Answers
Answer:
Domain: input values, independent variables
Range: output vales, dependent variables
Step-by-step explanation:
Think of it like a graph: the domain are the x-values and the range is the y-values. if you're doing a problem with time, the time will go on the x-axis and cannot be influenced by the y-values, but the y-vales are depending on what the x-values are (independent/dependent). for the input/output, usually when solving equations on a graph, you plug in the x-value and find the y-value. you're INPUTTING the x-value to receive the OUPUT.
Domain = set of allowed inputs
The input x is the independent variable as it can do whatever it wants without relying on y.
-------------------------
Range = set of possible outputs
The output is the dependent variable. It depends on what the input x is. Often, we make y the output dependent variable.
-------------------------
For example, with y = 2x+5, we can plug in anything we want for x (it doesn't need to look to y for guidance or anything). Once we pick something for x, it will directly determine what y is.
Let's say we picked x = 10. That would mean y = 2x+5 = 2*10+5 = 25. The input x = 10 in the domain leads to y = 25 in the range. We see that the output y = 25 depends entirely on the independent input x = 10.
Related Questions
Paul can install a 300-square-foot hardwood floor in 18 hours. Matt can install the same floor in 22 hours. How long would it take Paul and Matt to install the floor working together?
4 hours
9.9 hours
13.2 hours
30 hours
Answers
Answer:
9.9 hours
Step-by-step explanation:
The formula to determine the time together is
1/a+1/b = 1/c where a and b are the times alone and c is the time together
1/18 + 1/22 = 1/c
The least common multiply of the denominators is 198c
198c(1/18 + 1/22 = 1/c)
11c+ 9c = 198
20c = 198
Divide by 20
20c/20 =198/20
c =9.9
Answer:
B - 9.9 hrs
Step-by-step explanation:
took the test.
please help brainliest to correct answer
Answers
Answer:
Question to number 6 is-3
Question to number 7 is 3
Question to number 8 is 2 to the second power
Step-by-step explanation:
please correct me if I’m wrong and for number 8 I am correct it’s just I didn’t know how to put the little 2 on top of the big one
Step-by-step explanation:
question 6 is - 3
question 7 is 3
question 8 is 4
4. A solution of 60% fertilizer is to be mixed with a solution of 21% fertilizer to form 234 liters of a 43% solution. How many liters of the 60% solution must be used?
SHOW YOUR WORK
Answers
Given:
A solution of 60% fertilizer is to be mixed with a solution of 21% fertilizer to form 234 liters of a 43% solution.
To find:
The quantity of the 60% solution in the mixture.
Solution:
Let x be the quantity of the 60% solution and y be the quantity of the 21% solution.
Quantity of mixture is 234. So,
[tex]x+y=234[/tex]
[tex]x=234-y[/tex] ...(i)
The mixture has 43% fertilizer. So,
[tex]\dfrac{60}{100}x+\dfrac{21}{100}y=\dfrac{43}{100}\times 234[/tex]
Multiply both sides by 100.
[tex]60x+21y=10062[/tex] ...(ii)
Using (i) and (ii), we get
[tex]60(234-y)+21y=10062[/tex]
[tex]14040-60y+21y=10062[/tex]
[tex]-39y=10062-14040[/tex]
[tex]-39y=-3978[/tex]
Divide both sides by -39.
[tex]\dfrac{-39y}{-39}=\dfrac{-3978}{-39}[/tex]
[tex]y=102[/tex]
Putting this value in (i), we get
[tex]x=234-102[/tex]
[tex]x=132[/tex]
Therefore, 132 liters of the 60% solution must be used.
State if the scenario involves a permutation or a combination. Then find the number of possibilities.
A team of 15 basketball players needs to choose two players to refill the water cooler.
Permutation/Combination:
Answer:
Answers
Answer:
Permutation ; 210 ways
Step-by-step explanation:
Permutation and combination methods refers to mathematical solution to finding the number of ways of making selection for a group of objects.
Usually, selection process whereby the order of selection does not matter are being treated using permutation, while those which takes the order of selection into cognizance are calculated using combination.
Here, selecting 2 players from 15 ; since order does not matter, we use permutation ;
Recall :
nPr = n! ÷ (n - r)!
Hence,
15P2 = 15! ÷ (15 - 2)!
15P2 = 15! ÷ 13!
15P2 = (15 * 14) = 210 ways
Seven and one-half foot-pounds of work is required to compress a spring 2 inches from its natural length. Find the work required to compress the spring an additional 3 inch.
Answers
Answer:
Apply Hooke's Law to the integral application for work: W = int_a^b F dx , we get:
W = int_a^b kx dx
W = k * int_a^b x dx
Apply Power rule for integration: int x^n(dx) = x^(n+1)/(n+1)
W = k * x^(1+1)/(1+1)|_a^b
W = k * x^2/2|_a^b
From the given work: seven and one-half foot-pounds (7.5 ft-lbs) , note that the units has "ft" instead of inches. To be consistent, apply the conversion factor: 12 inches = 1 foot then:
2 inches = 1/6 ft
1/2 or 0.5 inches =1/24 ft
To solve for k, we consider the initial condition of applying 7.5 ft-lbs to compress a spring 2 inches or 1/6 ft from its natural length. Compressing 1/6 ft of it natural length implies the boundary values: a=0 to b=1/6 ft.
Applying W = k * x^2/2|_a^b , we get:
7.5= k * x^2/2|_0^(1/6)
Apply definite integral formula: F(x)|_a^b = F(b)-F(a) .
7.5 =k [(1/6)^2/2-(0)^2/2]
7.5 = k * [(1/36)/2 -0]
7.5= k *[1/72]
k =7.5*72
k =540
To solve for the work needed to compress the spring with additional 1/24 ft, we plug-in: k =540 , a=1/6 , and b = 5/24 on W = k * x^2/2|_a^b .
Note that compressing "additional one-half inches" from its 2 inches compression is the same as to compress a spring 2.5 inches or 5/24 ft from its natural length.
W= 540 * x^2/2|_((1/6))^((5/24))
W = 540 [ (5/24)^2/2-(1/6)^2/2 ]
W =540 [25/1152- 1/72 ]
W =540[1/128]
W=135/32 or 4.21875 ft-lbs
Step-by-step explanation:
if U>T, R>Q, S>T and T>R, which of the following is TRUE?
1. S>Q
2. U > S
3.U > R
A. 1 only
B. 2 only
C. 1 and 2
D. 2 and 3
Answers
Answer:
C. 1 and 2
Step-by-step explantation:
First, i would order them as U>T, T>R, R>Q, S>T
we can rewrite them as
U>T>R>Q,
now adding S, we get U>S>T>R>Q,
so U>S
We can also rewrite all of them as inequalities:
U-T>0
T-R>0
R-Q>0
S-T>0
Add R-Q and T-R
(R-Q)+(T-R)>0
-Q+T>0
T>Q, but because S>T we can say S>Q
Find 0.2B
B=[50 10
25 15]
Answers
Multiplying a matrix by a scalar results in every entry in a matrix get multiplied by that scalar, as defined,
[tex]a\begin{bmatrix}b&c\\d&e\\\end{bmatrix}=\begin{bmatrix}ab&ac\\ad&ae\\\end{bmatrix}[/tex]
So in our case, ([tex]0.2=\frac{1}{5}[/tex]
[tex]\frac{1}{5}\begin{bmatrix}50&10\\25&15\\\end{bmatrix}=\begin{bmatrix}\frac{50}{5}&\frac{10}{5}\\\frac{25}{5}&\frac{15}{5}\\\end{bmatrix}=\boxed{\begin{bmatrix}10&2\\5&3\\\end{bmatrix}}[/tex]
Hope this helps :)
If path has 56 marbles and he gave Sandra 34 how many marbles will he have left?
Answers
Answer:
22
Step-by-step explanation:
You just subtract them
56-34
= 22
Therefore your answer is 22
find the missing side of the triangle
Answers
Answer:
x = 34
Step-by-step explanation:
Pytago:
x[tex]30^{2} + 16^{2} = x^2\\x = \sqrt{30^2 + 16^2} \\x = 34[/tex]
A 40-foot ladder is leaning against a building and forms a 29.32° angle with the ground. How far away from the building is the base of the ladder? Round your answer to the nearest hundredth.
45.88 feet
34.88 feet
22.47 feet
19.59 feet
Answers
Answer:
34.88
Step-by-step explanation:
I took the test
The distance between the building and the ladder is 34.88 foot, the correct option is B.
What is a Right Triangle?A triangle in which one of the angle measure is equal to 90 degree is called a right triangle.
The ladder forms a right triangle with the building and the ground,
The length of the triangle is 40 foot
The angle made by the ladder is 29.32 degree
By using Trigonometric Ratios
cos 29.32 = Base / Hypotenuse
cos 29.32 = Base / 40
Base is the distance between the building and the ladder.
Base = 34.88 foot
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Find an equation of the plane orthogonal to the line
(x,y,z)=(0,9,6)+t(7,−7,−6)
which passes through the point (9, 6, 0).
Give your answer in the form ax+by+cz=d (with a=7).
Answers
The given line is orthogonal to the plane you want to find, so the tangent vector of this line can be used as the normal vector for the plane.
The tangent vector for the line is
d/dt (⟨0, 9, 6⟩ + ⟨7, -7, -6⟩t ) = ⟨7, -7, -6⟩
Then the plane that passes through the origin with this as its normal vector has equation
⟨x, y, z⟩ • ⟨7, -7, -6⟩ = 0
We want the plane to pass through the point (9, 6, 0), so we just translate every vector pointing to the plane itself by adding ⟨9, 6, 0⟩,
(⟨x, y, z⟩ - ⟨9, 6, 0⟩) • ⟨7, -7, -6⟩ = 0
Simplifying this expression and writing it standard form gives
⟨x - 9, y - 6, z⟩ • ⟨7, -7, -6⟩ = 0
7 (x - 9) - 7 (y - 6) - 6z = 0
7x - 63 - 7y + 42 - 6z = 0
7x - 7y - 6z = 21
so that
a = 7, b = -7, c = -6, and d = 21
An equation of the plane orthogonal to the line 7x - 7y - 6z = 21.
The given line is orthogonal to the plane you want to find,
So the tangent vector of this line can be used as
The normal vector for the plane.
The tangent vector for the line is,
What is the tangent vector?A tangent vector is a vector that is tangent to a curve or surface at a given point.
d/dt (⟨0, 9, 6⟩ + ⟨7, -7, -6⟩t ) = ⟨7, -7, -6⟩
Then the plane that passes through the origin with this as its normal vector has the equation
⟨x, y, z⟩ • ⟨7, -7, -6⟩ = 0
We want the plane to pass through the point (9, 6, 0), so we just
translate every vector pointing to the plane itself by adding ⟨9, 6, 0⟩,
(⟨x, y, z⟩ - ⟨9, 6, 0⟩) • ⟨7, -7, -6⟩ = 0
Simplifying this expression and writing it in standard form gives
⟨x - 9, y - 6, z⟩ • ⟨7, -7, -6⟩ = 0
7 (x - 9) - 7 (y - 6) - 6z = 0
7x - 63 - 7y + 42 - 6z = 0
7x - 7y - 6z = 21
So that, a = 7, b = -7, c = -6, and d = 21.
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Write the standard form of the equation of the circle with center (8,−1) that passes through the point (6,7)
Answers
Answer:
(x - 8)^2 + (y + 1)^2 = 68
Step-by-step explanation:
The standard form of the equation of the circle with center (8,−1) is :
(x - 8)^2 + (y + 1)^2 = R^2
If the circle passes through the point (6,7) that means that the point (6,7) is a solution of the equation and we can replace (x,y) with (6,7) to find R.
How many edges are there?
Answers
9514 1404 393
Answer:
24
Step-by-step explanation:
The front face is an 8-sided star, so has 8 edges. We presume the back face is the same, so it also has 8 edges. Each of the front vertices is connected by an edge to each of the corresponding back vertices, so there are 8 more edges connecting front and back.
The total number of edges is 8 + 8 + 8 = 24.
Round 573.073 to the greatest place
Answers
Answer:
574
Step-by-step explanation:
To round a two-digit number to the nearest ten, simply increase it or decrease it to the nearest number that ends in 0: When a number ends in 1, 2, 3, or 4, bring it down; in other words, keep the tens digit the same and turn the ones digit into a 0
Hope this helps <3
which of the following illustrates commutative property of addition? 17+4=4+17
Answers
9514 1404 393
Answer:
17 +4 = 4 +17
Step-by-step explanation:
The only expression shown here illustrates that property.
Reason Can you subtract a positive integer from a positive integer
and get a negive result? Explain your answer.
Answers
Answer:
No
Step-by-step explanation:
No matter the situation, when you multiply a negative by a negativeyou get a positive and a positive by a positive you get a positive. but if its two different like a negative and a positive then its NEGITIVE.
let's say you have 23 and you're multiplying by 2.
It's always increasing so it doesnt ever reach the negitive numbers.
John runs a computer software store. Yesterday he counted 140 people who walked by the store, 63 of whom came into the store. Of the 63, only 25 bought something in the store.
(a) Estimate the probability that a person who walks by the store will enter the store. (Round your answer to two decimal places.)
(b) Estimate the probability that a person who walks into the store will buy something. (Round your answer to two decimal places.)
(c) Estimate the probability that a person who walks by the store will come in and buy something. (Round your answer to two decimal places.)
(d) Estimate the probability that a person who comes into the store will buy nothing. (Round your answer to two decimal places.)
Answers
Answer:
.................
Step-by-step explanation:
............
b. 39.68%
c. 17.86%
d. 60.32%
1. A helicopter is at a position from two VORS (VHF Omnidirectional
Radio Range, an aircraft navigation system operating in the VHF band -
not covered in chapter) as in the diagram shown below. Given the angles
shown, find the third angle.
Helicopter
74.0°
66.0°
VOR
VOR
Answers
The position of the helicopter and the two VORs forms a triangle and the third angle formed by these three entities is 40 degrees
The diagram is not shown; however, the question can still be answered.
The given angles are:
[tex]\theta_1 = 74.0^o[/tex]
[tex]\theta_2 = 66.0^o[/tex]
Represent the third angle as [tex]\theta_3[/tex]
The helicopter and the 2 VORs form a triangle.
So, we make use of the following theorem to calculate the third angle
[tex]\theta_1 + \theta_2 + \theta_3= 180^o[/tex] ---- sum of angles in a triangle
Substitute known values
[tex]74.0^o + 66.0^o + \theta_3= 180^o[/tex]
[tex]140.0^o + \theta_3= 180^o[/tex]
Collect like terms
[tex]\theta_3= 180 -140.0^o[/tex]
[tex]\theta_3= 40^o[/tex]
Hence, the third angle is 40 degrees.
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Find the slope of the line that goes through the
(2,6) and (-1, -6)
Answers
Find the equation of the linear function represented by the table below in slope-intercept form.
Answers
Answer:
y=-4x-5
Step-by-step explanation:
The slope of the line is - 4, the equation of line is y=-4x-5
8.9 x 10^3 in standard notation
Answers
Answer:
that is n standard notation mah frand
8.9 × 10^3 being scientific notation of " 8900 "
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{8.9}\times\large\textsf{10}^\mathsf{3}\\\\\mathsf{10^3}\\\mathsf{= 10\times10\times10}\\\mathsf{= 100\times10}\\\mathsf{= \bf 1,000}\\\\\large\textsf{8.9}\times\large\textsf{1,000}\\\\\large\textsf{= \bf 8,900}\\\\\\\boxed{\boxed{\huge\text{Answer: \boxed{\underline{\underline{\bf 8,900}}}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\boxed{\huge\text{}\boxed{\frak{Amphitrite1040:)}}}[/tex]
A line contains the piont (4,5) and is perpendicular to a line with a slope of -2/3. Write an equarion of the line satisfying the given conditions. Write the answer in slope-intercept form
Answers
Answer:
[tex]y=\frac{3}{2}x-3.5[/tex] or, preferably, [tex]y=\frac{3}{2}x-\frac{7}{2}[/tex]
Step-by-step explanation:
First is to find the perpendicular slope. In this case, you swap the numerator and denominator and then multiply that fraction by -1.
In this case, -2/3's inverse slope is 3/2.
Now, the initial y=3/2 passes through 7.5,5
So, you must subtract 3.5 from that to make it pass through 4,5.
In this way, you get the answer in slope-intercept form.
Answer:
y = [tex]\frac{3}{2}[/tex] x - 1
Step-by-step explanation:
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{3} }[/tex] = [tex]\frac{3}{2}[/tex] , then
y = [tex]\frac{3}{2}[/tex] + c ← partial equation in slope- intercept form
To find c substitute (4, 5) into the partial equation
5 = 6 + c ⇒ c = 5 - 6 = - 1
y = [tex]\frac{3}{2}[/tex] x - 1 ← equation of line
Find an upper bound for E(h) the error of the machine approximation of the two-point forward difference formula for the first derivative and then find the h corresponding to the minimum of E(h).
The two-point forward difference formula for f'(x) is:_________
Answers
Answer:
I doubt it is not going to be a great
Solve for X and show your work and explain please
Answers
Answer: x = 45
Step-by-step explanation:
Given
(2/3)x + 4 = (4/5)x - 2
Add 2 on both sides
(2/3)x + 4 + 2 = (4/5)x - 2 + 2
(2/3)x + 6 = (4/5)x
Subtract (2/3)x on both sides
(2/3)x + 6 - (2/3)x = (4/5)x - (2/3)x
6 = (12/15)x - (10/15)x
6 = (2/15)x
Divide 2/15 on both sides
6 / (2/15) = (2/15)x / (2/15)
[tex]\boxed{x=45}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
x = 45
Step-by-step explanation:
2/3 x + 4 = 4/5x - 2 Add 2 to both sides
2/3 x + 4 + 2 = 4/5x Combine
2/3x + 6 = 4/5x Subtract 2/3 x from both sides.
6 = 4/5x - 2/3 x Multiply both sides by 15
6*15 = 4/5 x * 15 - 2/3x * 15
6*15 = 12x - 10x Combine the left and right
90 = 2x Divide by 2
x = 45
Let's see if it works.
LHS = 2/3 * 45 + 4
LHS = 2*15 + 4
LHS = 30 + 4
LHS = 34
RHS
Right hand side = 4/5 * 45 - 2
RHS = 36 - 2
RHS = 34 which is the same as the LHS
Please Help!! Whoever helps and gets it correct gets Brainliest and 5 star rating!!
Answers
Answer:
the reasoning states that "all the numbers begin with a 7 or an 8"
however this is not accurate as they can be in different placements
which can make a big difference in the total estimate.
for example:
the number could've been an 8, or an 80
they both begin with an 8
however have totally different values and could have messed up the total estimated number.
hope this helps :D
If the mean of a given dataset is
42 and the standard deviation is
4, where will a majority of the
data lie?
Answers
Answer:
A majority of the data will lie between 38 and 46.
Step-by-step explanation:
It can be said that a majority of the data of a distribution lies within 1 standard deviation of the mean.
In this question:
Mean of 42, standard deviation of 4.
42 - 4 = 38
42 + 4 = 46
A majority of the data will lie between 38 and 46.
look at the image for the question
Answers
You would multiply height (4) by the base (length(2) x width(2)=4) which is 16
Find the length of the arc.
A. 539π/12 km
B. 9π/3 km
C. 9π/2 km
D. 18π km
Answers
Answer:
b because it is I found out cus I took test
The length of the arc 9π/2 km.
The answer is option C.9π/2 km.
What is the arc of the circle?
The arc period of a circle can be calculated with the radius and relevant perspective using the arc period method.
⇒angle= arc/radius
⇒ 135°=arc/6km
⇒ arc =135°*6km
⇒arc=135°*π/180° * 6km
⇒arc = 9π/2 km
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State the counting number in the periodic table of elements of the element considered to be the heaviest gas. (the answer should consist of numbers only)
Answers
9514 1404 393
Answer:
118
Step-by-step explanation:
Oganesson is the heaviest element ever created. It is a "super-heavy" noble gas with a half-life less than 1 millisecond. Its atomic number is 118.
Find the area of the figure. (Sides meet at right angles.)
Answers
Answer:
56
Step-by-step explanation:
A=(3*4)+(4*(4+3+4))=56
