The expression that results in rational number is P+N
What is rational numbers?Any integer that can be expressed as p/q, where q ≠ 0, is referred to as rational.
The form of a rational number, which is a type of real number in mathematics, is p/q when q is not equal to 0. Examples of rational numbers include 1/2, 1/5, 3/4, and other such values. For example, any integer is a rational number. The number one can be written as 10,000/10000, -2 over -2, or 1/1.
Here, L = √2
M=3√3
N =√16
P = √9
we know [tex]\sqrt{16} =4 , \sqrt{9} =3[/tex]
only P and N are rational numbers.
P+N = 4+3 = 7/1
which is a rational number.
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y 12 11 10 9 18 5 NCS A 1 X -12-11-10-9-8-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 -1 3 ó do & och ich -10 -11 -12
To find out the equation of the line we need two points
so
we take
(1,-3) and (2,-9)
step 1
Find the slope
m=(-9+3)/(2-1)
m=-6/1
m=-6
step 2
Find the equation in slope intercept form
y=mx+b
we have
m=-6
point (1,-3)
substitute
-3=-6(1)+b
solve for b
-3=-6+b
b=6-3
b=3
therefore
y=-6x+3What is the state tax withheld on this W-2? Responses $25,670 $25,670 $2009.04 $2009.04 $1309.17 $1309.17 $567 $567
Answer: The answer is $2009.04
Step-by-step explanation:
I hope this helps.
the variance of a sample of 81 observations is 64. calculate the standard deviation. round your answer to two decimals.
The standard deviation is 8.
What is standard deviation?Data dispersion in regard to the mean is quantified by a standard deviation, or. Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high. A measure of a group of values' variance or dispersion in statistics is called the standard deviation. The values tend to be close to the set's mean when the standard deviation is low, while the values are dispersed over a larger range when the standard deviation is high. The dispersion of the data around the mean value is measured by the standard deviation. It might be helpful when comparing data sets that may have the same mean but a different range.
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Evaluate the function when x=-2; f(x)=4x+3
Answer:
Replace the variable x with -2 in the expression
f(-2) =4(-2)+3
f(-2) = -8+3
f(-2) = -5 (final answer)
If a football team received the ball on the 50-yard line, what represents zero in this situation? _______ because this spot represents neither a gain or loss of yards in the first play. plsss helpp
If the football team started a play on the 50-yard line, gained 7 yards, and then lost 10 yards on the next play, the ball would be on the 47-yard line at the conclusion of the second play.
The 50-yard line is where the start is.
After the opening play, the football team gained 7 yards.
After the first play, the new yard line equals (the starting point) plus (Number of yards gained)
following the conclusion of the first play, the new yard line
If a football team started a play on the 50-yard line, gained 7 yards, and then lost 10 yards on the next play, the ball would be on the 47-yard line at the conclusion of the second play.
After the first play, the new yard line is equal to 50 plus 7.
After the first play, the new yard line is the 57-yard line.
The second play cost the football team 10 yards.
The yard line following the conclusion of the second play equals the yard line following the conclusion of the first play (The number of yards lost)
The new yard line following the conclusion of the second play is 57-10.
47 is the new yard line following the conclusion of the second play.
The second half of the second
47 is the new yard line following the conclusion of the second play.
The ball was on the 47-yard line after the second play when it was over.
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a) Complete the table of values for y = x² - 2x - 3
-2 -1 0 1
2
3
4
0
X
y
-3
5
Answer:
On worksheet: 5, -3, -4, 0
Step-by-step explanation:
See attached worksheet.
Find the value of x b) 3x = 27
3x = 27
3x = 27 x
3x = 27/3
x. = 9
Between which two whole numbers is square root of 12?
Which of the two numbers is a better estimate for square root of 12 explain.
Answer:
3 and 4Step-by-step explanation:
square root 12 lies between (square root 9 and 16) so it is between 3 and 4
Jada keeps 175 hair beads in a storage box. She chooses a bead without looking what
color it is, and returns it to the box. She does this severaltimes.
Pink - 7
Green - 8
Red - 10
How many pink beads are in Jadas storage box
The probability of getting a pink bead out of the storage box containing a sum total of 175 beads is 0.1428
As per the question statement, we are supposed to find the probability of getting a pink bead out of the storage box containing a sum total of 175 beads.
It is given that there are 25 pink beads in the storage box.
Probability = Favorable outcome / Total value
Probability = 25/175
Probability = 0.1428
Hence, the probability of getting a pink bead out of the storage box containing a sum total of 175 beads is 0.1428
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I need help with the following questions. Please show your work.
1) Find the inverse of f(x)=3 sqrt x-1/2
2) Let f(x)-2/2x-1
Show that this function is one-to-one algebraically.
3) Determine whether f(x)=3x-5 and g(x)=x/3+5 are inverses. Explain how you know.
please help
Considering the given functions, we have that:
1) The inverse of function f(x) is defined by: [tex]f^{-1}(x) = \frac{4x^2}{9} + 1[/tex]
2) It is shown in the Item 2 section that the function is one-to-one.
3) The functions are not inverses, due to the result of their composition.
Item 1 - Inverse functionThe find the inverse of a function, we exchange x and y on the original function, and then isolate y.
The original function is given by:
[tex]y = 3\frac{\sqrt{x - 1}}{2}[/tex]
Exchanging x and y, we have that:
[tex]x = 3\frac{\sqrt{y - 1}}{2}[/tex]
Now we do the procedures to isolate y, as follows:
[tex]3\sqrt{y - 1} = 2x[/tex]
[tex]\sqrt{y - 1} = \frac{2x}{3}[/tex]
[tex](\sqrt{y-1})^2 = \left(\frac{2x}{3}\right)^2[/tex]
[tex]y - 1 = \frac{4x^2}{9}[/tex]
[tex]y = \frac{4x^2}{9} + 1[/tex]
[tex]f^{-1}(x) = \frac{4x^2}{9} + 1[/tex]
Item 2 - One-to-one functionTo verify if the function is one-to-one, we first find the numeric values at x = a and x = b, then:
f(a) = -2/(2a - 1).f(b) = -2/(2b - 1).Now we have to verify how many outcomes of a and b are possible for them to be equal. Since they have the same numerator, they will be equal when the denominators are equal, that is:
2a - 1 = 2b - 1.
Simplifying the one and then by 2:
a = b.
Only equal when a = b, hence the function is one-to-one. (this is the algebraic proof).
Item 3 - Are they inverses?The functions will be inverses if the composition of the functions result in x, that is, if inputting function g(x) into function f(x) results in x.
The result of the composition is given by:
f(g(x)) = f(x/3 + 5) = 3(x/3 + 5) - 5 = x + 15 - 5 = x + 10.
x + 10 is different of x, hence the two functions are not inverses.
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a random variablegroup of answer choicesis the result of a measurement.can only be discrete.assigns one and only one numeric value to each experimental outcome.is a binomial, poisson, or hypergeometric variable.
A random variable assigns one and only one numeric value to each experimental outcome.
A random variable used in experimental trials assign numerical values to the members or elements of the trial. This random variable is used to study the outcome of a trial conveniently.
A random variable assigns one and only one numeric value to each experimental outcome. This assigned numeric value may not be exact. In an experimental trial the possible outcomes are denoted by a random variable. So these values are just practically assigned and not theoretically exact.
There are discrete and continuous random variables. They are usually denoted by capital letters such as X, Y,.. etc. These random variables are used to calculate the probability of each outcome in a trial.
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Given the function g(x) = −3x + 4, compare and contrast g(−2) and g(4). Choose the statement that is true concerning these two values.
1. The value of g(−2) is smaller than the value of g(4)
2. The value of g(−2) is the same as the value of g(4).
3. The values of g(−2) and g(4) cannot be compared.
4. The value of g(−2) is larger than the value of g(4).
The function g(x) = −3x + 4, after putting the values we find out that the value of g(-2) is greater than the value of g(4). Hence, option 4 is correct.
What is a function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for creating physical links in the sciences.
According to the given information in the question,
g(x) = -3x + 4
Substitute g(-2) in the above equation,
g(-2) = -3(-2) + 4
g(-2) = 10
Now, substitute g(4) in the above equation,
g(4) = -3(4) + 4
g(4) = -8
Hence, it is clear that the value of g(-2) is larger than the value of g(4).
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an order from an online bookstore takes at least four weeks to arrive. you ordered some books online nine days ago.
please help!!!!
Answer:
jahajshsisjsjssk sjshejei sjshshisbs
Find the mean, the median, and the mode(s), if any, for the given data. Round noninteger means to the nearest tenth. (If there ismore than one mode, enter your answer as a comma-separated list. If an answer does not exist, enter DNE.)18,3, 40, 19, 42, 48, 51, 43meanmedianmode(s)
The data are listed in ascending order to be:
[tex]3,18,19,40,42,43,48,51[/tex]MEAN
The mean is the average of a data set. This can be calculated using the formula:
[tex]Mean=\frac{Sum\text{ }of\text{ }numbers}{Number\text{ }of\text{ }Numbers}[/tex]From the question, we can calculate the mean to be:
[tex]\begin{gathered} Mean=\frac{3+18+19+40+42+43+48+51}{8}=\frac{264}{8} \\ Mean=33 \end{gathered}[/tex]The mean is 33.
MEDIAN
The median is the middle of the set of numbers.
The middle terms are 40 and 42. Therefore, the median will be the average of the two numbers:
[tex]\Rightarrow\frac{40+42}{2}=41[/tex]The median is 41.
MODE
The mode is the most common number in a data set.
The modes of the data are 3, 18, 19, 40, 42, 43, 48, and 51.
weekly wages at a certain factory are normally distributed woth a mean of $400 and a standard deviation of $50. find the probability that a worker selected at random makes between $450 and $500
Answer:
See below
Step-by-step explanation:
450 is 1 standard deviation above mean : z - score +1 corresponds to
.8413 (from z-score table)
500 is 2 S.D. for z-score of 2 corresponds to .9772
.9772 - .8413 = .1359 or 13 . 59 %
A flagpole is anchored to the ground by a guy wire that is 12 m long. The guy wire makes an angle of 63 deg with the ground. How far from the base of the flagpole must the guy wire be anchored into the ground?
Answer: ~ 5.45 m
Step-by-step explanation: The pole would create an altitude for the triangle, and the wire attached from the ground to the pole would be create a hypotenuse of 12m. Since the wire makes a 63 degree angle with the ground, we can use a trig ratio to find the base. The base of the triangle would be the distance from the wire in the ground to the pole itself. Using cosine, (adjacent to 63 degrees over 12m) you can find the measure of the base.
cos (63 deg.) = x / 12
12 • cos (63 deg.) = x
5.44788599687 = x.
Hope this helps! (Added pic for clarity!)
Consider this function.() = -31 + 3Which graph represents the inverse of function ?5XE3*-W.x3-12ZАwDZ
To know the inverse function, we have to change variables of the original function as follows:
[tex]f(x)=y=-3x+3[/tex][tex]x=-3y+3[/tex]Isolating for y:
[tex]x+3y=3[/tex][tex]3y=3-x[/tex]Thus, the inverse function is:
[tex]y=-\frac{1}{3}x+1[/tex]Based on the latter, we can see that the intersection with y -axis = 1, coordinate (0, 1). While the intersection with x - axis = 3, coordinate (3, 0)
Answer: C. Y
Of 734 students, 442 are taking mathematics. What angle (in degrees) of a circle would show the percent of students taking mathematics? (Round your answer to the nearest whole degree.)
We need to find the angle (rounded to the nearest whole degree) of a circle that would represent the percent of students taking mathematics.
Since a complete turn around the circle has 360º, we have the following proportion:
Number of students Angle
734 360º
442 x
Then, cross multiplying the above values, we obtain:
[tex]\begin{gathered} 734x=442\cdot360\degree \\ \\ x=\frac{442\cdot360\degree}{734} \\ \\ x\cong217\degree \end{gathered}[/tex]Answer: 217º
Answer:
217°
Step-by-step explanation:
The fraction of students taking math is 442/734
we need this same fraction of the 360 degrees in a circle
442/734 * 360 = 217°
A bicyclist rides 11.2 kilometers
east and then 5.3 kilometers south.
What is the magnitude of the
bicyclist's resultant vector?
Hint: Draw a vector diagram.
[ ? ] kilometers
Round your answer to the nearest tenth.
The magnitude of the bicyclist's resultant vector is 12.5 km.
Given that, a bicyclist rides 11.2 kilometers east and then 5.3 kilometers south.
What is vector?A vector is an object that has both a magnitude and a direction. Geometrically, we can picture a vector as a directed line segment, whose length is the magnitude of the vector and with an arrow indicating the direction.
Now, using Pythagora's theorem
The magnitude of the bicyclist's resultant vector is
x² = (11.2)² + (5.3)²
⇒ x² = 125.44 + 28.09
⇒ x² = 153.53
⇒ x = √153.53
⇒ x = 12.47
⇒ x ≈ 12.5 km
Therefore, the magnitude of the bicyclist's resultant vector is 12.5 km.
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Answer:
12.4 km (nearest tenth)
Step-by-step explanation:
The resultant vector of the bicyclist after riding 11.2 km east and then 5.3 km south is:
b = 11.2i - 5.3jThe magnitude of a vector b is written | b |.
Magnitude is a scalar, and it’s always positive.
The i and j components of a vector form a right triangle, so use Pythagoras’ theorem to find a vector’s magnitude.
[tex]\begin{aligned} |\textbf{b}|&=\sqrt{11.2^2+5.3^2\\&=\sqrt{125.44+28.09\\&=\sqrt{153.53}\\&=12.4\; \sf (nearest\;tenth)\end{aligned}[/tex]
Therefore, the magnitude of the bicyclist's resultant vector is 12.4 km (nearest tenth).
Kate and Hellen buy a car. Kate pays £1200 and Helen pays the remaining 23 of the
total cost. How much does the car cost in total?
Answer:1223 pounds?
Step-by-step explanation:
Your good friend Carlos, offers you the opportunity to join his game. The rules are:
If you pick a spade from a shuffled pack, you win $9.00.
If you lose you owe him $2.00
Find the expected value you win the game?
If Your good friend Carlos, offers you the opportunity to join his game. The rules are: If you pick a spade from a shuffled pack, you win $9.00. If you lose you owe him $2.00 . The expected value you win the game is $.075.
Expected valueProbability of getting spade = 13/52
Probability of getting spade = 1/4
Probability of getting another thing = 1 - 1/4
Probability of getting another thing = 3 / 4
Now let find the expected value
E(x) = Σxp(x)
Expected value = 9 × 1/4 + (-2) (3 /4)
Expected value = 9 /4 - 6 /4
Expected value = 3 /4
Expected value = $0.75
Therefore the expected value is $0.75.
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Help plssssssssssssssssss
Answer:
2
Step-by-step explanation:
→ Find 2 points
( 3, 5 ) and ( 2 , 3 )
→ Find the change in y coordinates
3 - 5 = -2
→ Find the change in x coordinates
2 - 3 = -1
→ Divide y by x
-2 ÷ -1 = 2
Please I really need help
Determine which integers in the set S: {-40, "-10," 20, 40} will make the inequality 1/5 (m - 5) <_ 1/10 (m - 20) false.
S:{-40, -10}
S:{-10, 20}
S:{20, 40}
S:{-40, 40}
The integers in the set S that make the inequality false are 20 and 40, so the correct option is the third one.
Which elements in the set will make the inequality false?Here we have the following inequality:
(1/5)*(m - 5) ≤ (1/10)*(m - 20)
First, let's simplify the inequality:
(1/5)*(m - 5) ≤ (1/10)*(m - 20)
(10/5)*(m - 5) ≤ (m - 20)
2*(m - 5) ≤ (m - 20)
2m - 10 ≤ m - 20
2m - m ≤ -20 + 10
m ≤ -10
So the only solutions are the values of m that are equal to or smaller than -10.
And the set is {-40, "-10," 20, 40}, then the elements of that set that make the inequality false are 20 and 40 (both are larger than -10).
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A farmer picked 725 pounds of apples one week. Hepicked 693 pounds of pears in the same week. Whichcalculation can be used to find out how many morepounds of apples than pears he picked?
a farmer picked 725 pounds of apple,
also
The city of Raleigh has 10,000 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 450 randomly selected registered voters was conducted. 166 said they'd vote for Brown, 257 said they'd vote for Feliz, and 27 were undecided.
Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown.Round your
answer to four decimal places.
This sample statistic suggests that we might expect
voters to vote for Brown.
of the 10,000 registered
The sample statistic for the number of respondents who said they would vote for Brown is 0.3689, and the number of respondents who indicated they would vote for Brown is 3689.
The population in this survey are the registered voters in Raleigh. There are 10000 registered voters in Raleigh from which a sample is group selected of 450 randomly selected registered voters was conducted in which 166 said they'd vote for Brown, 257 said they'd vote for Feliz, and 27 were undecided.
So, according to the given data
The sample statistic is the number who would vote for Brown divided by the total number in the sample, means
[tex]\frac{166}{450}[/tex]
0.3689
To find sample statistic suggests that we might expect voters to vote for Brown of the 10,000 registered, we multiply the sample statistic (0.3689) with the total number of voters (10000) means
0.3689 * 10000 = 3689.
Therefore we can conclude that the sample statistic for the proportion of voters surveyed who said they'd vote for Brown is 0.3689 and the voters to vote for brown is 3689.
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how to solve this equation (x2/3)6/5
Answer:
[tex] \frac{2}{5} {x}^{2} [/tex]
Step-by-step explanation:
x²/3(6/5)
=2/5x²
Answer:
[tex]=\frac{4x}{5}[/tex]
Step-by-step explanation:
[tex]\frac{\left(x\frac{2}{3}\right)\cdot \:6}{5}=\frac{4x}{5}[/tex]
Remove parentheses: :3
[tex]=\frac{x\frac{2}{3}\cdot \:6}{5}[/tex]
Multiply [tex]x\frac{2}{3} * 6 : 4x[/tex]
ANd u get
[tex]=\frac{4x}{5}[/tex]
hope thjis helps
~~Wadfads~~
Noah bought `4` tickets and paid `\$103`. What was the cost per ticket?
Answer: 25.75
Step-by-step explanation: 103 divided by 4 = 25.75
En los juegos olimpicos del 2012 en londres usain bolt gano medalla de oro al recorrer 100 metros en 9.69 segundos cual fue su velocidad ?
Answer:
la respuesta es 10.3199...
Step-by-step explanation:
solo divides 100 por 9.69
$2,300 at 7% interest for 9 years. What would the interest be?
We want to find the simple interest accrued on $2,300 at 7% interest for 9 years.
The formula for simple interest is given as;
[tex]I=\frac{P\times R\times T}{100}[/tex]Inserting the values, we have;
[tex]I=\frac{2300\times7\times9}{100}=\text{ \$1449}[/tex]Therefore, the interest is $1449
se the given frequency distribution to find the (a) class width. (b) class midpoints. (c) class boundaries. temperature (f) frequency question content area bottom part 1 (a) what is the class width?
The class width is 5 for the given frequency distribution.
What are class boundaries?
The values used to demarcate classes are called class borders. The difference between a class's upper-class limit and its lower-class limit indicates the extent of the gap between classes.(a) Class width is the same for all the classes. It is the difference between the lower class limit of two consecutive classes
Therefore Lower limit of 50 - 54 = 50
Lower limit of 55 - 59 = 55
Class width = 55 - 50
Class width = 5
If calculated all have the same class width.
(b) Midpoint is the average of the sum of lower and upper-class limits of the class.
Temp Freq Midpoint
50-54 1 52
55-59 3 57
60-64 5 62
65-69 11 67
70-74 7 72
75-79 7 77
80-84 1 82
(c) Class boundaries are to make the classes continuous mostly. We can find this by first calculating the difference between the upper-class limit and the lower-class limit of the next class and taking its average.
Add this average to the upper limit and subtract this average from the lower limit
Lower boundary for 50 - 54 = 50 - 0.5 = 49.5
Upper boundary for 50 - 54 = 54 + 0.5 = 54.5
Temp Freq Class Boundaries
50-54 1 49.5-54.5
55-59 3 54.5-59.5
60-64 5 59.5-64.5
65-69 11 64.5-69.5
70-74 7 69.5-74.5
75-79 7 74.5-79.5
80-84 1 79.5-84.5
The class width is 5 for the given frequency distribution.
Complete question: Use the given frequency distribution to find the
(a) class width.
(b) class midpoints.
(c) class boundaries.
Temperature (°F) Frequency
32-36 1
37-41 3
42-46 5
47-51 11
52-56 7
57-61 7
62-66 1
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