4i, then the factor for that is
(x - 6 + 4i).
FOILing that together gives you a long string of x- and i-terms with a constant or 2 thrown in:
[tex]x^2-6x+4ix-6x+36-24i-4ix+24i-16i^2[/tex]
What's nice here is that 4ix and -4ix cancel each other out; likewise 24i and -24i. Once that is all canceled away, we are left with
[tex]x^2-12x+36-16i^2[/tex]
The i-squared is what makes this complex. i-squared = -1, so
[tex]x^2-12x+36-16(-1)[/tex] and
[tex]x^2-12x+36+16[/tex] and
[tex]x^2-12x+52=y[/tex]
Need some help with this
Answer:
Step-by-step explanation:
number 2 is false
Every week rolando works at starbucks during the day and at a youth soccer league at night he can work a maximum of 40 hours a week he calculates he needs to earn at least $368 every week to cover his expenses. Rolando earn $13 an hour at starbucks and $9 an hour at the youth soccer league. Write a system of linear inequalities to represent the situation. Pls i need an answer before monday plsssssss
Answer:
The linear inequalities representing the given situation is -
x≥0 , y≥0
13x + 9y ≥ 368
x + y ≤ 40
Step-by-step explanation:
Let Rolando work 'x' hours a week at starbucks and 'y' hours a week at the youth soccer league.
∵ No. of hours cannot be negative -
x≥0 , y≥0
Given that Rolando earns $13 an hour at starucks -
Total earning at starbucks per week = 13x
Also Rolando earns $9 an hour at the youth soccer league -
Total earning at the youth soccer league per week = 9y
Total earnings for Rolando per week = 13x+9y
Since his total earnings needs to be atleast $368 -
13x+9y ≥ 368
Total number of hours for which Rolando can work per week is -
x+y
Since he cannot work for more than 40 hours a week -
x+y ≤ 40.
∴ x≥0 , y≥0
13x + 9y ≥ 368
x + y ≤ 40
Final answer:
Rolando's work situation can be modeled by the linear inequalities 13x + 9y ≥ 368 and x + y ≤ 40, where x is the number of hours at Starbucks and y is the number at the youth soccer league.
Explanation:
To represent Rolando’s work situation with linear inequalities, let us define two variables: let x be the number of hours Rolando works at Starbucks, and let y be the number of hours he works at the youth soccer league. Given that Rolando earns $13 per hour at Starbucks and $9 per hour at the youth soccer league, the inequality to ensure he makes at least $368 per week is 13x + 9y ≥ 368.
Furthermore, because Rolando can work a maximum of 40 hours per week, we have another inequality: x + y ≤ 40. Thus, the system of linear inequalities that models Rolando’s situation is:
13x + 9y ≥ 368
x + y ≤ 40
These inequalities define the range of hours Rolando can work at both jobs to meet his weekly earnings goal without exceeding the maximum number of allowed hours.
Mr. Croft is getting ready for Thanksgiving and needs some help. He needs some advice on cooking his turkey. He bought a 16 1/2 pound turkey. The cookbook says to cook the turkey for 20 minutes per pound and 25 minutes per pound if the turkey is stuffed. He plans on stuffing his turkey. If he has to have dinner ready for 12:45 pm what is the exact time he needs to put the turkey in the oven? Oh yeah, the cookbook says to let the turkey cool for 10 minutes after coming out the oven.
Answer: 5:42:2 am
Step-by-step explanation:
He bought a 16 1/2 pound turkey. Converting to improper fraction, it becomes 33/2 pounds of turkey.
The cookbook says to cook the turkey for 20 minutes per pound and 25 minutes per pound if the turkey is stuffed. Since he wants to stuff the Turkey, he would have to cook for 25 minutes per pound. The total amount of time that he would have to cook the stuffed turkey will be 25 × 33/2 = 412.5 minutes
Let us converted to hours
If 60 minutes = 1 hour,
412.5 minutes = 412.5/60 = 6.875
He would spend 6.875 = 55/8 hours
in cooking the stuffed turkey.
The cookbook also says to let the turkey cool for 10 minutes after coming out the oven. Let us convert the 10 minutes to hours
60 minutes = 1 hour
10 minutes = 10/60 = 1/6
Total time it will take to get the Turkey ready for dinner will be
1/6 + 55/8 = 169/24 = 7.042 hours which means 7 hours, 2 minutes and 58 seconds
If he has to have dinner ready for 12:45 pm, he needs to put the turkey in the oven at 5:42:2 am at most
The acceleration due to gravity, g, is given by g=GMr2, where M is the mass of the Earth, r is the distance from the center of the Earth, and G is the uniform gravitational constant.
(a) Suppose that we increase from our distance from the center of the Earth by a distance Δr=x. Use a linear approximation to find an approximation to the resulting change in g, as a fraction of the original acceleration: Δg≈ g× (Your answer will be a function of x and r.)
(b) Is this change positive or negative? Δg is (Think about what this tells you about the acceleration due to gravity.)
(c) What is the percentage change in g when moving from sea level to the top of Mount Elbert (a mountain over 14,000 feet tall in Colorado; in km, its height is 4.29 km; assume the radius of the Earth is 6400 km)? percent change =1
(a) The formula for linear approximation: Δg ≈ g × (Δr / r). (b) The acceleration will be negative. (c) The percentage change in acceleration due to gravity when moving from sea level to the top of Mount Elbert is approximately 0.06703%.
(a) To find the linear approximation to the change in acceleration due to gravity, Δg, when increasing the distance from the centre of the Earth by Δr = x, use the formula for linear approximation:
Δg ≈ g × (Δr / r)
Here, g is the original acceleration due to gravity, Δr is the change in distance (x), and r is the original distance from the centre of the Earth.
(b) The change in acceleration, Δg, will be negative. This is because as you move farther away from the centre of the Earth, the gravitational acceleration decreases, which means Δg is a negative value.
(c) Given the height of Mount Elbert, Δr = 4.29 km, and assuming the radius of the Earth is r = 6400 km, we can use the linear approximation formula from part (a) to find the percentage change in acceleration due to gravity:
Δg ≈ g × (Δr / r)
Δg ≈ g × (4.29 / 6400)
Take the absolute value to find the percentage change:
Percentage Change = |(Δg / g)| × 100
Percentage Change = (Δg / g) × 100
Percentage Change = [(g × 4.29 / 6400) / g] × 100
Percentage Change = (4.29 / 6400) × 100
Calculate the percentage change:
Percentage Change ≈ (0.0006703125) × 100
Percentage Change ≈ 0.06703%
So, the formula for linear approximation: Δg ≈ g × (Δr / r), the acceleration will be negative, and the percentage change in acceleration due to gravity when moving from sea level to the top of Mount Elbert is approximately 0.06703%.
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The gravitational acceleration decreases as you move away from the Earth, with the rate of change proportional to the amount you increase your distance away from the Earth. The decrease is negative and is very minuscule even when moving from sea level to the top of Mount Elbert in Colorado.
Explanation:The acceleration due to gravity, g, is inversely proportional to the square of the distance from the center of the Earth, r. Therefore, as we move away from the Earth, the value of g decreases.
For part (a), the change in acceleration due to an increase in distance (Δg) would be the derivative of g concerning r, times Δr=x. Therefore, Δg is approximately equal to -GM/r3x, where G is the gravitational constant and M is the mass of the Earth. When divided by g (which is GM/r2), this gives Δg/g = -x/r.
For part (b), this means that as you increase your distance away from the Earth, the gravitational acceleration decreases, therefore Δg is negative.
For part (c), the percentage change in g is given by the change in distance (4.29 km in this case), divided by the original radius of the Earth (6400 km), times 100%. Therefore, the percentage change is approximately 0.067% or an extremely small change.
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these triangles do not have enough information to prove they are congruent what new information
The owner of a souvenir shop wants to order some custom printed mugs and t-shirts what is the price per t-shirt for 75 T-shirts if the t-shirts cost 637.50 dollars
Answer:
The price per t-shirts is $8.5.
Step-by-step explanation:
Let us assume the price per t- shirt = $m
The cost of 75 t-shirts = $637.50
Now, the total cost for 75 t-shirts = 75 x ( cost of 1 t-shirt)
⇒ $637.50 = 75 x ( m)
⇒ m = $637.50 / 75
or, m = 8.5
Hence, the price per t-shirts is $8.5.
PLEASE ANSWER ASAP!!!
Find the length of the missing side. Leave your answer in simplest radical form.
Answer:The length of the missing side can be calculated by the following formula;
Step-by-step explanation:
A game spinner has eight equal sections: three sections numbered 1, one section numbered 2, and four sections numbered 3. The spinner is spun twice. What is the probability that the sum of the two spins will be five?
The probability that the sum of two spins on this spinner will be five is 7/32, which can be calculated by determining individual probabilities for each combination that gives a sum of 5 and then adding these probabilities together.
Explanation:The question is asking for the probability that the sum of two spins on a specific spinner will be equal to five. First, we need to look into the different ways we can achieve a sum of 5. These possible combinations include (1,4), (2,3), and (3,2), where the values in the parentheses represent the results of the first and second spins respectively.
Now we calculate the probability of each combination happening. The probability of getting a 1 on a spin is 3/8 because there are three sections numbered 1 out of eight total sections. The probability of getting a 2 on a spin is 1/8 because there's only one section numbered 2. Likewise, the probability of getting a 3 is 4/8 (simplified to 1/2) because there are four sections numbered 3.
The combined probability of each scenario would be (3/8*1/2) for (1,4), (1/8*1/2) for (2,3) and (1/2*1/8) for (3, 2). To find the total probability, we simply add these probabilities together. That gives us (3/16) + (1/32) + (1/32) = 7/32. Therefore, the probability that the sum of two spins will be five is 7/32.
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The lenght of the library is 13 inches.The lenght of the actual library is 78 feet. Which scale leon use to create the scale drawing of the school library?
So the scale used was
1 inch = 6 feet
Step-by-step explanation:
Given
Length of library on drawing = 13 inches
Actual length of library = 78 feet
In order to find the scale we divide the actual length by the length of library on drawing.
So,
Scale = [tex]Scale = \frac{Actual\ length}{Length\ on\ drawing}\\=\frac{78}{13}\\=6[/tex]
So the scale used was
1 inch = 6 feet
Keywords: Scale, Maps
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After 14 boys leave a concert,the ratio of boys to girls is 3:10 there are p girls at the concert,write an algebraic expression for the number of boys at the beginning of the concert in terms of p
Answer:
p*(3/10)+14
Step-by-step explanation:
There are 10 girls for every 3 boys. Therefore, if we have the number of girls, p, the number of boys is equal to p*(3/10). Then, adding the 14 boys that left, our answer is p*(3/10)+14
Among 46- to 51-year-olds, 28% say they have called a talk show while under the influence of peer pressurepeer pressure. Suppose sevenseven 46- to 51-year-olds are selected at random. (a) What is the probability that at least one has not called a talk showcalled a talk show while under the influence of peer pressurepeer pressure? (b) What is the probability that at least one has called nbspcalled a talk showa talk show while under the influence of peer pressurepeer pressure?
Answer:
0.8997, 0.9999
Step-by-step explanation:
Given that among 46- to 51-year-olds, 28% say they have called a talk show while under the influence of peer pressure.
i.e. X no of people who say they have called a talk show while under the influence of peer pressure is binomial with p = 0.28
Each person is independent of the other and there are only two outcomes
n =7
a) the probability that at least one has not called a talk showcalled a talk show while under the influence of peer pressure
=[tex]P(Y\geq 1)[/tex] where Y is binomial with p = 0.72
= [tex]1-(1-0.72)^7\\=0.9999[/tex]
b) the probability that at least one has called a talk showcalled a talk show while under the influence of peer pressurepeer pressurethe probability that at least one has not called a talk showcalled a talk show while under the influence of peer pressure
=[tex]P(x\geq 1) =1-P(0)\\= 1-(1-0.28)^7\\=0.8997[/tex]
One pump can empty a pool in 4 days, whereas a second pump can empty the pool in 10 days. How long will it take the two pumps, working together, to empty the pool? (Fractional answers are OK.)
Answer:
20/7 days (just less than 3 days)
Step-by-step explanation:
Recall that (1 job) = (rate)(time), so time = (1 job) / (rate).
Set up and solve the following equation:
1 job
------------------------------- = time required for 2 pumps working together
1 job 1 job
---------- + -------------
4 days 10 days
This comes out to:
1 job
------------------------------------------- = time required
10 job-days 4 job-days
------------------ + -----------------
40 days 40 days
or:
1 job
-------------------- = (40/14) days, or 20/7 days (just less than 3 days)
14 job·days
-----------------
40 days
The number of days required to complete the work together by the pump is 20 / 7 days.
What is an expression?The mathematical expression combines 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 denote the logical syntax's operation order and other properties.
Given that one pump can empty a pool in 4 days, whereas a second pump can empty the pool in 10 days.
The number of days will be calculated as,
1 / N = ( 1 / 10 ) + ( 1 / 4 )
1 / N = (10 + 4 ) / 40
1 / N = 14 / 40
1 / N = 7 / 20
N = 20 / 7 days
Therefore, the number of days required to complete the work together by the pump is 20 / 7 days.
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Let the geometric sequence {an} be defined as follows: {12, 6, 3, 3 /2 , 3 /4 , 3/ 8 ,...} Find the sum of the entire sequence, S∞. A) 24 B) 240 C) 1,080 Eliminate D) 2,176,782,336
Answer:
A) 24
Step-by-step explanation:
The given geometric series is {12, 6, 3, 3 /2 , 3 /4 , 3/ 8 ,...}
Each term can be represented as a product of its previous term and \[\frac{1}{2}\]
The generic term of the series can be represented as the product of the first term 12 and \[\frac{1}{2}^{n-1}\] where n is the index of the term in the series.
The sum to infinity of such a series is given by the following formula:
\[\frac{term1}{1-ratio}\]
Substituting and calculating:
\[\frac{12}{1-\frac{1}{2}}\]
=\[\frac{12}{\frac{1}{2}}\]
=12*2 = 24
In survey conducted by Quinnipiac University from October 25-31, 2011, 47% of a sample of 2,294 registered voters approved of the job Barack Obama was doing as president. What is the 99% confidence interval for the proportion of all registered voters who approved of the job Barack Obama was doing as president?
Answer:
Confidence interval = [ 0.4432, 0.4968]
Step-by-step explanation:
Registered voters approved of the job Barack Obama was doing as president,
p = 47% = 0.47
Total sample size, n = 2,294
Confidence level = 99%
now,
confidence interval for the proportion of all registered voters who approved of the job Barack Obama was doing as president
= p ± [tex]z\times\sqrt{\frac{p\times(1-p)}{n}}[/tex]
for 99% confidence level, z value is 2.58
= 0.47 ± [tex]2.58\times\sqrt{\frac{0.47\times(1-0.47)}{2294}}[/tex]
= 0.47 ± 0.0268
or
Confidence interval = [0.47 - 0.0268, 0.47 + 0.0268 ]
or
Confidence interval = [ 0.4432, 0.4968]
Can someone answer ?
Answer:
X is less sign but is greater than sign -2
Step-by-step explanation:
Jordan enters 3.4 x6.8 into his calculator. He writes the digits 2312 from the display and forgets the decimal point. Where should Jordan put her decimal point? Explain
Answer:
23.12
Step-by-step explanation:
Jordan has entered 3.4 x 6.8 on his calculator.
3.4 x 6.8 = (34/10) x (68/10) = (34 x 68) / (100) = 23.12
Or an easier way would be, observing the two numbers.
In 3.4 , there is one digit after decimal point.
In 6.8 there is one digit after decimal point.
So in their product there should be two digits after the decimal point.
So the answer is 23.12
exam p A drawer contains four pairs of socks, with each pair a different color. One sock at a time is randomly drawn from the drawer until a matching pair is obtained. Calculate the probability that the maximum number of draws is required.
Answer:
The probability that the maximum number of draws is required is 0.2286
Step-by-step explanation:
The probability that the maximum number of draws happens when you pick different colors in the first four pick.
Assume you picked one sock in the first draw. Its probability is 1, since you can draw any sock.
In the second draw, 7 socks left and you can draw all but the one which is the pair of the first draw. Then the probability is [tex]\frac{6}{7}[/tex]
In the third draw, 6 socks left and you can draw one of the two pair colors which are not drawn yet. Its probability is [tex]\frac{4}{6}[/tex]
In the forth draw, 5 socks left and only one pair color, which is not drawn. The probability of drawing one of this pair is [tex]\frac{2}{5}[/tex]
In the fifth draw, whatever you draw, you would have one matching pair.
The probability combined is 1×[tex]\frac{6}{7}[/tex] ×[tex]\frac{4}{6}[/tex]× [tex]\frac{2}{5}[/tex] ≈ 0.2286
Final answer:
The probability that the maximum number of draws is required to get a matching pair of socks from four pairs is 1/7, or about 14.29%.
Explanation:
The question is asking for the probability that the maximum number of draws (7) from 8 socks (4 pairs) is needed before obtaining a matching pair. To calculate this probability, consider that with each draw, you are less likely to pick a sock that matches the ones already drawn, until the last pair remains.
The first sock can be any of the 8, so there's no chance of failure here. For the second sock, to avoid a match, we have 6 out of 7 chance, since one would match the first. For the third sock, to continue avoiding a match, there is a 4 out of 6 chance. This pattern continues until we are left with just two socks, and we must draw the one that matches the last sock drawn.
Therefore, the probability that the maximum number of draws is required is:
(6/7) * (4/6) * (2/4) * (1/2) = 1/7 or about 14.29%.
A poll that does not attempt to generate a random sample, but instead invites people to volunteer to participate is called:________
Answer:
Self selection sampling.
Step-by-step explanation:
A poll that does not attempt to generate a random sample, but instead invites people to volunteer to participate is called - self selection sampling.
Self-selection sampling is a sampling method where researchers allow the people or individuals, to choose to take part in research on their own accord.
Marcy has $150 to buy packages of hot dogs and hamburgers for her booth at the carnival. At her local grocery store she found packages of hot dogs at cost six dollars and packages of hamburger is that cost $20. Right in equation that could marcy has $150 to buy packages of hot dogs and hamburgers for her booth at the carnival. At her local grocery store she found packages of hot dogs that cost six dollars in packages of hamburgers that cost $20. Right in equation that could be used to find the possible combination of hot dog and hamburger packages Marcy can by using her budget of exactly $150.
Answer:
Step-by-step explanation:
Marcy wants to buy packages of hot dogs and hamburgers for her booth at the carnival and the total cost must not exceed her budget of $150
she found packages of hot dogs that cost $6 per one and packages of hamburger is that cost $20 per one .
Let x = number of packages of hot dogs that she can buy.
Let y = number of packages of hamburgers that she can buy.
The cost of x packages of hot dogs = 6×x = $6x
The cost of y packages of hamburgers = 20×y = $20y
The equation will be
Since 6x + 20y must not exceed 150
The equation will be
6x + 20y lesser than or equal to 150
A family has a monthly budget of $2,400. How much money is spent on each category? 44% is spent on housing. 23% is spent on food. 6% is spent on clothing. 17% is spent on transportation. The rest is put into savings.
Answer:
housing, $1056food, $552transportation, $408savings, $240clothing, $144Step-by-step explanation:
Multiply the budget total by the percentage for each category:
housing: 44% × $2400 = $1056food: 23% × $2400 = $552clothing: 6% × $2400 = $144transportation: 17% × $2400 = $408savings: 10% × $2400 = $240__
Find "the rest" by subtracting the total of percentages from 100%, or by subtracting the total of budget categories from $2400. Here, everything (not including savings) adds to 90% × $2400 = $2160, so the amount to savings is 10%, or $240.
In a family's monthly budget of $2,400, $1,056 is spent on housing, $552 on food, $144 on clothing, $408 on transportation, and the remaining $240 is put into savings.
Explanation:To calculate how much money is spent on each category for a family with a monthly budget of $2,400, we need to multiply each percentage by the total budget. For example:
Housing: 44% of $2,400 is $1,056.00,Food: 23% of $2,400 is $552.00,Clothing: 6% of $2,400 is $144.00,Transportation: 17% of $2,400 is $408.00.
The rest of the money, which is 10% of the total budget (the remaining percentage when subtracting the other categories from 100%), is put into savings. Therefore, the amount put into savings is 10% of $2,400, which equals $240.00.
Learn more about Budget Allocation here:https://brainly.com/question/36705672
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Describe where the function has a vertical asymptote and how you found your answer. Remember that an asymptote is represented by an equation of a line and not just a single value.
Answer:
x=-4 is a vertical asymptote
Step-by-step explanation:
A vertical asymptote of the graph of a rational function f(x) is a line x=a, such that one of of these statements is fulfilled
[tex]\displaystyle \lim _{x\to a^{+}}f(x)=\pm \infty[/tex]
[tex]\displaystyle \lim _{x\to a^{+}}f(x)=\pm \infty[/tex]
Our function is
[tex]\frac{x^2+7x+10}{x^2+9x+20}[/tex]
To find the candidate values of a, we set the denominator to zero
[tex]x^2+9x+20=0[/tex]
Factoring
[tex](x+4)(x+5)=0[/tex]
Which gives us two possible vertical asymptotes: x=-4 or x=-5
We now must confirm if one of the two conditions are true for each value of a
[tex]\displaystyle \lim _{x\to -4^{-}}\frac{x^2+7x+10}{x^2+9x+20}[/tex]
The numerator can be factored as
[tex]x^2+7x+10=(x+2)(x+5)[/tex]
So our limit is
[tex]\displaystyle \lim _{x\to -4^{-}}\frac{(x+2)(x+5)}{(x+4)(x+5)}[/tex]
Simplifying:
[tex]=\displaystyle \lim _{x\to -4^{-}}\frac{(x+2)}{(x+4)}=+\infty[/tex]
We can see x=-4 is a vertical asymptote
Checking with x=-5, and using the simplified limit:
[tex]\displaystyle \lim _{x\to -5^{-}}\frac{(x+2)}{(x+4)}=3[/tex]
[tex]\displaystyle \lim _{x\to -5^{+}}\frac{(x+2)}{(x+4)}=3[/tex]
The limit exists and is 3, so x=-5 is NOT a vertical asymptote
The only vertical asymptote of the function is x=4
A composition of transformations maps ?XYZ to ?X"Y"Z". The first transformation for this composition is , and the second transformation is a 90° rotation about point X'.
Answer:
Answer is reflection across line. When transformation maps X"Y"Z" .Then first transformation for this composition is , and the second transformation is 90° rotation about point X'.
Step-by-step explanation:
When you transform a point across a line y=x then x-coordinate and y-coordinate changes.
Similarly when you reflect a point across the line y=-x then signs are changed and both coordinate change places.
It is the first transformation across the line.
Answer:
d, a reflection across line m
Step-by-step explanation:
Just did it on edge 2020
(its right)