Answers
Answer:
Constant of proportionality: [tex]\frac{1}{3}[/tex]
Equation: [tex]y=\frac{1}{3}x[/tex]
Step-by-step explanation:
The constant of proportionality is the ratio between y and x, according to the following formula
constant of proportionality = k = y/x
Take the given pairs and replace the data.
1.
[tex]k=\frac{\frac{2}{3}}{2}[/tex]
[tex]k = \frac{1}{3}[/tex]
2.
[tex]k = \frac{1}{3}[/tex]
3.
[tex]k=\frac{\frac{10}{3}}{10}[/tex]
[tex]k = \frac{1}{3}[/tex]
4.
[tex]k = \frac{4}{12}[/tex]
[tex]k = \frac{1}{3}[/tex]
As you can see, the constant is the same for all the pairs.
constant of proportionality = [tex]\frac{1}{3}[/tex]
Now, in order to know the equation make a graph of the given data.
The graph is in the picture
Since it is a line, use the equation of the line in point slope form
[tex]y- { y }_{ 1 } = m \left( x- { x }_{ 1 } \right)[/tex]
where (x1, y1) = any pair of the data
m = slope = constant of proportionality
Replace the data in the equation
[tex]y-1 = \dfrac{ 1 }{ 3 } \left( x-3 \right)[/tex]
Use the distributive property to multiply [tex]\frac{1}{3}[/tex] by x - 3
[tex]y-1=\frac{1}{3}x-1[/tex]
Add 1 to both sides
[tex]y = \dfrac{ 1 }{ 3 } x-1+1[/tex]
Add −1 and 1 to get 0
[tex]y=\frac{1}{3}x[/tex]
or
[tex]y=\frac{x}{3}[/tex]
Related Questions
Keisha is buying a pair of jeans that are regularly
$54.99. If they are on the clearance rack for 35%
off and sales tax is 7.2%, what is the total amount
she will pay?
Answers
The answer is 20.64 dollars
Ramon read twice on Saturday. In the morning, he read for
1
2
hour. That afternoon, he read for
5
12
of an hour. How much time did Ramon spend reading on Saturday?
Answers
Answer:
if the numbers are separated by a fraction bar the response should be 11/12th of an hour on Saturday.
Step-by-step explanation:
1/2=6/12
5/12+6/12=11/12
please help meeeeee
Grace takes out a loan of $9,573.00 at a 4% simple rate for 4 years. a) How much interest will be paid after 2 years? b) How much total interest will be paid for this loan?
Answers
#1
Time=T=2yrsInterest be I
[tex]\\ \rm\hookrightarrow I=PRT/100[/tex]
[tex]\\ \rm\hookrightarrow I=9573(4)(2)/100=76584/100=765.84\$[/tex]
#2
T=4yrs[tex]\\ \rm\hookrightarrow I=9573(4)(4)/100=153168/100=1531.68\$[/tex]
Answer:
a) $765.84
b) $1,531.68
Step-by-step explanation:
Simple interest formula: SI = PRT
where P = principal amount of loan, R = annual rate of Interest in decimal format, and T = Time.
Given:
P = 9573R = 4% = 4/100 = 0.04a) when T = 2:
SI = 9573 x 0.04 x 2 = 765.84
b) when T = 4:
SI = 9573 x 0.04 x 4 = 1531.68
What number is half way between –3 and 4 ?
Answers
Explanation:
-3 + 3 = 0
4 - 3 = 1
And the number in between 0 and 1 is .5
Hope this helps!
Please consider giving me brainliest.
Answer:
.5?
Step-by-step explanation:
I think I'm right.................maybe?????
describe the slope of the line (-3,1) and (2,-2)
Answers
Answer:
1,5
Step-by-step explanation:
You do 2-1 which is 1
Then do 2-(-3) which is 5 so the answer is (1,5)
If x - 5y = 6, what is the value of y when
X= -4?
A:-2
B-2/5
C:2/5
D:2
Answers
Answer:
I think the answer is D. 2
Answer:
The answer is A
Step-by-step explanation:
x is equal to - 4
so the the x is replaced by the- 4 and then you will group like- items
Divide both sides by - 5 to get - 2
an employee earns 8% commission on the sale on clothing sold if she sells 4,500 with of clothing worth will help commission be
Answers
Answer:
360
Step-by-step explanation:
8% of 4500 is 360
Find the missing side lengths. Help pleaseee
Answers
a = 3
~ hopefully I did the math right!
find the nth term in the sequence:
-5, -2, 3, 10, 19
Answers
Answer:
75
Step-by-step explanation:
Start by adding 3 then each time add an odd number to the sequence
First time add 3 then add 5 then add 7 then add 9 etc.
so we have:
-5, -2, 3, 10, 19, 30, 43, 58, 75
so its 75
Please mark Brainliest :)
Answer:
The pattern in +3, +5, +7, +9, +11, +13, +15, +17, +19. . .
6th = 30
7th = 43
8th = 58
9th = 75
10th = 94
Mr.cheeks collects 95 strawberries to feed his family. He provides the same number of strawberries to each of his 6 hamster children. After giving out as many strawberries as possible, how many will mr. Cheeks have leftover for himself
Answers
Answer:
Each Children gets = 15 strawberry
leftover for Mr.Cheek = 5 strawberry
Step-by-step explanation:
Given;
Mr.cheeks collects 95 strawberries to feed his family.
He provides the same number of strawberries to each of his 6 hamster children.
To Find;
After giving out as many strawberries as possible, how many will mr. Cheeks have leftover for himself
Solve;
Since, Mr.cheeks total strawberries is 95 and he has 6 hamster children
we have to divide to see how much each children gets
95/6 = 15 with 5 remainder.
Hence, we can conclude that each children gets 15 and Mr.Cheeks have 5 leftover for himself
[RevyBreeze]
How do I solve this?
Answers
Answer:
below the ans
Step-by-step explanation:
cos k = 5/23
= .21
533.93 divided by 2 PLEASE help
Answers
Answer:
The answer is 266.965
Please help me it’s a long but easy question :(
Suhaila works mowing lawns and babysitting. She earns $7.80 an hour for mowing and $7.60 an hour for babysitting. How much will she earn for 6 hours of
mowing and 1 hour of babysitting?
Answers
Answer:
she earns 7.80 an hour for mowing and 7.60 for babysitting so
6 hours of mowing that is 7.80 x 6 which is $46.8
and 1 hour of babysitting is $7.60 so we add up which is $54.40 in total
Answer:
$54.40
Step-by-step explanation:
You do 7.80*6=46.80 and 760*1=7.60 then add 46.80+7.60=54.40.
Help me please I really need help ,,,,…
Answers
I have 10 apples and lost 5 then got 5 more apples from my mom. My mom also gave me 20 oranges so i ate 12 oranges and 5 apples how many oranges do i have left over?
Answers
Answer:
you would have 8 oranges and 5 apples
0.9(x−20)=830
x=
0.9x+20=830
x=
Answers
Answer:
Step-by-step explanation:
1) x-20 = 830/0.9 = 8300/9
So x-20 = 8300/9 -> x=8300 /9 + 20 = 8480/9
2)try on your own
4. Eddie invests £4000 into a savings account, the bank pays him 4% compound
interest per annum. At the end of n years he has £4679.43 to the nearest
penny. What is the value of n?
Answers
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\pounds 4679.43\\ P=\textit{original amount deposited}\dotfill &\pounds 4000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years \end{cases}[/tex]
[tex]4679.43=4000\left(1+\frac{0.04}{1}\right)^{1\cdot t}\implies \cfrac{4679.43}{4000}=(1.04)^t \\\\\\ \log\left( \cfrac{4679.43}{4000} \right)=\log(1.04^t)\implies \log\left( \cfrac{4679.43}{4000} \right)=t\log(1.04) \\\\\\ \cfrac{\log\left( \frac{4679.43}{4000} \right)}{\log(1.04)}=t\implies 4\approx t[/tex]
Find the next two terms in this sequence, 4,8 ,16
Answers
The sequence is going by each number so 4+4= 8
8+8= 16
Now 16+16= 32
Answer:
32, 64
Step-by-step explanation:
There is a common ratio between consecutive terms , that is
[tex]\frac{8}{4}[/tex] = [tex]\frac{16}{8}[/tex] = 2
to obtain a term in the sequence multiply the previous term by 2
16 × 2 = 32
32 × 2 = 64
Circle the smallest fraction:
1/4
1/5
5/16
1/3
Answers
Answer:
B
Step-by-step explanation:
1/4=25%
1/5=20%
5/16=31.25%
and 1/3=33%
Eddie had 6 boxes of crayons. Each box contained an equal number of crayons After giving her friend 10 crayons, she was left with a total of 26 crayons. How many crayons were in each box before Eddie gave the crayons to her friend?
Answers
Answer:
6
Step-by-step explanation:
6x-10=26
+10 +10
6x=36
divide by 6
x=6
An amphitheatre has 18 seats in the first row, 20 in the second, 22 in the third, and so on, for 22 rows. How many seats are in the amphitheatre?
The amphitheatre has seats,
Answers
Since it’s 18 first then 20 and 22 you have to add two to 22 19 more times and then add 18 and 20
A store manager gathers some demographic information from the store's customers. The following chart summarizes the age-related information they collected:
Age Number of Customers
< 20 <20 83
20-29 63
30-39 99
40-49 65
50-59 73
≥ 60 ≥60 69
One customer is chosen at random for a prize giveaway. (Round answers to 4 decimal places.)
a. What is the probability that the customer is at least 20 but no older than 59?
b. What is the probability that the customer is either older than 60 or younger than 40?
c. What is the probability that the customer is at least 60?
Answers
Using it's concept, it is found that the probabilities are as follows:
a) 0.6637.
b) 0.6947.
c) 0.1527.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there is a total of 83 + 63 + 99 + 65 + 73 + 69 = 452 customers.
Item a:
63 + 99 + 65 + 73 = 300 are at least 20 but no older than 59, hence:
p = 300/452 = 0.6637.
Item b:
83 + 63 + 99 = 245 are younger than 40.
69 are older than 60.
Hence:
p = (245 + 69)/452 = 0.6947.
Item c:
69 customers are at least 60, hence:
p = 69/452 = 0.1527.
More can be learned about the probability concept at https://brainly.com/question/15536019
Sally went to buy candy for her valentine. The box of candy was $5.65 before tax. If tax is 5.25%, what will Sally’s total be with tax?
Answers
Answer:
5.946625
Step-by-step explanation:
i think this is right
A store pays $5 for a computer mouse and marks the price up by 45% what is the amount of the mark-up
Answers
Answer:
Mark-up = $2.25
Total price after mark-up = $7.25
Step-by-step explanation:
Well, 45% of $5 is $2.25, so now you just add that back to the total, which would be $7.25.
Solve for x and y.
2 answers
Answers
To find the x-intercept, set y = 0 \displaystyle y=0 y=0.
To find the y-intercept, set x = 0 \displaystyle x=0 x=0.
Simplify the following expression 5(m+1)-1
Answers
[tex]5(m + 1) - 1 \\ 5m + 5 - 1 \\ 5m + 4[/tex]
Answer:
5m+4
Step-by-step explanation:
Find the area of the shape.
Either enter an exact answer in terms of π or use 3.14and enter your answer as a decimal.
some one plssssss
Answers
Answer:
50.24 units^2
Step-by-step explanation:
A=(3.14)(4)^2
jayden and chandra are cleaning the house. it has 12 rooms, and each room is about the same size. when jayden cleans by himself, it takes him 6 hours. when chandra cleans by herself, it takes her 12 hours. when they clean the house together, they finish in 4 hours. when they work together, how many rooms does jayden clean and how many does chandra clean?
Answers
Jayden's work rate is twice Chandra's work rate, and, the rooms cleaned
by Jayden is twice the number of rooms cleaned by Chandra.
Response:
Jayden cleans 8 rooms while Chandra cleans 4 roomsWhich method can be used to find the number of rooms cleaned by Jayden and Chandra?Number of rooms in the house = 12
The time that Jayden takes to clean the house = 6 hours
Time that it takes Chandra to clean the house by herself = 12 hours
Time it takes both of them to clean the house = 4 hours
Required:
The number of rooms that Jayden clean and the number of rooms that
Chandra cleans when they work together.
Solution:
Given that the time it takes Jayden to clean the house is half the time
taken by Chandra.
Therefore;
The number of rooms Jayden cleans in 4 hours is twice the number of rooms cleaned by Chandra, which gives;
Ratio of the number of rooms cleaned by Jayden to the number cleaned by Chandra is 2 : 1
Total number of rooms cleaned = 12
[tex]Number \ of \ rooms \ cleaned \ by \ Jayden = \dfrac{2}{2 + 1} \times 12 = \underline{8 \ rooms}[/tex]
The number of rooms cleaned by Chandra = 12 - 8 = 4 rooms
Learn more about ratios here:
https://brainly.com/question/3568924
Question is in the picture
What's the ratio for tan B
Answers
Answer:
C. [tex]tan(B) =2[/tex]
Step-by-step explanation:
Here we can see tan(B) has a opposite side of 2 and adjacent of 1.
[tex]tan(B) = \frac{opposite}{adjacent}[/tex]
[tex]tan(B) = \frac{2}{1}[/tex]
[tex]tan(B) =2[/tex]
Answer:
[tex]\textsf{tan(B)}=2[/tex]
Step-by-step explanation:
The trig ratio for tan is tan(x) = O/A
where x is the angle,
O = side OPPOSITE to the angle, and
A = side ADJACENT to the angle
For angle B:
O = 2
A = 1
Therefore, [tex]\textsf{tan(B)}=\frac{2}{1}=2[/tex]
6 × 1 + 5 × 1/10 please answer
Answers
Answer: 13/2 or 6 1/2
Step-by-step explanation:
6 × 1 + 5 × 1/10
6 + 5 x 1/10 <-- Reduce 5 and 10 in 1/10 by the GCF, 5
6 + 1/2
Use 2 as a common denominator so multiply 6 by 2
12/2 + 1/2
13/2 or 6 1/2