A father leaves his money to his four children the first received 1/3 the second received 1/6 and the third received 2/5 how much did the remaining child receive
Answer:
The remaining child got a fraction of [tex]\frac{1}{10}[/tex].
Step-by-step explanation:
Lets take the fraction of the money fourth child got is [tex]x[/tex]
Addition of all these fractions should be equal to 1.
⇒[tex]\frac{1}{3} +\frac{1}{6} +\frac{2}{5} +x=1[/tex]
⇒[tex]\frac{10+5+12+30x}{30} =1[/tex] (Taking a common denominator)
⇒[tex]\frac{27+30x}{30} =1[/tex]
⇒[tex]27+30x=30[/tex]
⇒[tex]30x=3[/tex]
⇒[tex]x=0.1[/tex]
Therefore,
The remaining child got a fraction of [tex]\frac{1}{10}[/tex].
By calculating the combined fractions of the inheritance received by the first three children, we've determined that 27/30 of the inheritance has been allocated. Subtracting this from the whole leaves us with 3/30, which simplifies to 1/10 of the inheritance for the remaining child.
The student has asked about how much the remaining child will receive from a father's inheritance if the first received 1/3, the second received 1/6, and the third received 2/5 of the inheritance. To answer this, let's first add up the portions of the inheritance that the first three children received:
First child: 1/3
Second child: 1/6
Third child: 2/5
Now, we will find a common denominator to add these fractions. The least common multiple of 3, 6, and 5 is 30. Let's convert each fraction:
First child: 1/3 = 10/30
Second child: 1/6 = 5/30
Third child: 2/5 = 12/30
Now, add these fractions:
10/30 + 5/30 + 12/30 = 27/30
Once we add up these portions, we get 27/30 which represents the total part of the inheritance that has been given out to the first three children. To find out the portion for the remaining child:
30/30 (the whole inheritance) - 27/30 (the part given away) = 3/30
Reducing the fraction 3/30 gives us 1/10. So, the remaining child would receive 1/10 of the inheritance.
Three roads lead into a stadium's parking areas. Each road has four lanes (two in each direction) with a capacity oftwo parking attendants are required to park cars for each type a lot, while just one can handle each type b lot. Of the ten lots that will be used tonight, six are type a and four are type b. How many parking attendants are required for tonight's event?1,00vehicles/lane/hour. If 10,000 vehicles are expected for a game, how long will it take for all of them to enter the parking areas?
In this scenario, the combined capacity of the three roads leading to the stadium is 12,000 vehicles per hour. Therefore, to park 10,000 vehicles, it would take approximately 50 minutes.
Explanation:The question involves an understanding of traffic flow and rates. To find the total capacity of these roads leading to the stadium, we multiply the number of roads by the number of lanes on each road and the capacity of each lane, resulting in 4 lanes per road x 3 roads x 1,000 vehicles per lane per hour, equal to 12,000 vehicles per hour.
With 10,000 vehicles expected for the game, we can then divide the total number of vehicles by the total capacity of the roads per hour to find out how many hours it will take for all vehicles to enter the parking lots. Therefore, it will take approximately 10,000 vehicles / 12,000 vehicles per hour = 0.83 hours, or about 50 minutes.
The increased traffic due to a new manufacturing plant, increased businesses, and route changes in the nearby streets can also affect the traffic flow, however these factors are not quantified in the question. In the real world, proper planning and infrastructure can solve campus parking issues, as the example mentioned about Twelfth and Locust Streets.
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What is the contrapositive of the statement “If a polygon is a square, then it has four right angles.”
Answer:
If a polygon has not got four right angles then it is not a square.
Step-by-step explanation:
Contrapositive is
if A implies B then not B implies not A.
What is greater one inch or one centimeter
One inch is greater than centimeter
what is the domain and range?
{(4,2), (-9,2), (5,4), (4,17)}
Answer:
Domain = {4,-9,5}
Range = {2,4,17}
Step-by-step explanation:
We are given ordered pairs as
{(4,2), (-9,2), (5,4), (4,17)}
This is a subset of cartesian product AXB where
A = {4,-9,5} and B = {2,4,17}
Note: Repeated values are written only once in the set.
Hence we find that 4 is mapped on to 2 and 17,
-9 to 2 and 5 to 4
Domain = I item in the ordered pair of mapping = {4,-9,5}
Range = II item in the ordered pair of mapping = {2,4,17}
Hey there!!
What is a coordinate form?
... Coordinate form is written as ( x , y )
What is domain?
... Domain are also called as the 'x' values.
What is the range?
... Range is the other word for the 'y' values.
Given ordered pairs :-
( 4 , 2 ) ; ( -9 , 2 ) ; ( 5 , 4 ) ; ( 4 , 17 )
Hence, the domain is :-
... { 4 , -9 , 5 )
Hence, the range is :-
... { 2 , 4 , 17 )
Remember :- The values "can not" be repeated!
Hope my answer helps!!
Solve for x. y=bx+a Enter your answer in the box.
Answer:
The value of the equation is [tex]x=\frac{y-a}{b}[/tex].
Step-by-step explanation:
Consider the provided equation.
[tex]y=bx+a[/tex]
We need to solve the provided equation for x.
Subtract a from both side.
[tex]y-a=bx+a-a[/tex]
[tex]y-a=bx[/tex]
Divide both sides by b.
[tex]\frac{y-a}{b}=\frac{bx}{b}[/tex]
[tex]x=\frac{y-a}{b}[/tex]
Hence, the value of the equation is [tex]x=\frac{y-a}{b}[/tex].
The variable 'x' as the subject of the formula of the equation y = bx + a is x = ( y - a )/b.
How to make 'x' the subject of the formula of the equation?Given the equation in the question:
y = bx + a
To make the variable 'x' the subject of the formula of the equationy = bx + a, first isolate term with the variable 'x'.
y = bx + a
To isolate the term containing variable 'x', first subtract 'a' from both sides of the equation:
y - a = bx + a - a
y - a = bx
Reaorder:
bx = y - a
Now, divide both sides by 'b':
bx/b = ( y - a )/b
x = ( y - a )/b
Therefore, the variable 'x' equals ( y - a )/b.
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Carrie spent
1
4
of her allowance on a shirt,
1
3
of her allowance on a skirt, and $8 on a belt. If she spent $22 in all, how much was Carrie’s allowance?
Equation:
1
4
a +
1
3
a + 8 = 22
Carrie’s allowance was $
.
24 dollars.
1/4 + 1/3 = 3/12 + 4/12 = 7/12
7/12 a + 8 = 22
7/12 a = 14
a = 14 x 12/7
a = 24 dollars
At a pet store ,davina counted 12parrots out of 20 birds ,which is an equivalent ratio of parrots to birds at the pet store
Every 3 Parrots there will be 5 Birds
3/5
Answer:
Every 3 Parrots there will be 5 Birds
3/5
Step-by-step explanation:
Least common multiple of 26,39 using prime factorization
26 is a multiple of 2 but 39 isn't
39 is a multiple of 3 but 26 isn't
Dividng by the next three prime numbers, neither 26 nor 39 is a multiple of 5, 7, or 11
Moving up to the sixth prime number (13), we see that BOTH 26 and 39 are divisible by 13. 26 = 2 * 13 and 39 = 3 * 13 and 13 is the lowest common multiple of 26 and 39.
Translate this sentence into an equation. 32 is the product of Mabel's age and 2 . Use the variable m to represent Mabel's age. URGENT
To translate the given sentence into an equation, use the equation 2m = 32 and then divide both sides by 2 to solve for Mabel's age, which is 16 years old.
The sentence '32 is the product of Mabel's age and 2' can be translated into an equation using the variable m to represent Mabel's age. The product of two numbers means you multiply them together. We are given that when you multiply Mabel's age by 2, you get 32. The equation that represents this relationship is:
2m = 32
To find Mabel's age, we simply divide both sides of the equation by 2 to isolate m, which gives us:
m = 32 / 2
m = 16
Mabel's age is 16 years old.
Richard can read 1/4 of a book in 4/5 of an hour.At this rate ,how much can richard read in one hour
Assuming that Richard always reads with the same rate, there is a direct proportion between the time spent reading and the portion of book read:
[tex] \text{portion}_1 : \text{time}_1 = \text{portion}_2 : \text{time}_2 [/tex]
So, we can set up and solve the following proportion:
[tex] \dfrac{1}{4} : \dfrac{4}{5} = x : 1 \iff x = \dfrac{\frac{1}{4}}{\frac{4}{5}} = \dfrac{1}{4}\cdot \dfrac{5}{4} = \dfrac{5}{16} [/tex]
HELP HELP HELP DUE TODAY PLEASEEE WILL GIVE ANYTHING
What is the recursive rule for the sequence?
4.4, 5.8, 7.2, 8.6, 10, …
an=an−1−1.4 , where a1=4.4
an=an+1+1.4 , where a1=4.4
an=an+1−1.4 , where a1=4.4
an=an−1+1.4 , where a1=4.4
Answer:
a_n=a_(n−1)+1.4 , where a_1=4.4
Step-by-step explanation:
Given a sequence as
4.4, 5.8, 7.2, 8.6, 10, …
We find that first term is 4.4
II term = 5.8 = 4.4+1.4
III term = 7.2 = 5.8+1.4
Iv term = 8.6 = 7.2+1.4
V term = 10.0 = 8.6+1.4
i.e. each term is got by adding 1.4 to the previous term.
In other words, this is an arithmetic sequence with I term =4.4 and d = common difference =1.4
I term = a_1 = 4.4
and a_2 = a_1+1.4 and so on.
Hence correct answer is
a_n=a_(n−1)+1.4 , where a_1=4.4
60 POINTS FOR THE THISS!!!
Does the following table show a proportional relationship between the variables x and y?
There is a certain pattern:
As x is increased by 1/4 every time, y is increased by 3 every time. You can make a proper ratio and set up proportions with these numbers.
Please Help It Is Past Due!
Prove the Pythagorean Theorem using similar triangles. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the legs of the triangle equals the squared length of the hypotenuse. Be sure to create and name the appropriate geometric figures.
Explanation:
First we consider ΔABC and ΔBCD,
∠C=∠C (common)
∠B=∠D=[tex]90\textdegree[/tex]
So, ΔABC ≈ ΔBCD (By AA similarity rule )
So by taking corresponding sides in ratios we get
[tex]\frac{AB}{BD}=\frac{AC}{BC}=\frac{BC}{CD}[/tex]
Now
[tex]AC.CD=BC.BC\\BC^{2} =AC.CD[/tex] -------- Eqn (1)
Similarly,
We consider ΔABD and ΔABC
∠A=∠A (Commom)
∠B=∠D=[tex]90\textdegree[/tex]
So,
ΔABD ≈ ΔABC (By AA similarity rule )
So by taking corresponding sides in ratios we get
[tex]\frac{BC}{BD}=\frac{AC}{AB}=\frac{AB}{AD}[/tex]
Now,
[tex]AB.AB=AC.AD\\AB^{2} =AC.AD[/tex] --------Eqn (2)
By Adding both the equation we get
[tex]AB^2+BC^2=AC.CD+AC.AD\\AB^2+BC^2=AC(CD+AD)\\AB^2+BC^2=AC.AC\\AB^2+BC^2=AC^2[/tex]
Hence, we proved the pythagorean theorem by using similarity of triangle.
Please help 20 POINTS. Problem below
An even function is when f(x) = f(-x) ... or ... g(x) = g(-x).
f(x) = - (x + 1)(x - 4)
= -(x² - 3x - 4)
= -x² + 3x + 4 f(x) = -x² + 3x + 4
f(-x) = -(-x)² + 3(-x) + 4
= -x² - 3x + 4 f(-x) = -x² - 3x + 4
f(x) ≠ f(-x) so it is NOT even.
********************************************************
g(x) = [tex]\frac{3}{2}|x|[/tex]
g(-x) = [tex]\frac{3}{2}|-x|[/tex]
= [tex]\frac{3}{2}|x|[/tex] since absolute value becomes positive
g(x) = g(-x) so it IS even
Answer: C
item 6 for what value of a is 8x−8+3ax=5ax−2a an identity?
Let's rewrite the expression as
[tex] 8x+3ax-5ax = 8-2a \iff 8x - 2ax = 8-2a \iff 2x(4-a) = 2(4-a) [/tex]
So, if [tex] a \neq 4 [/tex], you may divide both sides by [tex] 4-a [/tex], the equation becomes [tex] 2x=2 [/tex], and the only solution is [tex] x=1 [/tex], which means that this is not an identity (an indentity is tautologically true, no matter the value of x).
If instead [tex] a = 4 [/tex], you are multiplying both sides by zero, so the equation becomes
[tex] 2x \cdot 0 = 2 \cdot 0 \iff 0=0 [/tex]
So, it doesn't matter which value for x you choose, because you will always end up with [tex] 0=0 [/tex], which is obviously always true.
. Anna gets paid $8.75/hour working as a barista at Coffee Break. Her boss pays her
$9.00/hour for creating the weekly advertisement signs. She works a total of 25
hours each week.
a. Let x represent the hours that Anna works each week as a barista.
Write a function ℎ(x) to represent the amount of money that Anna earns working as
a barista.
b. Write a function, f(x) to represent the hours Anna works creating the signs.
c. Let s represent the number of hours that Anna works creating the signs.
Create a function g(s) to represent the money Anna earns creating the signs.
d. Find g( f(x) ). What does this composite function represent?
e. What functions could be combined to represent Anna’s total earnings?
Combine the functions to write an expression that can be used to represent
Anna’s total earnings, where x represents the number of hours she works as a
barista
Explanation:
Anna gets paid $8.75/hour working as a barista.
She gets paid $9.00/hour for creating weekly advertisement signs.
In total she works 25 hours a week.
Let 'x' represent the number of hours that she works as a barista, then [tex]25-x[/tex] would represent the number of hours she works to create signs.
A. We need to write a function h(x) that represents the amount of money that Anna earns working as a barista.
Since she is earning $8.75 per hour and she works as a barista for 'x' hours a week so the function is:
[tex]h(x)=8.75\times x=8.75x[/tex]
[tex]h(x)=8.75x[/tex]
B. We need to write a function f(x) to represent the hours Anna works creating the signs.
Since, in total she works for 25 hours a week so the function to represent the number of hours she work to create signs can be given by:
[tex]f(x)=(25-x)[/tex]
C. If 's' represents the number of hours that Anna works creating signs, we need to create a function g(s) that represents her earning creating signs.
So the number of hours Anna works creating signs for the coffee break is [tex]s[/tex], she gets paid $9.00 an hour for creating signs, so:
[tex]g(s)=9\times s=9s[/tex]
[tex]g(s)=9s[/tex]
D. We need to finf a composite function [tex]g(f(x))[/tex], to find the desired function we need to plug value of f(x) in the function g(s):
[tex]g(f(x))=9s=9(f(x))=9(25-x)=225-9x[/tex]
[tex]g(f(x))=225-9x[/tex]
The composite function g(f(x)) represents Anna's earnings while working just to create signs for the Coffee break.
E. To represent Anna's total earnings the functions that can be combined are h(x) and g(f(x)) because h(x) represents Anna's earnings while working as a barista and g(f(x)) represents Anna's earnings while she creates signs for the coffee break.
The function to represent Anna's total earnings can be given as:
[tex]T(x)=h(x)+g(f(x))=8.50x+225-9x[/tex]
where we must keep in mind that 'x' represents the number of hours she spent working as a barista in a 'week'.
Francesca spent 45 minutes on the internet yesterday if this is 5/6 of the time she spent on the computer,how long did she spend on the computer but not on the internet?
Answer:
37.5
Step-by-step explanation:
x= time not spent on the internet while on the computer
5/6 = 45/x
45*6/5 = x
This is the equation you should use
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!
A cleaning company charges x dollars per hour to clean floors and y dollars per hour to clean the rest of a house.
• When the company spends 2 hours to clean floors and 3 hours to clean the rest of a house, the total charge is $80.
• When the company spends 1 hour to clean floors and 4 hours to clean the rest of a house, the total charge is $100.
Which ordered pair represents the hourly charges to clean floors and to clean the rest of the house?
A) (2, 12)
B) (4, 24)
C) (12, 2)
D) (24, 4)
The answer is b. I see you got it. You are welcome.
2x-5=x+25 what is the answer for x because am stuck
2x - 5 = x + 25
-x -x
x - 5 = 25
+5 +5
x = 30
Answer: x = 30
Geometry help please Two Column Proofs
Find the value of k so that 48x-ky=11 and (k+2)x+16y=-19 are perpendicular lines.
Answer: k = -1 +/- √769
Step-by-step explanation:
48x - ky = 11
-48x -48x
-ky = -48x + 11
[tex]\frac{-ky}{-k} = \frac{-48x}{-k} + \frac{11}{-k}[/tex]
[tex]y =\frac{48x}{k} - \frac{11}{k}[/tex]
Slope: [tex]\frac{48}{k}[/tex]
*************************************************************************
(k + 2)x + 16y = -19
- (k + 2)x -(k + 2)x
16y = -(k + 2)x - 19
[tex]\frac{16y}{16} = -\frac{(k + 2)x}{16} - \frac{19}{16}[/tex]
[tex]y = -\frac{(k + 2)x}{16} - \frac{19}{16}[/tex]
Slope: [tex]-\frac{(k + 2)}{16}[/tex]
**********************************************************************************
[tex]\frac{48}{k}[/tex] and [tex]-\frac{(k + 2)}{16}[/tex] are perpendicular so they have opposite signs and are reciprocals of each other. When multiplied by its reciprocal, their product equals -1.
[tex]-\frac{(k + 2)}{16}[/tex] * [tex]\frac{k}{48}[/tex] = -1
[tex]\frac{(k + 2)k}{16(48)}[/tex] = 1
Cross multiply, then solve for the variable.
(k + 2)(k) = 16(48)
k² + 2k - 768 = 0
Use quadratic formula to solve:
k = -1 +/- √769
Candle food is on sale for 20% of the original price what is the discount of the key if the original price is $1.35
Hi there!
To calculate a discount or a mark-up in the price of a retail item, you need to multiply the given price of the item by the percentage, like so:
1.35 × 0.2 = 0.27
Then you add or subtract as necessary. In your case you would subtract since you are trying to find a discount price.
1.35 - 0.27 = 1.08
So the final price of the product after the discount is $1.08
Your friend, ASIAX
Romona is asked to draw a tree using a scale of 1 inch 3 meters she drwas a 4 inch tree how tall is the tree
1 inch : 3 meters
x 4 x 4
4 inch : 12 meters
Answer: 12 meters
A company can sell 2000 magazine subscriptions at $40 each. For each $5 increase in the price, it will sell 200 fewer subscriptions. What subscription price will provide the maximum revenue for the company?
$55
$40
$45
$50
ANSWER
The subscription price of $45 provides the maximum revenue for the company
EXPLANATION
When the price is $[tex]40[/tex], the company sells [tex]2000[/tex] quantities.
The total revenue accrued
[tex]=40\times2000[/tex]
[tex]=$80,000[/tex]
When the price increases to $[tex]45[/tex] the quantity sold will decrease by 200 magazines which is [tex]2000-200=1800[/tex]
The total revenue accrued
[tex]=45\times 1800[/tex]
[tex]=81000[/tex] dollars
When the price increases to $[tex]50[/tex] the quantity sold will decrease by 200 magazines again which is [tex]1800-200=1600[/tex]
The total revenue accrued
[tex]=50\times 1600[/tex]
[tex]=80000[/tex] dollars
When the price increases to $[tex]55[/tex] the quantity sold will decrease by 200 magazines which is [tex]1600-200=1400[/tex]
The total revenue accrued
[tex]=55\times 1400[/tex]
[tex]=77000[/tex] dollars
Hence a subscription price of $45 provides the maximum revenue for the company.
please help asap 30 pts
x - length of side of a square
A perimeter of a square: P = 4x
We know:
20 ≤ P ≤ 32
20 ≤ 4x ≤ 32 |divide by 4
5 ≤ x ≤ 8
Answer: b. 5 ≤ x ≤ 8
Answer:
ans in b
Step-by-step explanation:
HELP WILL GIVE BRAINLIEST! 45 POINTS IF YOU GIVE CORRECT ANSWER!!!!
Among the following arithmetic operations, which could the symbol □ represent given that the equation is (2□1)4+(6□3)2=10
1. Addition
2. Subtraction
3. Division
It would be subtraction because 2-1 would result into 1 multiplied by 4 would make 4 your answer. And then 6-3 would equal to 3, multiply 3 by 2, you would get 6. Then finally when you add both 4 and 6, you would get the final answer of 10.
The distance between the baseball stadium and the airport is 1.6×10^6 centimeters.Which unit of measurement is most appropriate to measure this distance?
Answer:
'Kilometers' is the most appropriate unit to measure this distance.
Step-by-step explanation:
The distance between the baseball stadium and the airport is [tex]1.6\times 10^6[/tex] centimeters.
[tex](1.6\times 10^6)cm = (16\times 10^5)cm[/tex]
Now, 10⁵ centimeters is equal to 1 kilometer.
That means, [tex](16\times 10^5)cm = (16\times 1)km= 16 km[/tex]
So, 'Kilometers' is the most appropriate unit to measure this distance.
Your local radio station is having their yearly music player and concert ticket giveaway. For one minute, every 5^\text{th}5 th 5, start superscript, t, h, end superscript caller will win a music player and every 7^\text{th}7 th 7, start superscript, t, h, end superscript caller will win concert tickets. You were just the first caller to win both a music player and concert tickets! What number caller were you?
Answer:
You were the 35th caller.
Step-by-step explanation:
For one minute, every 5th caller will win a music player and every 7th caller will win concert tickets.
If you were just the first caller to win both a music player and concert tickets, that means we need to find a least number which is divisible by both 5 and 7.
Actually we will find the LCM(Least common multiple) of 5 and 7.
[tex]5=1*5\\ \\ 7=1*7\\ \\ So, LCM = 1*5*7=35[/tex]
That means, you were the 35th caller.
Answer:
35
Step-by-step explanation:
Joyce is helping her aunt create craft kits. Her aunt has 138 pipe cleaners, what is the total numher of craft kits they can make?
Answer:
138 pipe cleaners can make 23 kit
Step-by-step explanation:
6 pipe cleaners = 1 kit
1 pipe cleaner = 1/6 kit
138 pipe cleaners = 1/6 x 138
138 pipe cleaners = 23