Answer:
R = { ( 3 , 1 ) , (4 , 1) , (4 , 2) }
Step-by-step explanation:
Which ordered pairs are in the relation {(x, y) | x > y + 1} on the set {1, 2, 3, 4}
Assuming that:
R should be the set of real numbers such that:
R = { (x,y) | x > y + 1} on the set {1, 2, 3, 4}
Then:
The ordered pairs for the relation can be computed as:
R = { ( 3 , 1 ) , (4 , 1) , (4 , 2) }
.........................help
A simple random sample of college students was performed recently in which the students were asked to self identify as to whether they are binge drinkers or not. In a 1995 study it was found that about 44% of students were self identified as such and the researcher believed that this number has increased. In this study 7851 of the 17592 students interviewed self identified as binge drinkers. A 90% confidence interval of the estimated binge drinking rate is
Answer:
The 90% confidence interval is [tex]0.445< p < 0.456[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 17592[/tex]
The number of binge drinkers is [tex]k = 7851[/tex]
Given that the confidence level is 90% then the level of significance is mathematically represented as
[tex]\alpha = (100 - 90)\%[/tex]
[tex]\alpha = 0.10[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
The sample proportion is mathematically represented as
[tex]\r p = \frac{ 7851}{ 17592}[/tex]
[tex]\r p = 0.45[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{ \frac{x}{y} } * \sqrt{\frac{\r p(1 - \r p )}{n} }[/tex]
[tex]E =1.645 * \sqrt{\frac{ 0.45 (1 - 0.45 )}{17592} }[/tex]
[tex]E =0.00617[/tex]
The 90% confidence interval is mathematically represented as
[tex]\r p -E < p < \r p +E[/tex]
[tex]0.45 -0.00617 < p < 0.45 + 0.00617[/tex]
[tex]0.445< p < 0.456[/tex]
Which expression is equivalent to -6(-2/3+2x)
Answer:
Step-by-step explanation:
Using the Distributive Property of Multiplication, we get
12
---- - 12x. or 4 - 12x, or 4(1 - 3x)
3
A very large tank initially contains 100L of pure water. Starting at time t = 0 a solution with a salt concentration of 0.8kg/L is added at a rate of 5L/min. The solution is kept thoroughly mixed and is drained from the tank at a rate of 3L/min.
1. Let y(t) be the amount of salt (in kilograms) in the tank after t minutes. What differential equation does y satisfy?
2. How much salt is in the tank after 40 minutes?
Answer:
1. [tex]\dfrac{dy}{dt}=4-\dfrac{3y(t)}{100+2t}[/tex]
2. [tex]y(40) = 110.873 \ kg[/tex]
Step-by-step explanation:
Given that:
A very large tank initially contains 100 L of pure water.
Starting at time t = 0 a solution with a salt concentration of 0.8kg/L is added at a rate of 5L/min.
. The solution is kept thoroughly mixed and is drained from the tank at a rate of 3L/min.
As 5L/min is entering and 3L/min is drained out, there is a 2L increase per minute. Therefore, the amount of water at any given time t = (100 +2t) L
t = (50 + t ) L
Since it is given that we should consider y(t) to be the amount of salt (in kilograms) in the tank after t minutes.
Then , the differential equation that y satisfies can be computed as follows:
[tex]\dfrac{dy}{dt}=rate_{in} - rate_{out}[/tex]
[tex]\dfrac{dy}{dt}=(0.8)(5) -\dfrac{y(t)}{100+2t} \times3[/tex]
[tex]\dfrac{dy}{dt}=(0.8)(5) -\dfrac{3y}{100+2t}[/tex]
[tex]\dfrac{dy}{dt}=4-\dfrac{3y(t)}{100+2t}[/tex]
How much salt is in the tank after 40 minutes?
So,
suppose : [tex]e^{\int \dfrac{3}{100+2t} \ dt} = (t+50)^{3/2}[/tex]
Then ,
[tex]( t + 50)^{3/2} y' + \dfrac{3}{2}(t+50)^{1/2} y = 4(t+50)^{3/2}[/tex]
[tex]( t + 50)^{1.5} y' + \dfrac{3}{2}(t+50)^{0.5} y = 4(t+50)^{3/2}[/tex]
[tex][y\ (t + 50)^{1.5}]' = 4(t+ 50)^{1.5}[/tex]
Taking the integral on both sides; we have:
[tex][y(t + 50)^{1.5}] = 1.6 (t + 50)^{2.5} + C[/tex]
[tex]y = 1.6 (t+50)+C(t+50)^{-1.5}[/tex]
[tex]y(0) = 0 = 1.6(0+50) + C ( 0 + 50)^{-1.5}[/tex]
[tex]0 = 1.6(50) + C ( 50)^{-1.5}[/tex]
[tex]C= -1.6(50)^{2.5}[/tex]
[tex]y(40) = 1.6 (40 + 50)^1 - 1.6 (50)^{2.5}(50+40)^{-1.5}[/tex]
[tex]y(40) = 144 - 1.6 \times 17677.66953 (90)^{-1.5}[/tex]
[tex]y(40) = 144 - 1.6 \times 17677.66953 \times 0.001171213948[/tex]
[tex]y(40) = 144 - 33.12693299[/tex]
[tex]y(40) = 110.873 \ kg[/tex]
CORRECT ANSWER GET BRAINLIEST!! PLS HELP FAST!!
Answer:
1. 0.5 for x, 3 for y
2. 1.5 for x, 9 for y
3. 2.5 for x, 15 for y
Step-by-step explanation:
I will explain later if you still need help...but you said you need it fast, so I don't want to be too slow. :)
If a menu has a choice of 4 appetizers, 5 main courses, and 5 desserts, how many dinners are possible if each includes one appetizer, one main course, and one dessert?
Answer:
100 dinners
Step-by-step explanation:
There are 4 choices for the appetizer, 5 choices for the main course and 5 choices for the dessert so the total number of dinners that are possible is 4 * 5 * 5 = 100.
What value of c makes x2 − 24x + c a perfect square trinomial? −144 −48 48 144
Answer:
144
Step-by-step explanation:
Hello, please consider the following.
[tex]x^2-24x+c[/tex]
is a perfect square means that the discriminant is 0.
[tex]\Delta = b^2-4ac=24^2-4c=0\\\\<=>24^2-4c =0<=> 4c=576\\\\\text{We divide by 4}\\\\c= \dfrac{576}{4}=144[/tex]
Thank you
The value of c which make a perfect square trinomial is,
⇒ c = 144
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equation is,
⇒ x² - 24x + c
Now, We can it squared as;
⇒ x² - 24x + c
⇒ x² - 2 × 12x + 144
⇒ x² - 24x + 12²
⇒ (x - 12)²
Thus, The value of c which make a perfect square trinomial is,
⇒ c = 144
Learn more about the mathematical expression visit:
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Consider the following sets. U = {all real number points on a number line} A = {solutions to the inequality 3x + 4 ≥ 13} B = {solutions to the inequality One-halfx + 3 ≤ 4} For which values of x is A ⋃ B = Ø? 2 3
Answer:
2 < x < 3
Step-by-step explanation:
Set A)
3x + 4 ≥ 13
3x ≥ 9
x ≥ 3
Set B)
0.5x + 3 ≤ 4
0.5x ≤ 1
x ≤ 2
Plot it out on a number line, and you'll see that 2 < x < 3
Answer:
It's A
Step-by-step explanation:
Which of these random samples qualifies as a representative sample to find out what parents think about the levels of college tuition fees in the state? a.) 50 residents of a city in the state b.) 50 parents of college students from another state c.) 50 parents of college students from the state d.) 50 residents of a county in the state
The correct answer is C) 50 parents of college students from the state
Explanation:
The purpose of representative samples is to study a population by only selecting a small group in it. Due to this, the individuals selected as part of the sample need to match the characteristics of the population being studied.
In this context, if the focus is the opinion of parents about college tuition fees in a specific state, it is expected the sample includes parents of college students rather than students, citizens, etc. because the opinion of parents of college students is being evaluated. Moreover, those parents selected should have children in the state being studied. According to this, the correct option is C because this includes individuals who can appropriately represent the population that is being analyzed.
Answer:
50 parents of college students from the state.
Step-by-step explanation:
Sophia Statistics
Sketch the region bounded by the curves, and visually estimate the location of the centroid. Then find the exact coordi nates of the centroid. y=2x, y=0, x=1
Answer:
coordinates of the centroid = [tex](\frac{2}{3} , \frac{2}{3} )[/tex]
Step-by-step explanation:
The curves to be plotted are : y =2x, y = 0, x =1
The coordinates of the centroid ( visually estimated ) can be found by first calculating the area of the region
A = [tex]\int\limits^1_0 {2x} \, dx[/tex] = 2[tex](\frac{x^2}{2} )[/tex] hence A = 1
attached below is the remaining part of the solution
(8x2 + 9) - (3x2 + 2x + 5)
Answer:
5x^2 -2x +4
Step-by-step explanation:
(8x^2 + 9) - (3x^2 + 2x + 5)
Distribute the minus sign
(8x^2 + 9) - 3x^2 - 2x - 5
Combine like terms
5x^2 -2x +4
Help me please thank you
Answer:
x = 7
Step-by-step explanation:
5x + 9 = 6x + 2
5x - 6x = 2 - 9
-x = -7
x = 7
probe:
5*7 + 9 = 6*7 + 2
35 + 9 = 42 + 2 = 44
Answer:
x = 11
Step-by-step explanation:
The angles shown are alternate exterior angles. If they are equal, then the lines are parallel
5x+9 = 6x-2
Subtract 5x from each side
5x-5x+9 = 6x-5x-2
9 = x-2
Add 2 to each side
9+2 = x
11 =x
Andre has been practicing his math facts. He can now complete 135 multiplication
facts in 90 seconds.
a. If Andre is answering questions at a constant rate, how many facts can he
answer per second?
b. Noah also works at a constant rate, and he can complete 75 facts in 1 minute.
Who is working faster? Explain or show your reasoning.
Division is one of the four fundamental arithmetic operations. Andrew is faster than Noah.
What is Division?The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Given that Andre can now complete 135 multiplication facts in 90 seconds.
A.) If Andre is answering questions at a constant rate, then the number of facts that Andre can answer per second can be written as,
Number of facts per seconds = 135 facts / 90 seconds
= 1.5 facts per seconds
B.) Noah also works at a constant rate, and he can complete 75 facts in 1 minute. Therefore, the number of facts that Noah can answer per second can be written as,
Number of facts per seconds = 75 facts / 60 seconds
= 1.25 facts per seconds
Now, since the number of facts that Andrew can read in a second is 1.5 facts, while the number of facts that Noah can read in a second is 1.25 facts.
Hence, Andrew is faster than Noah.
Learn more about Division:
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cual es los primeros tres digitos de pi
Answer:
3.14
Step-by-step explanation:
Los primeros tres son 3.14
County had 112 cases on June 22. On July 22 there were 553 cases. At that rate, how many days will it take before there are 1000 cases?
Answer:
30.4 days or 31 days
Step-by-step explanation:
553 - 112 = 441
it took 30 days for 441 cases
30 / 441 = 0.06802721088
1000 - 553 = 447
0.06802721088 x 447 = 30.4081632653
30.4 days or 31 days
Hello, there are three questions and pictures of them in the links If you could solve them that would be awesome, thank you!
Answer:
1. 1 * [tex]x^{3/6}[/tex] = [tex]x^{3/6}[/tex] (it will be equal to the sixth root of x cube)
2. No, the expression [tex]x^{3}[/tex] X [tex]x^{3}[/tex] X [tex]x^{3}[/tex] will be equal to [tex]x^{3 + 3 + 3 }[/tex] since the powers of numbers with the same base are added
3. B and D 1/[tex]x^{-1}[/tex] is the same as 'x'
as mentioned in the last answer, powers of numbers with same base are added. hence, option D will be [tex]x^{3/3}[/tex] which will be equal to x
Find the value of x.
Answer:
or,6x+6=9x-9
or,6+9= 9x-6x
or,15=3x
or,15/3=X
therefore,X=5ans
Answer:
x=3
Step-by-step explanation:
32/24=(6x+6)/(9x-9)
simplify by 8 in the left
4/3=6(x+1)/9(x-1)
simplify by 3 in the right
4/3=2(x+1)/3(x-1)
*3 *3
4=2(x+1)/(x-1)
(x+1)/(x-1)=4/2=2
so x+1=2(x-1)=2x-2
-x -x
1=x-2
+2 +2
3=x
so x=3
verify (6*3+6)/(9*3-9)=32/24
24/18=32/24
simplify by 6 in the left
4/3=32/24
simplify by 8 in the right
4/3=4/3 TRUE
Give 5 different names for this line? Will give to the brainliest! Thank you.
Step-by-step explanation: The figure shown here is a straight path between points that extends forever in both directions, so it's called a line.
Since a line doesn't have endpoints, it doesn't matter which
two points on the line we use to name the line.
I have attached 5 possible names for the line below.
Answer:
DE ED DF FD and line lStep-by-step explanation:
e Because lines continue infinitely, we can name them forwards or backwards. We can also use any two points on a line to identify it, unlike with rays or segments. The l and the end of the line can also be used to identify it.
Different names for the line include: DE ED DF FD and line l.
I'm always happy to help :)the martin fruit co charges 7% commission for selling fruit. the commission for selling 516 crates of oranges at 16.30 per crate is:
Answer:
588.76
Step-by-step explanation:
Commission is 7% of total
Total selling price of 516 crates of oranges:
516*16.3 = 8410.8Commission amount:
0.07*8410.8 ≈ 588.76Google maps has told Juanita that her car trip will be 32 miles. Juanita has already gone 14 miles. How fast, in miles per hour, must Juanita drive to arrive in 16 more minutes?
Answer:
Speed= 67.5 miles per hour
Step-by-step explanation:
Google maps has told Juanita that her car trip will be 32 miles.
Juanita has already gone 14 miles.
Remaining miles left to travel
= 32-14
Remaining miles left to travel
= 18 miles
She has only 16 minutes to reach her destination.
The required speed for her to reach her destination
= Distance/time
Her time = 16 minutes
Her time = 16/60
Her time =4/15 hours
Speed= distance/time
Speed= 18 /(4/15)
Speed=18* 15/4
Speed= 67.5 miles per hour
Juanita needs to drive at 67.5 miles per hour to arrive in 16 more minutes
The total distance (D) is given as:
[tex]\mathbf{D = 32miles}[/tex]
She has traveled 14 miles;
So, the remaining distance (d) is:
[tex]\mathbf{d = D -14}[/tex]
This gives
[tex]\mathbf{d = 32 -14}[/tex]
[tex]\mathbf{d = 18}[/tex]
Speed is calculated as:
[tex]\mathbf{Speed = \frac{distance}{time}}[/tex]
Where: distance = 18 miles and time = 16 minutes
So, we have:
[tex]\mathbf{Speed = \frac{18\ miles}{16\ minutes}}[/tex]
Convert time to hour
[tex]\mathbf{Speed = \frac{18\ miles}{16/60\ hour}}[/tex]
So, we have:
[tex]\mathbf{Speed = \frac{18 \times 60\ miles}{16\ hour}}[/tex]
[tex]\mathbf{Speed = \frac{1080\ miles}{16\ hour}}[/tex]
Divide
[tex]\mathbf{Speed = 67.5\ miles/ hour}[/tex]
Hence, the speed is 67.5 miles per hour
Read more about speed and distance at:
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Suppose that the function fis defined on the interval (-2,2) as follows.
find f(-1) f(0.5) f(1)
Answer:
Step-by-step explanation:
Hello,
-1 <= -1 < 0
so f(-1)=-1
0 <= 0.5 < 1
so f(0.5)=0
1 <= 1 < 2
so f(1)=1
Thank you.
Which of the following is an example of the difference of two squares
a 22 - 9
B + +9)
C23 -9
D(2 - 9)
Complete Question: Which of the following is an example of the difference of two squares?
A x² − 9
B x³ − 9
C (x + 9)²
D (x − 9)²
Answer:
A. [tex] x^2 - 9 [/tex].
Step-by-step explanation:
An easy way to spot an expression that is a difference of two squares is to note that the first term and the second term in the expression are both perfect squares. Both terms usually have the negative sign between them.
Thus, difference of two squares takes the following form: [tex] a^2 - b^2 = (a + b)(a - b) [/tex].
a² and b² are perfect squares. Expanding [tex] (a + b)(a - b) [/tex] will give us [tex] a^2 - b^2 [/tex].
Therefore, an example of the difference of two squares, from the given options, is [tex] x^2 - 9 [/tex].
[tex] x^2 - 9 [/tex] can be factorised as [tex] x^2 - 3^2 = (x + 3)(x - 3) [/tex].
an administrator is asked to file papers in a box which has the following dimensions:height 15cm, width 300mm and depth 0.2m. calculate the volume of the box. give your answer in cm
Answer:
900cm^3
Step-by-step explanation:
1 cm= 10 mm
x=300mm (criss cross)
1cm*300mm/10mm= 10mm*x/10mm
30cm=x
30cm=300mm
1m=100cm
0.2m=x
1m*x/1m=0.2m*100cm/1m
x=0.2*100cm
x=20cm
0.2m=20cm
l=15cm
w=30cm
h=20cm
v=l*w*h
v=15cm*30cm*20cm
v=450cm^2*20cm
v=900cm^3
Answer:
9000cm^3
Step-by-step explanation:
Width:300mm=30cm
Height:15cm=15cm
Depth:0.2m=20cm
V=DxWxH
V= 20x30x15
V=9000cm^3
Determine whether the relation is a function. {(−3,−6),(−2,−4),(−1,−2),(0,0),(1,2),(2,4),(3,6)}
Answer:
Yes, this is a function
Step-by-step explanation:
This relation is function because 1 x value corresponds to 1 y value
what is the next two sequence -1, 5, -25, 125
Answer:
-625,3125
Step-by-step explanation:
Im not saying this is correct but it looks like its multipling by 25
Jana's friend draws a card that shows a 0. Draw a point at 0. What is the opposite of 0?
Explain.
Answer:
There is no opposite of 0.
Step-by-step explanation:
There cannot be a zero the opposite of zero. If there was, then there would be two 0's, and there is only one.
What is the difference in finding the length of a segment that is drawn on a sheet of blank paper and segment that is drawn on a coordinate plane?
If you have tickmarks on the segment, on a blank piece of paper, then you count out the spaces to get the length of the segment. This is assuming the tickmarks are properly spaced out. If there aren't any tickmarks, then you'll have to use a ruler to find the length. Either way, a ruler is encouraged.
The coordinate plane makes things easier to find the length of any segment. Use either the pythagorean theorem or the distance formula to find the length of the segment.
for simplicity, let X=M G = 1 I = 2 if you like decimals C = 3 + 0.75Y or if you prefer fractions C = 3 + 3/4Y the simple multiplier is equal to
Answer:
the simple multiplier is equal to 4
Step-by-step explanation:
In an economic model,
Y= C + I + G + (X - M)
the average expenditure Y must be equal to the totality of the output
If C = 3 + 0.75Y
where;
marginal propensity to consume MPC = 0.75
Then,
Y = 3 + 0.75Y + 2 + 1
Y = 6+0.75 Y
Y - 0.75 Y = 6
0.25 Y = 6
Y = 6/0.25
Y = 24
However, the simple multiplier can be expressed as:
[tex]=\dfrac{1}{1 - MPC}[/tex]
[tex]=\dfrac{1}{1 - 0.75}[/tex]
[tex]=\dfrac{1}{0.25}[/tex]
= 4
What is the meaning of the ∝ sign?
Answer:
"proportional to"
Step-by-step explanation:
The sign ∝ means 'is proportional to'. This is used to show that one variable of value is proportional to another value or variable.
Example:
x ∝ y ('x' is proportional to 'y')Hope this helps.
In order to go to college, Chris goes from working full-time making $30,000 per year to working part-time at half the salary for two years. The cost of his education will be $5,000. If Chris makes $35,000 per year after getting his degree, approximately how many years will it take him to recover his investment?
Answer:
Step-by-steIn order to go to college, Chris goes from working full-time making $30,000 per year to working part-time at half the salary for two years. The cost of his education will be $5,000. If Chris makes $35,000 per year after getting his degree, approximately how many years will it take him to recover his investment? *
it would take him 7 years to recover the 35,000 he invested
p explanation:
he was in college two years and it cost him a total of 5000 and he lost 30000 from the two years he worked part time