If both faucets are used together, it time taken by them to fill the tub is 4.8 minutes.
What is the concept of time and work?Time and work share a fundamental idea in common with other arithmetic topics, namely the idea of proportionality.
When the amount of work is constant, efficiency is inversely proportional to the length of time required.
Important Time and Work Formula:
Work Done = Time Taken × Rate of Work.Rate of Work = 1 / Time Taken.Time Taken = 1 / Rate of Work.If a piece of work is done in x number of days, then the work done in one day = 1/x.Total Wok Done = Number of Days × Efficiency.Efficiency and Time are inversely proportional to each other.Calculation for the time taken by both faucet to fill the tub.
The unit should be tub per minute.
Then, do the reciprocal of the result to have minute per tub.
The hot water faucet can fill the tub in 12 minutes.
The cold water faucet can fill the tub in 8 minutes.
The filling rate for both faucets filling the tub at the same time is the sum of their rates.
Let 't' be the time taken by both faucets.
Then,
[tex]\frac{1}{12} +\frac{1}{8} =\frac{1}{t}[/tex]
[tex]\frac{8+12}{8*12} =\frac{1}{t}[/tex]
[tex]\frac{1}{t} =\frac{20}{96}[/tex]
[tex]\frac{t}{1} =\frac{96}{20}[/tex]
t = 4.8
Therefore, the time taken by both faucets to fill the tub is 4.8 minutes.
To know more about the formula for calculating power, here
https://brainly.com/question/20290932
#SPJ4
If the area of the rectangle avove is 180 spuare inches, then x =
Given the dimension of the length and area of the rectangle, the dimension of the breadth x is 9in.
Hence, option A is the correct answer.
This question is incomplete, the missing diagram is uploaded along this answer below.
What is the value of x?Area of a rectangle is expressed as; A = l × b
Given that;
Length of the rectangle l = 20inBreadth b = xArea A = 180in²A = l × b
180in² = 20in × x
x = 180in² / 20in
x = 9in
Given the dimension of the length and area of the rectangle, the dimension of the breadth x is 9in.
Hence, option A is the correct answer.
Learn more about area of rectangle here: brainly.com/question/12019874
#SPJ1
PLEASE HELP ME AS SOON AS POSSIBLE
a) The linear function that models the population in t years after 2004 is: P(t) = -200t + 29600.
b) Using the function, the estimate for the population in 2020 is of 26,400.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The initial population in 2004, of 29600, is the y-intercept. In 12 years, the population decayed 2400, hence the slope is:
m = -2400/12 = -200.
Hence the equation is:
P(t) = -200t + 29600.
2020 is 16 years after 2004, hence the estimate is:
P(16) = -200(16) + 29600 = 26,400.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
Compare [tex]99![/tex] and [tex]50^{99}[/tex].
Hint: Identity [tex](a+b)(a-b)=a^2-b^2[/tex].
50^99 is greater than 99!
How to compare the numbers?The numbers are given as:
99! and 50^99
When the above numbers are estimated using a calculator, we have:
99! = 9.332622e+155
50^99 = 1.577722e+168
Next, we compare the exponents
168 and 155
168 is greater than 155
Hence, 50^99 is greater than 99!
Read more about number comparison at:
https://brainly.com/question/1732960
#SPJ1
Triangle is reflected across the y-axis and then dilated by a factor of centered at the origin. Which statement correctly describes the resulting image, triangle ?
Image of right triangle ABC in a graph with vertices A (minus 4, minus 2), B (4, minus 2), and C (4, 4)
A.
The reflection preserves the side lengths and angles of triangle . The dilation preserves angles but not side lengths.
B.
Both the reflection and dilation preserve the side lengths and angles of triangle .
C.
Neither the reflection nor the dilation preserves the side lengths and angles of triangle .
D.
The dilation preserves the side lengths and angles of triangle . The reflection does not preserve side lengths and angles.
Answer:
A. The reflection preserves the side lengths and angles of triangle . The dilation preserves angles but not side lengths.
Step-by-step explanation:
Reflection is a rigid transformation. It preserves both angles and side lengths. Dilation preserves angles, but changes all lengths by the same scale factor.
ApplicationThe described triangle was subject to reflection, which preserves angles and lengths. It was also subject to dilation, which preserves angles, but not lengths.
The appropriate description is that of choice A.
The diagonals of a rectangle measure x+5 feet and 2x+1 feet what is the value of x?
The value of x is 4.
Given that diagonals of a rectangle measure x+5 feet and 2x+1 feet as shown in the attached figure.
The diagonal of a rectangle is a line or straight line that connects the opposite corners or vertices of the rectangle.
In the given figure ABCD is a rectangle.
OA=2x+1 and OD=x+5 [Given]
AC and BD are diagonals of a rectangle.
As we know that the diagonals of a rectangle are always equal.
So, AC = BD
We can also write it as,
2×OA=2×OD
2×(2x+1) =2×(x+5)
Apply the distributive property a(b+c)=ab+ac, we get
4x+2=2x+10
Subtract 2x from both sides, we get
4x+2-2x=2x+10-2x
2x+2=10
Subtract 2 from both sides, we get
2x+2-2=10-2
2x=8
Divide both sides by 2, we get
2x/x=8/2
x=4
Hence, the value of x=4 when diagonals of a rectangle measure x+5 feet and 2x+1 feet.
Learn more about rectangles from here brainly.com/question/1549055.
#SPJ4
To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle.
At approximately what angle does the wire meet the ground?
33.6°
39.8°
50.2°
56.4°
Using relations in a right triangle, it is found that the tree meets the wire at an angle of 56.4º.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.In this problem, we have that:
The opposite side to the angle is of 10 feet.The hypotenuse is of 12 feet.Hence:
[tex]\sin{\alpha} = \frac{10}{12}[/tex]
[tex]\alpha = \sin^{-1}{\left(\frac{10}{12}\right)}[/tex]
[tex]\alpha = 56.4^\circ[/tex].
More can be learned about relations in a right triangle at https://brainly.com/question/26396675
#SPJ1
Can someone help me with this problem and show work please !
Answer: Length - 20, Width - 10
Step-by-step explanation:
First we will use the formula to find area:
Area = Length * Width --- However, since it's double the length we will do 2Length.
Area = 2x*x
Given Area = 200
Next we will solve to find Width:
[tex]2x^{2} =200[/tex]
Divide by 2:
[tex]x^{2} =100[/tex]
Take square root:
[tex]x=10[/tex]
Width = 10
Now we multiply 10 by 2, as length is twice it's width:
[tex]2*10=20[/tex]
Length = 20
Final answer: Width = 10, Length = 20
I hope this helps!
Find the volume of this sphere.
Answer:
4ft^3
Step-by-step explanation:
1.333333*3*1^3=4
To start finding the volume of this sphere, we get the following data:
π = 3r = 2 ft²To find the volume we apply the following formula:
[tex]\boldsymbol{\sf{V= \dfrac{3}{4}\pi r^{2} }}[/tex], wherev = volumeπ = pir = radiusWe substitute our data in the formula and solve:
Substituting values into the equation
[tex]\boldsymbol{\sf{V=\dfrac{3}{4}*3*(2 \ ft)^{3} }}[/tex]Calculate exponent cubed
[tex]\boldsymbol{\sf{V=\dfrac{3}{4}*3*8 \ ft^{3} }}[/tex]Multiplying
[tex]\boxed{\boldsymbol{\sf{V=32 \ ft^{3} }}}[/tex]Therefore, the volume of the sphere is 32 ft³.
Each edge of a graph is colored with one of the four colors red, blue, yellow, or green. How could you represent the edges in this graph using a variation of the adjacency matrix structure
G is the matrix representation of the four colored graph.
According to the statement
we have given that a graph is colored with one of the four colors red, blue, yellow, or green.
And we have to represent the edges of this graph using a variation of the adjacency matrix structure
So, Adjacency Matrix Structure is a way of representing a graph as a matrix of booleans (0's and 1's). A finite graph can be represented in the form of a square matrix on a computer, where the boolean value of the matrix indicates if there is a direct path between two vertices.
And in this graph representation the Adjacency Matrix Structure denoted by a matrix G.
so, there are a four colors used that's why there are 4 into 4 matrix is formed to represent the edges.
G = [tex]\left[\begin{array}{cccc}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{array}\right][/tex]
And this is the matrix representation of the graph which is colored with four graphs.
So, G is the matrix representation of the four colored graph.
Learn more about Matrix here https://brainly.com/question/2456804
#SPJ4
Fill in the blank: In data analytics, a _____ refers to all possible data values in a certain dataset
In data analytics, a population refers to all possible data values in a certain dataset
Data analysis is a systematic computer-aided analysis of data or statistics. [1] It is used to discover, interpret, and convey meaningful patterns in the data. It also includes applying data patterns for effective decision-making.
It may be useful in areas where there is a lot of recorded information. The analysis relies on the simultaneous application of statistics, computer programming, and operations research to quantify performance.
Organizations can apply analytics to business data to describe, predict, and improve business performance. Areas within the analysis include descriptive analysis, diagnostic analysis, predictive analysis, prescriptive analysis, and cognitive analysis in particular. [2] Analysis can be applied in various fields such as marketing, management, finance, online systems, information security, and software services.
Learn more about the population here: https://brainly.com/question/25630111
#SPJ4
CORRECT ANSWER GETS BRAINLIST
Answer:
y = -1x + 1
Step-by-step explanation:
y = mx + c
y = gradient(x intercept) + y intercept
y = -1x + 1
Suppose you are looking to purchase a new TV. You are placing it in an opening that is 136 cm wide but want to leave at least 2 cm of room on either side of the TV. If the TV screen measures 86 cm high, what is the largest size TVin inches, that you can purchase? TV's are measured based on the diagonal measure. (1inch = 2.54cm) Write your answer as an integer
Answer:
404 inches
Step-by-step explanation:
Since a room of 2cm is to be left of either side of the TV, thus, the permissible required length of the TV is 136-2 = 134cm
Use Pythagoras Theorem,
h² = 134² + 86² = 17956 + 7396 = 25352
h = √25352 = 159.22 ≈ 159cm = 404.41 inches ≈ 404 inches.
x = 8, y = 11
The variables x and y vary inversely. Use the given values to write an equation relating x and y . Then find y when x=2.
[tex]y = \frac{1}{mx} [/tex]
[tex]11 = \frac{1}{8m} [/tex]
[tex]m = \frac{1}{88} [/tex]
[tex]y = \frac{1}{ \frac{1}{88}x } = \frac{88}{x} [/tex]
[tex]when \: x = 2 \\ y = \frac{88}{2} = 44[/tex]
Mario is 63 years older than his grandson Jonas. How many years ago was Mario's age 10 times Jonas's age if Mario's age is currently four times Jonas's age?
Answer:
14 years ago
Explanation:
Let Mario's age be m, Jonas age be j.
From, Mario is 63 years older than Jonas
Equation 1: m = j + 63
From, Mario's age is four times Jonas age
Equation 2: m = 4j
Solve them by substitution:
m = j + 63
4j = j + 63
4j - j = 63
3j = 63
j = 21
Find Mario's age:
m = j + 63
m = 21 + 63
m = 84
Follow this steps:
m - y = 10(j - y)
84 - y = 10(21 - y)
84 - y = 210 - 10y
-y + 10y = 210 - 84
9y = 126
y = 14
The answer is 14 years ago.
Let Mario's age be M, and Jonas' age be J.
The formed equations :
M = J + 63M = 4JTo find their current ages, substitute the 2nd equation in the 1st equation.
4J = J + 63
3J = 63
J = 21
M = 4(21)
M = 84
For Mario to be 10 times Jonas' age, he has to be an age that is a multiple of 10.
Case (1) : Mario's age = 80
Subtract 4 from both their ages.
Mario : 84 - 4 = 80
Jonas : 21 - 4 = 17
17 × 10 ≠ 80
Case (2) : Mario's age = 70
Subtract 14 from both their ages.
Mario : 84 - 14 = 70
Jonas : 21 - 14 = 7
7 × 10 = 70
What is the factored form of 27 - 530?
(2 - 10 ) ( - 590) (9 - 510)
( 20 + 1820م + 18 ) ( 10 - 2) -
O
O
0
(2 - 10) ( 9 + 9 10 + 510)
(2 - 10 ) ( 18 + 2 510 + 20 )
A deck of 52 cards contains an equal amount of hearts, diamonds, clubs, and spades. If one card is picked at random from the deck, the probability that it is a club is:
a)1/52
b)1/13
c) 1/10
d) 1/4
Answer: B) 1/13
Step-by-step explanation:
There are 52 cards. So, there are 52/4 = 13 cards of each amount of hearts, diamonds, clubs and spades. In this case, we're looking for the probability of picking a club. Since there are 13 club cards and we want to know the probability of picking ONE, our answer is b) 1/13.
Considering the definition of probability, the correct answer is option d): if one card is picked at random from the deck, the probability that it is a club is 1/4.
Definition of probabilityThe higher or lower possibility that a particular event will occur is known as the probability. This is, the probability establishes a relationship between quantity of favorable events and the total quantity of possible events.
The ratio of favorable situations (the number of cases in which event A may or may not occur) to all possible cases is used to calculate the the probability of any event A. This is called Laplace's Law:
probability= number of favorable cases÷ total number of possible cases
Probability that the picked card is a clubIn this case, you know:
Total number of cards = 52 (number of possible cases)The deck of cards contains an equal amount of hearts, diamonds, clubs, and spades.Total number of cards that are clubs= 52÷4= 13 (number of favorable cases)Replacing in the definition of probability:
probability= 13÷ 52
Solving:
porbability= 1/4
Finally, if one card is picked at random from the deck, the probability that it is a club is 1/4.
Learn more about probability:
brainly.com/question/3283947
#SPJ2
The numbers in this chart represent the weights in kilograms of five members of a middle school boys’ baseball team.
Whose record represents an outlier in this data set?
A. Jim’s
B. Tom’s
C. Ben’s
D. John’s
The record that represents an outlier in this data set is John's weight.
What is an outlier?An outlier is a data point that differs significantly from other observations.
In other words, an outlier is a value or point that differs substantially from the rest of the data.
Therefore, the record that represents an outlier in this data set is John's weight. This is because it is on the
learn more on outliers here: https://brainly.com/question/12978982
#SPJ1
Please help me solve this random answers will be removed
Answer:
AB-46 cm
Step-by-step explanation:
Use law of cosines
AB^2 = 24^2 + 26^2 - 2 (24)(26)cos 134
AB= 46 cm
PLS HELP ME QUICKLY PLSSS IM BEGGINGG
Answer:
Khan Academy.
Step-by-step explanation:
You can go on khan academy and search up "GRAPHS." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.
Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite. x + y = 6 x - y = 0
The solution of the system of equations contains one point
How to determine the number of solutions?The system is given as:
x + y = 6
x - y = 0
Add both equations
2x = 6
Divide by 2
x = 3
Substitute x = 3 in x - y = 0
3 - y = 0
Solve for y
y = 3
So, we have x =3 and y = 3
Hence, the solution of the system of equations contains one point
Read more about system of equations at:
https://brainly.com/question/14323743
#SPJ1
Find the mixed number halfway between 6.4 and 6½. Give
your answer in its simplest form.
Answer:
6.45
Step-by-step explanation:
I am not staring at zero. I am starting at 6.4, so I take 6.4 and add that to half way between 6.5 and 6.4.
6.4 + 1/2(6.5-6.4) Combine in the parentheses
6.4 + 1/2(.5) Take half of .5
6.4 + .05 add
6.45
The inequality |2x - 5 > 8 can be written as which two inequalities?
Answer:
2x - 5 < -8 or 2x - 5 > 8
Step-by-step explanation:
|2x - 5| > 8
2x - 5 < -8 or 2x - 5 > 8
The two inequalities that can be written from the |2x - 5| > 8 are:
2x - 5 > 8
-2x + 5 > 8
We have,
To split the inequality |2x - 5| > 8 into two separate inequalities, we consider both the positive and negative cases for the absolute value expression.
Positive case:
When 2x - 5 is positive, we have:
2x - 5 > 8 _____(1)
Negative case:
When 2x - 5 is negative, we have:
-(2x - 5) > 8
Simplifying the negative case:
-2x + 5 > 8 ______(2)
Now, we have two inequalities:
2x - 5 > 8
-2x + 5 > 8
These are the two inequalities resulting from the given inequality
|2x - 5| > 8.
Thus,
The two inequalities that can be written from the |2x - 5| > 8 are:
2x - 5 > 8
-2x + 5 > 8
Learn more about inequalities here:
https://brainly.com/question/20383699
#SPJ7
Write an equation of the line that passes through (2, 0) and is perpendicular to the line
y = -x-3.
An equation of the perpendicular line is y =
Answer:
y =x - 2
Step-by-step explanation:
If the slope of the line is 'm', then the slope of the perpendicular to the given line = [tex]\sf \dfrac{-1}{m}[/tex] (opposite reciprocal)
y = -x - 3
Compare with equation of line in slope y-intercept form: y = mx +b
m = -1
[tex]\sf \text{Slope of the perpendicular line = $-(\dfrac{1}{-1})= 1$}[/tex]
This line passes through (2, 0);
Equation of the line in slope - point form:
[tex]\sf y - y_1 = m(x - x_1)[/tex]
y - 0 = 1 (x - 2)
y = x - 2
I WILL GIVE BRAINLIEST!!!!
2 step equation:
4x + 3 = 19
2 step equation w/ fractions:
(4/3)x + 5 = 17
Distributive Property:
4x(6 - 2) - 10 = 20
Decimals:
4.3x + 0.7 = 5
Real world equation:
Sharon's restaurant is bringing in money from customers, and she needs to know how much she needs to pay off the bill for the electricity to run the place. To turn the electricity on, she has to pay $25. For every hour that the electricity is on for, she has to pay $4. How many hours can she have the electricity on for if she makes $49 profit?
i really need some help solving these
The answers to the questions are:
1. x = 4
2. x = 1.5
3. x = 1.875
4. x = 1
2 step equation:1. 4x + 3 = 19
4x = 19 - 3
4x = 16
divide by 4
x = 4
2 step equation w/ fractions:(4/3)x + 5 = 17
= 1.33x + 5 = 7
Take like terms
1.33x = 7-5
1.33x = 2
divide through by 1.33x to get 2
x = 2/1.33
x = 1.5
3. Distributive Property:4x(6 - 2) - 10 = 20
Multiply and open the bracket
24x - 8x - 10 = 20
Take like terms
16x = 20+10
16x = 30
x = 30/16
= 1.875
4. Decimals:4.3x + 0.7 = 5
4.3x = 5 - 0.7
4.3x = 4.3
x = 1
Read more on distributive properties here:
https://brainly.com/question/2807928
#SPJ1
A 2-column table with 3 rows. Column 1 is labeled x with entries 2, 4, 5. Column 2 is labeled y with entries 5, 10, 12.5.
Use the information in the table to find the constant of proportionality and write the equation.
The constant of proportionality is
.
The equation that represents this proportional relationship is
.
The constant of proportionality is 2.5.
First, There is a proportional relationship
Two values x and y are said to be in a proportional relationship if y=kx, where x and y are variables and k is a constant.
y = kx
The constant k is the constant of proportionality
As shown that ,
A 2-column table with 3 rows.
Column 1 is labeled x with entries 2, 4, and 5.
Column 2 is labeled y with entries 5, 10, and 12.5.
According to the Above statement, the calculation is as follows:
5/2 = 2.5 , here we get is 2.5
10/ 4 = 2.5 so Here we get 2.5 and so on
Hence, The constant of proportionality is 2.5.
Learn more about proportional relationship variables here:
brainly.com/question/13082482
#SPJ1
Triangle A B C. Side A B is 4, B C is 5, A C is 3. Triangle A prime B prime C prime.
If the scale factor for the dilation shown is 3, which is the length of B'C'?
5/3
8
12
15
Answer:
The correct answer is 15.
Step-by-step explanation:
We are given that the original sides BC is 5. To find the length of B'C' we take the side of BC and multiply it by the scale factor.
5 (original BC) x 5 (the given scale factor) = 15
Answer:
15
Step-by-step explanation:
correct on edge 2023
Solve the equation
3(2x + 2) = 3x - 15
• Using distributive property
[tex]6x + 6 = 3x - 15[/tex]
• Solving the like terms
[tex]6x - 3x = - 15 - 6[/tex]
[tex]3x = - 2 1[/tex]
[tex]x = - \dfrac{21}{3} [/tex]
[tex]x = - 7[/tex]
Hope it helps you any confusions you may ask!
Prove that a positive integer is a sum of at least two consecutive positive integers if and only if it is not a power of two.
Answer:
45
Step-by-step explanation:
small brain
Find the sum: 5/8+3/10
Answer:
37/70
Step-by-step explanation:
5/8 + 3/10 = (5 × 5)/ (8 × 5) + (3 × 4)/ (10 × 4) =
25/40 + 12/40 = 37/40
how do u multiply 1x100000000000000000000000000000??
By using mind ig -,-
Hope Helpful ~