When both quantities in a rate are fractions, the strategy to write the rate as a unit rate is to divide both the numerator and denominator of the rate by their greatest common factor (GCF) to simplify the fraction.
To write the rate as a unit rate:
1. Identify the rate, which is a fraction with a numerator and a denominator.
2. Find the greatest common factor (GCF) of the numerator and denominator.
3. Divide both the numerator and denominator by the GCF to simplify the fraction.
4. The resulting simplified fraction is the unit rate.
For example, if the rate is 3/6, the GCF of 3 and 6 is 3. Divide both the numerator and denominator by 3:
3/6 ÷ 3/3 = 1/2
So, the unit rate of 3/6 is 1/2.
By converting the rate to a unit rate, we make it easier to compare the rate for a single unit of one quantity to a single unit of the other quantity, making it more convenient for comparison and analysis.
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Solve the equation
X-5 = - 4x-5
..
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The solution is
(Simplify your answer.)
OB. The solution is all real numbers.
O C. There is no solution
Step-by-step explanation:
x - 5 = -4x - 5
x + 4x = -5 + 5
5x = 0
x = 0/5
x = 0
A. x = 0
B. Yes, 0 is a real number
C. There is a solution
-x + 5x - 2x + 7 ?? i don’t know the answer
Answer:
-x + 5x - 2x + 7
=-3x+5x+7
=2x+7
Write the equation of the line parallel to y = 1/3x- 6 that passes through the point (-12,3) in slope-intercept form
Answer:
[tex]y=\frac{1}{3} x+7.[/tex]
Step-by-step explanation:
all the detail are in the attached picture, here is the short explanation step-by-step:
1) to select the values of slope and interception from the given equation;
2) using the rule of parallel lines to find the slope of the required line;
3) to write the required equation (the value of slope is known, the value of interception is inknown);
4) to calculate the unknown value of interception of the required equation after the substitution the coordinates of the point in the condition;
5) to make up the required equation using calculated slope and interception.
Integrate f(x,y,z) = (x+y+z) / (x^2 +y^2 + z^2) over the path r(t) = 2ti +2tj +t k, 0
The information about the path is incomplete, so I'll just use a domain of a ≤ t ≤ b, where a > 0 and b < ∞.
Differentiating r(t) gives
[tex]\vec r(t) = 2t\,\vec\imath + 2t\,\vec\jmath + t\,\vec k \implies \dfrac{\mathrm d\vec r(t)}{\mathrm dt} = 2\,\vec\imath + 2\,\vec\jmath + \vec k[/tex]
with magnitude √(2² + 2² + 1²) = √5.
Then we have
[tex]\displaystyle \int_C f(x,y,z)\,\mathrm ds = \int_a^b f(2t,2t,t) \left\|\frac{\mathrm d\vec r(t)}{\mathrm dt}\right\| \,\mathrm dt \\\\= \sqrt5 \int_a^b \frac{2t+2t+t}{(2t)^2+(2t)^2+t^2}\,\mathrm dt \\\\ = \sqrt5 \int_a^b \frac{5t}{5t^2} \,\mathrm dt \\\\ = \sqrt5 \int_a^b \frac{\mathrm dt}t \\\\ = \sqrt5 (\ln(b)-\ln(a)) = \boxed{\sqrt5 \ln\left(\frac ba\right)}[/tex]
22. What is the average(arithmetic mean) of all the integers
from -39 to 40, inclusive?
This range contains 80 numbers (40 in 1-40, and another 40 in -39-0).
We have
S = 1 + 2 + 3 + … + 38 + 39 + 40
S = 40 + 39 + 38 + … + 3 + 2 + 1
==> 2S = (1 + 40) + (2 + 39) + … + (39 + 2) + (40 + 1)
==> 2S = 40 × 41
==> S = 820
and
T = 0 + 1 + 2 + … + 37 + 38 + 39
T = 39 + 38 + 37 + … + 3 + 2 + 1
==> 2T = (0 + 39) + (1 + 38) + … + (38 + 2) + (39 + 0)
==> 2T = 40 × 39
==> T = 780
The average of the numbers in this range is equal to the total divided by the amount of numbers in the range, so
average = (40 + 39 + … + 1 + 0 + (-1) + … + (-38) + (-39))/80
average = (S - T )/80
average = (820 - 780)/80
average = 40/80 = 1/2
The school band has d drummers and 5 violinists. There are 2 more violinists than drummers. Which of the following equations represents the situation?
Answer:
A d = 5+2
Step-by-step explanation:
There are two more drummers than violinists
There are 5 violinists
5 + 2 = d
or in other words, d = 7
If my answer is incorrect, pls correct me!
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-Chetan K
Bronwyn wants to buy a house, so she has decided Savings to save one quarter of her salary. Bronwyn earns $47.00 per hour and receives an extra $28.00 a week because she declined How many hours must she work each week to achieve her goal? company benefits. She wants to save at least $550.00 each week.
Answer:
her goal is to have money 21250
I hope it helps u
A new car has a list price of $28,500 . Suppose that the dealer markup on this car is 10%. What is the dealer's cost?
Answer: 25650
Step-by-step explanation: 10% of 28500 is well 2850
28500-2850=25650
(if only i could get good rates on my car)
Change each base 10 number to a binary by the division method
5
Answer:
Step-by-step exA wall is 1200 sq ft.
A gallon of paint covers 200 sq ft.
Complete the conversion factor: 1 gallon / ? sq ftplanation:
Can you help me plzz i need it quick
Answer:
okbhyuugggfububububhhhukjgyi
Can someone help me please :00
Answer:
according to the dark spots which shows where each number goes to, it would be D.-2
What set(s) does the number ✓95 belong to? Mark all that applies: Natural, Whole, Integers, Rational, Irrational
Hi there!
»»————- ★ ————-««
I believe your answer is:
Irrational
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻[tex]\rightarrow \sqrt{95} = 9.74679...\\\\\text{This does \textbf{NOT} simplify into a whole number. This means that it's not a perfect square.}\\\\\text{Since } \sqrt{95} \text{ is not a perfect square, it is \textbf{irrational.}}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
mary bought 8 pounds of granola at 3.10 a pound for a family hiking trip how much did spend altogether?
Determine the expression for the perimeter of a rectangle with a length that is five less than twice its width
-(-v+y)-4(2y-4v)
How do I simplify this?
Step-by-step explanation:
hope you understand.
first simplify it by arranging correct signs then it's just subtraction or addition.
9,909.937 rounded to the nearest whole number
Answer and Step-by-step explanation:
To round to the nearest whole number, you look at the number in the tenths place.
- If this number is 5 and higher, then you round up (the number to the left of the tenths place [the ones place]).
- If it is lower than 5, then the number (in the ones place) stays the same.
9 is greater than 5, so we round up.
9,910 is the answer.
#teamtrees #PAW (Plant And Water)
I hope this helps!
please help me. thank you so much
Answer:
D. On sale at 60% of the original price
Step-by-step explanation:
That just means they are taking off 40% off the original price.
I hope this helps!
pls ❤ and mark brainliest pls!
If
,
then f(2) =
1/3
1
7
Answer:
7
Step-by-step explanation:
f(x) = 3x+1
f(2) means let x=2
f(2) = 3(2)+1
= 6+1
=7
[tex]\\ \sf\longmapsto f(2)[/tex]
[tex]\\ \sf\longmapsto 3(2)+1[/tex]
[tex]\\ \sf\longmapsto 6+1[/tex]
[tex]\\ \sf\longmapsto 7[/tex]
Maria has four hours of free time each day. She can spend it studying or working at the Wang's Chinese
Kitchen for $6.50 per hour. Curve A illustrates the trade-off between school grades and the wages Maria
could eam.
What are the maximum wages Maria could eam if she works five days a week?
b. What grades can she expect if she works 10 hours each week?
What advice would you give Maria if she were eaming $50 each week and making Ds?
a
c.
Opportunity cost is the cost of the alternative forgone;
The cost of Maria spending more time on her studies is the wages from working in the kitchen which she does not earn and vice versa
The correct values are as follows:
a. The maximum wages Maria could earn is $130
b. The grades she can expect if she works 10 hours each week is grade C
c. She should make a decision to either quit school or quit her job
d. To become a pharmacists, she should study more and quit her job
To become a restaurant owner/manager, she should develop her restaurant/managerial skills more at the
The reason for the above responses are as follows:
The known parameters are:
The number of hours of free time Maria has each day = 4 hours
The activities Maria can use the four hours for = Studying or working at the Wang's Chinese kitchen
The amount she can earn per hour working = $6.50 per hour
Question a. Required;
The maximum wages Maria could earn working 5 days a week
Solution;
Taking the each unit on the horizontal axis of the attached graph as one day. There are 5 units which equal 5 days
if she works for the five days, she spends all the available time working and she earns maximum wage on the graph which is $130The maximum wages Maria could earn if she works five days a week = $130
b. Required:
The grade she can expect by working 10 hours a week
Solution:
The number of hours available each week = 5 × 4 hours = 20 hours
If she works 10 hours each week, she spends the remaining 10 hours studying which is half of her available time
The grades she can expect by working 10 hours each week (half of her spare time) is giving by the value of the graph at the middle of the of half the length of the horizontal axis values which is grade C
c. Required:
The advice for Maria if she is earning $50 each week and is making Ds
Solution:
If Maria is earning $50 each week, the number of days she is working = One day
The number of days she spends reading = 4 days
In order to improve her grades, she should increase the number of days she spends reading, and therefore, she should spend more than 4 days or the 5 days reading and she should stop working and forgo the $50 for a grade C
Therefore;
Maria has to make a decision to either quit school or quit her job
d. Part of the question that can be included as seen from a similar question online is as follows;
The advice for her if she is interested in becoming a pharmacists or a restaurant owner/manager
If she is interested in becoming a pharmacist, she should stop working and focus on her studies; Quit her job
If she interested in becoming a restaurant owner or manager, she should spend less time reading and spend much of her time at the Wang's Chinese kitchen to develop are restaurant business skills;
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Please help with this worksheet I don’t know any of it
Answer:
4. 1/25
5. 1/16
6. 2/9
7. 5/567
8. 1/40
9. 2/175
10. 1/30
11. 2/5
12. 9/8
13. 4/3
14. 1
Step-by-step explanation:
sorry I only know how to do 4-14. I hope this helps you.
What is the distinguishing feature of a profession?
Answer:
Some things you must have in order to be that certain profession is:
Accounts receivable (order to cash)
Accounts payable (procure to payment)
Financial close.
Time and expense capture.
Fund accounting.
Project accounting.
Revenue recognition and management.
Step-by-step explanation:
If need anything else let me know, if not pls mark me as brainliest :)
what is trigonometry ?
no explanation required !
Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.
how high is a tree that cast a 23 ft Shadow at the same time a 6 ft pole has a shadow which is 14 feet long
Answer:
9.857142857 ft
Step-by-step explanation:
We can use a ratio to solve
23 ft shadow 14 ft shadow
-------------------- = ---------------
x ft high 6 ft high
Using cross products
23*6 = 14 * x
Divide each side by 14
23*6/14 = x
9.857142857 ft
the inequality -3n<12 is equivalent to
a. n < 4
b. n < -4
c. n > 4
d. n > -4
e. n > 36
Answer: D. n > -4
Step-by-step explanation:
Given
-3n < 12
Divide both sides by -3. REMEMBER to change the [>,<] signs when multiplying or dividing a negative term
-3n / -3 > 12 / -3
n > -4
Hope this helps!! :)
Please let me know if you have any questions
Hey there! I'm happy to help!
Inequalities are solved like normal equations with a few extra rules.
So, we could simply divide both sides by -3 to get our answer, but n<-4 would actually be incorrect. With inequalities, dividing by a negative number means you have to flip the inequality sign. This is because you turn the other side negative so you need to adjust the inequality sign to match it.
So, our final answer will actually be n>-4.
Have a wonderful day and keep on learning! :D
Use the approach in Guass's Problems to find the following sum of arithmetic sequence
a. 1+2+3+4...+101
b. 1+3+5+7...+997
c. 4+9+14+19...+494
d. 881+872+863+854+...+8
a. The sum of the sequence is
Answer:
a) 5151 b) 249001 c)24651 d)43561
Step-by-step explanation:
a) a1=1 a2=2
d=a2-a1= 2-1=1
Define the quantity of the terms of this sequence
an=a1+d(n-1)
101= 1+ 1(n-1)
n=101
Sn= (a1+an)/2*n=( (1+101)/2)*101=51*101=5151
b) a1=1 a2=3
d=a2-a1=3-1=2
an=a1+d(n-1)
997= 1+ 2(n-1)
498= n-1
n=499
Sn= (a1+an)/2*n= (1+997)/2*499= 249001
c) a1=4 a2=9
d=a2-a1=9-4=5
an=a1+d(n-1)
494=4+5(n-1)
n=99
Sn= (a1+an)/2*n=( 4+494) /2*99= 498/2*99= 249*99= 24651
d) a1=881, a2=872
d=a2-a1= 872-881=-9
an= a1+d(n-1)
8=881-9*(n-1)
9(n-1)= 873
n=98
Sn= (a1+an)/2*n= (881+8)/2*98= 889*49= 43561
2. Consider the addition operations below and choose whether the result can be
rational, irrational, or both.
Expressions
Rational
Irrational
4/5 + 3 /
(2 + 657) + (-655
√ √ + 2 VA
the length of a rectangle is 8cm and the height is 16cm find the answer of the above figures using this formular...
2(a + b) Perimeter
(B×H) Area
[tex]\\ \sf\longmapsto Perimeter=2(L+B)[/tex]
[tex]\\ \sf\longmapsto Perimeter=2(16+8)[/tex]
[tex]\\ \sf\longmapsto Perimeter=2(24)[/tex]
[tex]\\ \sf\longmapsto Perimeter=48cm[/tex]
Area:-
[tex]\\ \sf\longmapsto Area=Length\times Breadth[/tex]
[tex]\\ \sf\longmapsto Area=8(16)[/tex]
[tex]\\ \sf\longmapsto Area=128cm^2[/tex]
Pat was 32 when his daughter Emma was born, and 36 when his son Andy was born. If the sum of the tree ages is now 100, how old is Andy Now?
No clue what I’m doing. Please help.
Answer:
n1= -4
n2= 1
n3= 6
Step-by-step explanation:
the n column represents the numbers that are in n's place
eg n=1
n=2
n=3
5x1 - 9
5x2 -9
5x3 -9
Answer and Step-by-step explanation:
What this question wants you to do is fill out the right side (or the outputs) of the table.
To do this, plug in the value of n into the equation and solve.
n = n, 5n - 9
n = 1, 5(1) - 9 = -4
n = 2, 5(2) - 9 = 10 - 9 = 1
n = 3, 5(3) - 9 = 15 - 9 = 6
So, the values (in bold) should go into the table as so:
1 | -4
2 | 1
3 | 6
#teamtrees #PAW (Plant And Water)
I hope this helps!
if SP is equal to rupees 400 and loss percent is 20% find CP
100-20=80%=400
[tex]\\ \rm\longmapsto 80\%\:of\:CP=400[/tex]
[tex]\\ \rm\longmapsto CP=400\times \dfrac{100}{80}[/tex]
[tex]\\ \rm\longmapsto CP=5(100)[/tex]
[tex]\\ \rm\longmapsto CP=500[/tex]
Step-by-step explanation:
Given,
S.p.=Rs400
Loss percent(L%) =20%
C.p.=?
We know,
S.p. =(100-L) % of c.p.
or,400=(100-20)% *c.p.
or,400=80% *c.p.
or, 400=80/100*c.p.
or,c.p.=Rs.500
Here, c.p.=Rs.500