what is a rational and irrational number?
Answer:
In mathematics, a rational number is a number such as −3/7 that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Every integer is a rational number: for example, 5 = 5/1.
In mathematics, the irrational numbers are all the real numbers which are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers.
Step-by-step explanation:
hope it helps :)))
Write a quadratic function in standard form that models the table. X -5 -3 -1 13 y 0 12 12 16 12 0
Answer:
First, we need to find the quadratic function that models the given table. We know that a quadratic function has the form: y = ax^2 + bx + c where a, b, and c are constants to be determined. To find these constants, we need to use the values in the table. When x = -5, y = 0, we get: 0 = a(-5)^2 + b(-5) + c 0 = 25a - 5b + c When x = -3, y = 12, we get: 12 = a(-3)^2 + b(-3) + c 12 = 9a - 3b + c When x = -1, y = 12, we get: 12 = a(-1)^2 + b(-1) + c 12 = a - b
The PTO is selling raffle tickets to raise money for classroom supplies. A raffle ticket costs $4. There is 1 winning ticket out of the 280 tickets sold. The winner gets a prize worth $62. Round your answers to the nearest cent.
What is the expected value (to you) of one raffle ticket? $
Calculate the expected value (to you) if you purchase 12 raffle tickets. $
What is the expected value (to the PTO) of one raffle ticket? $
If the PTO sells all 280 raffle tickets, how much money can they expect to raise for the classroom supplies? $
The expected values of the raffle ticket for you are given as follows:
One ticket: -$3.76.12 tickets: -$45.12.For the PTO, the expected values are given as follows:
One ticket: $3.76.12 tickets: $45.12.What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
For you, the distribution is given as follows:
P(X = 62) = 1/280.P(X = -4) = 279/280.Hence the expected value for one ticket is given as follows:
E(X) = 62/280 - 4 x 279/280
E(X) = -$3.76.
For twelve tickets, the expected value is given as follows:
12 x -3.76 = -$45.12.
For the PTO, we use the inverse signals, as the distribution is the inverse, that is:
P(X = -62) = 1/280.P(X = 4) = 279/280.More can be learned about the expected value of a discrete distribution at https://brainly.com/question/27899440
#SPJ1
Can a parallelogram have more than 3 lines of symmetry?
Answer:
no
Step-by-step explanation:
Parallelograms have zero lines of symmetry because it is impossible to draw a line through the center of any parallelogram that divides the figure into two equal halves that are mirror images of each other.
Answer:
Technical answer no
BUT
if you are in a college/postgraduate level group theory class yes
Step-by-step explanation:
Imagine a square, and imagine 4 lines across the top, the side, and the two diagonal ones. Because the two diagonal lines of symmetry are technically the same, there are only three possible lines.
if you are in the group theory class, comment and ill give a lengthy answer on that.
2. Trapezoid WXYZ is located at W(2.1) X[3.
5) Y(6.5) and Z[7. 1). After being translated 6
Units down, what are the new coordinates
of Point Y?
Point Y is (6, -1)
Subtract 6 from the y coordinate in point y since it is translated down. keep the x coordinate since it is only being translated up and down, or by the y axis
Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.
4 is multiplied by the difference of 5 and a number.
The solution is, the expression is => 4*(5-x)
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
here, we have,
let, the number is x.
now, when,
4 is multiplied by the difference of 5 and a number.
so, we get,
the expression is => 4*(5-x)
Hence, The solution is, the expression is => 4*(5-x)
To learn more on Expression click:
brainly.com/question/14083225
#SPJ1
If 400 x 300 = 120,000
And 40 x 30 is 1,200
Fill in the blanks and show your work
*_____ x ______ = 12,000?
Answer:
this list
Step-by-step explanation:
1×12000=12000
2×6000=12000
3×4000=12000
4×3000=12000
5×2400=12000
6×2000=12000
8×1500=12000
10 ×1200=12000
12 ×1000=12000
What is the complete factorization of the polynomial below?
x³ + 3x2 +9x+27
OA. (x+3)(x+3)(x+3/)
B. (x+3)(x+3)(x-3/)
O C. (x-3)(x+3)(x+3/)
O D. (x-3)(x+3)(x-3i)
Answer:
(x - 3 i) (x + 3 i) (x + 3)
Step-by-step explanation:
Vanessa tried to prove that triangle KLM is congruent to triangle MNK. What is the first error Vanessa made in her proof?
Answer:
B. Vanessa only established some of the necessary conditions for a congruence criterion.
Step-by-step explanation:
The diagram does support the claim that \overline{KL}\cong\overline{MN}
KL
≅
MN
start overline, K, L, end overline, \cong, start overline, M, N, end overline because they both have two tick marks.
Step 1 is correct.
Step 2
The diagram does support the claim that \overline{LM}\cong\overline{NK}
LM
≅
NK
start overline, L, M, end overline, \cong, start overline, N, K, end overline because they both have a single tick mark.
Step 2 is correct.
Step 3
In this step, Vanessa claims that \triangle KLM\cong \triangle MNK△KLM≅△MNKtriangle, K, L, M, \cong, triangle, M, N, K using the side-side-side criterion. But Vanessa only established two pairs of congruent corresponding sides. To use this criterion, we must establish three pairs of congruent sides.
Vanessa would be able to use this criterion if she first established that \overline{MK}\cong\overline{KM}
MK
≅
KM
start overline, M, K, end overline, \cong, start overline, K, M, end overline (this can be done with the reason that line segments are congruent to themselves).
The first error Vanessa made in her proof was option B.
Vanessa only established two pairs of congruent corresponding sides
What is congruency?polygons are congruent if they may be identical in size and shape - that is, if their corresponding angles and sides are the same.
Congruent shapes are shapes that can be exactly equal. The corresponding facets are identical and the corresponding angles are equal.
⇒KL≅ MN 9K, L, end overline)
⇒LM≅ NK
⇒MNK△KLM≅△MNK (triangle, K, L, M)
Vanessa would be able to use this criterion if she first established that
⇒MK≅ KM
Learn more about concurrency here:-https://brainly.com/question/513871
#SPJ2
Solve the equation: x²-2x=8
Show all the Steps with explanation.
Answer:
x = 4, -2
Step-by-step explanation:
x^2-2x=8
Move the constant term to the right side of the equation.
x^2 - 2x = 8
Take half of the coefficient of x and square it.
(-2/2)^2 = 1
Add the square to both sides of the equation.
x^2 - 2x + 1 = 8 + 1
Factor the perfect square trinomial.
(x - 1)^2 = 9
Take the square root of both sides of the equation.
x-1=\(\sqrt{9}\)
x-1=±3
Isolate x to find the solutions.
Taking positive
x=3+1=4
x=4
Taking negative
x=-3+1
x=-2
The solutions are:
x = 4, -2
Answer:
\(x = -2,\;\;x=4\)
Step-by-step explanation:
To solve the quadratic equation x² - 2x = 8 by factoring, subtract 8 from both sides of the equation so that it is in the form ax² + bx + c = 0:
\(x^2-2x-8=8-8\)
\(x^2-2x-8=0\)
Find two numbers whose product is equal to the product of the coefficient of the x²-term and the constant term, and whose sum is equal to the coefficient of the x-term.
The two numbers whose product is -8 and sum is -2 are -4 and 2.
Rewrite the coefficient of the middle term as the sum of these two numbers:
\(x^2-4x+2x-8=0\)
Factor the first two terms and the last two terms separately:
\(x(x-4)+2(x-4)=0\)
Factor out the common term (x - 4):
\((x+2)(x-4)=0\)
Apply the zero-product property:
\(x+2=0 \implies x=-2\)
\(x-4=0 \implies x=4\)
Therefore, the solutions to the given quadratic equation are:
\(\boxed{x = -2,\;\;x=4}\)
100 pts!!
Thanh rents a car. He has a fixed rate of $49.00 weekly, pays $14.00 per week for the optional insurance, and he spends $12.00 weekly on gas. What will Thanh's cost be per month (four weeks)?
Thanh's cost per month (four weeks) will be $300.00.The given fixed rate for Thanh is $49.00 per week. Thanh also pays $14.00 per week for the optional insurance and $12.00 weekly on gas.
To find Thanh's cost per month (four weeks), we need to multiply his weekly cost by 4.We can use the formula below to calculate Thanh's monthly cost.
Total weekly cost = Fixed rate + Insurance cost + Gas cost
Total weekly cost = $49.00 + $14.00 + $12.00
Total weekly cost = $75.00
The cost for Thanh per month (four weeks) = Total weekly cost × 4
Cost for Thanh per month (four weeks) = $75.00 × 4
Cost for Thanh per month (four weeks) = $300.00
Therefore, Thanh's cost per month (four weeks) will be $300.00.
For more question on fixed rate
https://brainly.com/question/30096538
#SPJ8
what is the scale factor if 9in = 4ft
The scale factor is \($\frac{3}{16}$\) or approximately 0.1875.
What is Scale Factor?
In mathematics, a scale factor is a number that scales, or multiplies, a quantity or dimension by a certain amount. It is commonly used in geometry and is a measure of how much the size of an object or figure has been changed from its original size.
To find the scale factor when 9 inches is equivalent to 4 feet, we need to compare the ratio of the two measurements. We can start by converting the measurements to the same units, such as inches:
\(4 \text{ feet} &= 4 \times 12 \text{ inches}\) \(&= 48 \text{ inches}\)
Now we can compare the ratio of the two measurements:
\($$9 \text{ inches} : 48 \text{ inches}$$\)
To simplify this ratio, we can divide both numbers by their greatest common factor, which is 3:
\($\frac{9 \text{ inches}}{3} : \frac{48 \text{ inches}}{3}$$\)
\($$3 \text{ inches} : 16 \text{ inches}$$\)
The scale factor is the ratio of the corresponding lengths in the two figures, so in this case, the scale factor is:
\($$3 \text{ inches} : 16 \text{ inches}$$\)
or, in fractional form:
\($\frac{3}{16}$$\)
Therefore, the scale factor is \($\frac{3}{16}$\) or approximately 0.1875.
To know more about Scale Factor visit:
https://brainly.com/question/29967135
#SPJ1
Rick kept track of wins and losses for each game attempt in the following table.
Game Number of Wins Number of Losses
Get-It-Rolling (A) 26 173
Bag-of-Tokens (B) 54 141
Pick-Your-Tile (C) 17 175
Select the correct statement.
A.
The results from both game A and game C align closely with the theoretical probability of winning those games, while the results from game B do not.
B.
Only the results from game B align closely with the theoretical probability of winning that game.
C.
Only the results from game A align closely with the theoretical probability of winning that game.
D.
The results from both game B and game C align closely with the theoretical probability of winning those games, while the results from game A do not.
Answer:
The results from both game A and game C align closely with the theoretical probability of winning those games, while the results from game B do not.
Step-by-step explanation:
Given the data:
Game Number of Wins Number of Losses
Get-It-Rolling (A) 26 173
Bag-of-Tokens (B) 54 141
Pick-Your-Tile (C) 17 175
EXPERIMENTAL PROBABILITY:
Game A :
Number of games played = 26 + 173 = 199
Experimental probability :
Probability of winning = number of wins / number of games played = 26 / 199 = 0.1306
Theoretical probability :
1 / 8 = 0.125
Game B :
Number of games played = 54 + 141 = 195
Experimental Probability of winning = number of wins / number of games played = 54 / 195 = 0.2769
Theoretical probability = 1 / 7 = 0.1429
Game C :
Number of games played = 17 + 175 = 192
Experimental Probability of winning = number of wins / number of games played = 17 / 192 = 0.0885
Theoretical probability = 1 / 12 = 0.08333
From the results, we can see that the results from both game A and game C align closely with the theoretical probability of winning those games.
Market researchers selected a random sample of people from region A and a random sample of people from region B. The researchers asked the people in the samples whether they had tried a new product. The difference between the sample proportions (B minus A) of people in the regions who indicated they had tried the new product was 0.15. Under the assumption that all conditions for inference were met, a hypothesis test was conducted with the alternative hypothesis being that the population proportion of B is greater than that of A. The p-value of the test was 0.34.Which of the following is the correct interpretation of the pp-value?If the difference in proportions of people who have tried the new product between the two populations is actually 0.15, the probability of observing that difference is 0.34.A. If the difference in proportions of people who have tried the new product between the two populations is actually 0.34, the probability of observing that difference is 0.15.B. If the proportions of all people who have tried the new product is the same for both regions, the probability of observing a difference of at least 0.15 is 0.34.C. If the proportions of all people who have tried the new product is the same for both regions, the probability of observing a difference of at most 0.15 is 0.34.D. If the proportions of all people who have tried the new product is the same for both regions, the probability of observing a difference equal to 0.15 is 0.34.
Answer:
B. If the proportions of all people who have tried the new product is the same for both regions, the probability of observing a difference of at least 0.15 is 0.34.
Step-by-step explanation:
Null hypothesis:
H0: The population proportion B = population proportion A
Alternative hypothesis:
H1: The population proportion of B > population proportion A
The P value, also called calculated probability, is that of getting test results which are at least as extreme as the results which were observed in a Statistical test. We assume the null hypothesis to be true.
Therefore if the population proportion of B = A (H0 is true), then we conclude that the probability of observing a difference of at least 0.15 is = 0.34.
Given opposite rays JK and KL with point M not on either ray, m∠JKM = 6x - 8 and m∠MKL = 2x + 14, find m∠JKM.
Answer:
122.5°
Step-by-step explanation:
The angles add to form a linear pair, so the angles add to 180°. Thus, 8x=174, meaning x=21.75.
So, angle JKM is 6(21.75)-8 = 122.5°.
Solve for x in the problems below
Answer:
a)......1+2=90 degree.....
so,x+x-20=90=2x=110
x=55degree
Step-by-step explanation:
b)let it be a triangle....angle1=56
2=y
3=29....by vertically opposite angles
by ext angle property... x= 1+3=56+29= 85
Answer:
55 degrees is the answer
Which of the following statements best describes why the given expression is not simplified?
3x^2–2x+1 - 4x - 6
Answer:
3x²–6x–5
Step-by-step explanation:
3x²–2x+1–4x–6
collect like terms
3x²–2x–4x–6+1
3x²–6x–5
Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. Find Upper P 40, which is the IQ score separating the bottom 40% from the top 60%. Round your answer to nearest tenth.
Answer:
\(z=-0.253<\frac{a-100}{15}\)
And if we solve for a we got
\(a=100 -0.253*15=96.205\)
And for this case the value would be 96.2 for the P40
Step-by-step explanation:
Let X the random variable that represent the IQ scores of a population, and for this case we know the distribution for X is given by:
\(X \sim N(100,15)\)
Where \(\mu=100\) and \(\sigma=15\)
We want to find the P40 ( a) so we need to satisfy the following condition:
\(P(X>a)=0.60\) (a)
\(P(X<a)=0.40\) (b)
For this case we can look for the critical value in the normal standar ddistirbution who accumulate 0.4 of the area in the left and 0.6 in the right and we got z=-0.253.
If we use condition (b) from previous we have this:
\(P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})\)
\(P(z<\frac{a-\mu}{\sigma})=0.40\)
And we can set up the following equationL
\(z=-0.253<\frac{a-100}{15}\)
And if we solve for a we got
\(a=100 -0.253*15=96.205\)
And for this case the value would be 96.2 for the P40
Missing numbers
, 9.8 , 9.1
Answer:
10.5
Step-by-step explanation:
Missing number, 9.8, 9.1
We see that each time it subtracts 0.7
We take
9.8 + 0.7 = 10.5
So, the missing number is 10.5
Math Math Math Math Math
Answer:
see below
Step-by-step explanation:
sqrt(2)+ sqrt(98)
sqrt(2) + sqrt( 2*49)
sqrt(2) + 7sqrt(2)
8 sqrt(2)
Answer:
\(\sqrt{2}\)+ \(\sqrt{98}\)
\(\sqrt{2}\)+ \(\sqrt{2}\) *49
\(\sqrt{2}\) + 7\(\sqrt{2}\)
8 \(\sqrt{2}\)
An equation is shown below:
5(2x - 8) + 15 = -15
Write the steps you will use to solve the equation and explain each step. Brain list will be given if answered right
Answer:
x = 1
Step-by-step explanation:
5(2x - 8) + 15 = -15
First, let's move the 15 to the opposite side of the equation. We'll do this by subtracting 15 from BOTH sides of the equation.
5(2x - 8) + 15-15 = -15-15
5(2x-8) + 0 = -30
5(2x-8) = -30
Now let's expand that first term.
5(2x)-5(8) = -30
10x - 40 = -30
Now let's move the -40 to the opposite side of the equation. We'll do this by ADDING 40 to both sides of the equation.
10x - 40 + 40 = -30 + 40
10x -0 = 10
10x = 10
Now to solve for x, we divide BOTH sides by 10 to "isolate the variable" aka get x alone.
10x/10 = 10/10
x = 1
The answer is x = 1.
Let's check if our answer is correct!
Original equation: 5(2x - 8) + 15 = -15
Substitute 1 for x.
5(2*1-8) + 15 =
5(2-8) + 15 =
5(-6) + 15 =
-30 + 15 = -15 >>> which is exactly what we started with! So x is 1.
there are 25 student in a class. five of then scored A and 10 of them score B while the other scored C for Biostatistics. if a student is selected at random, calculate the probability that the selected student scored A or B in biostastics.
There is a 60% probability that a randomly selected student from the class scored either an A or B in Biostatistics.
To calculate the probability that a randomly selected student scored either an A or B in Biostatistics, we need to consider the number of students who scored A and B and divide it by the total number of students in the class.
Given that there are 25 students in the class, 5 of them scored an A and 10 scored a B. To calculate the probability, we add the number of students who scored A (5) to the number of students who scored B (10):
Number of students who scored A or B = Number of students who scored A + Number of students who scored B = 5 + 10 = 15.
Therefore, the probability that a randomly selected student scored A or B
in Biostatistics is:
Probability = Number of students who scored A or B / Total number of students = 15 / 25 = 0.6 or 60%.
for more such questions on probability
https://brainly.com/question/25839839
#SPJ8
If one order of fries and five burgers cost twice as much as three orders of fries and two burgers, how many times as much does a burger cost compared to one order of fries? to start the problem is 1f+5b=2 (3f+2b)
Answer:
A burger cost five times as much as a fries.
Step-by-step explanation:
Let F represent fries
Let b represent burgers
From the question:
An order of fries and five burger can be written as:
f + 5b
Three orders of fries and two burgers can be written as:
3f + 2b
But an order of fries and five burgers cost twice as much as three orders of fries and two burgers. This can be written as:
f + 5b = 2(3f + 2b)
Now, we shall make b the subject of the above equation. This is illustrated below:
f + 5b = 2(3f + 2b)
Clear bracket
f + 5b = 6f + 4b
Collect like terms
5b – 4b = 6f – f
b = 5f
Thus, a burger cost five times as much as a fries.
Solve for the exact solutions in the interval
List your answers separated by a comma, if it has no real solutions, enter DNE.
Answer:
\( \sqrt{2} \sin(3x) - 1 = 0\)
\( \sqrt{2} \sin(3x) = 1\)
\( \sin(3x) = \frac{ \sqrt{2} }{2} \)
3x = π/4 + 2kπ or 3x = 3π/4 + 2kπ
x = π/12 + 2kπ/3 or x = π/4 + 2kπ/3
0 < π/12 + 2kπ/3 < 2π
0 < 1/12 + 2k/3 < 2
0 < 1 + 8k < 24
-1 < 8k < 23, so k = 0, 1, 2
x = π/12, 3π/4, 17π/12
0 < π/4 + 2kπ/3 < 2π
0 < 1/4 + 2k/3 < 2
0 < 3 + 8k < 24
-3 < 8k < 21, so k = 0, 1, 2
x = π/4, 11π/12, 19π/12
What is the correct formula for calculating kinetic energy?
Answer:
K.E = 1/2mv²
Kinetic energy
y=3(2-1)2+1
Solución
Answer:
y = 7
Step-by-step explanation:
y = 3(2-1) 2 + 1
y = 3(1)(2) + 1
y = 6 + 1
y = 7
Since the Boston marathon began in 1897, the finish time has been incrementally decreasing. The mean finish time to date is 231 minutes with a standard deviation of 40 minutes. Based on this information, what would allow us to use a Z-score in order to construct a confidence interval to estimate the mean finishing time of the most recent Boston Marathon with a sample size of 40 participants. Choose all that apply.
Answer:
hello your question lacks the required options but i will provide a general answer to your question
answer : The mean value and the standard deviation would allow us use a Z-score
Step-by-step explanation:
mean value = 231 minutes
standard deviation ( std ) = 40 minutes
sample size = 40
The parameters that would be applicable while use Z-score are : The given mean value and the standard deviation
This is because the value of a z-score gives us an information on how far we are from the mean score i.e. number of standard deviations
+Zscore means that the score is above the average value
-Zscore means that the score is below the average value
If f(x) = 3x2 + 1 and g(x) = 1 – x, what is the value of (f – g)(2)?
12
14
36
38
Answer: 14
Step-by-step explanation:
A developer wants to purchase a plot of land to build a house. The area of the plot can be described by the following expression: (5x+1)(7x−7) where x is measured in meters. Multiply the binomials to find the area of the plot in standard form
Answer:
35x^2 - 28x - 7
Step-by-step explanation:
Find all values of for which the quadratic equation has two real solutions.5x^2+9x+h=0Write your answer as an equality or inequality in terms of .
Given the equation:
\(5x^2+9x+h=0\)we will find the value of h which the quadratic equation has two real solutions
We will use the discriminant of the equation (D)
\(\begin{gathered} a=5,b=9,c=h \\ D=b^2-4ac \end{gathered}\)substitute with the values of a, b, and c
\(\begin{gathered} D=9^2-4\cdot5\cdot h \\ D=81-20h \end{gathered}\)the quadratic equation has two real solutions when D≥0
So,
\(\begin{gathered} 81-20h\ge0 \\ -20h\ge-81\rightarrow(\div-20) \\ \frac{-20h}{-20}\le\frac{-81}{-20} \\ \\ h\le4.05 \end{gathered}\)So, the answer will be:
\(h\le4.05\)