[tex]\dfrac{10}{12} = \dfrac{10 \times \tfrac 12 }{12 \times \tfrac 12} =\dfrac{5}6[/tex]
Answer:
5/6Step-by-step explanation:
10 ÷ 2/12 ÷ 2=> 5/6Conclusion:
Therefore, the simplified form of 10/12 is 5/6.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Some information about a direct variation is given in the table below. If the equation
of this direct variation is y = kx , find the coefficient k and fill in the missing
information.
Answer:
Step-by-step explanation:
y = kx ;
k = [tex]\frac{y}{x}[/tex] ; x = [tex]\frac{y}{k}[/tex]
~~~~~~~~~~~~~
k = [tex]\frac{1}{2}[/tex] ÷ 1 = [tex]\frac{1}{2}[/tex]
[tex]y_{1}[/tex] = [tex]\frac{1}{2}[/tex] × ( - 8 ) = - 4
[tex]y_{2}[/tex] = [tex]\frac{1}{2}[/tex] × ( - 4 ) = - 2
[tex]y_{3}[/tex] = [tex]\frac{1}{2}[/tex] × 2 = 1
[tex]x_{5}[/tex] = [tex]\frac{1}{3}[/tex] ÷ [tex]\frac{1}{2}[/tex] = [tex]\frac{2}{3}[/tex]
[tex]x_{6}[/tex] = - [tex]\frac{1}{4}[/tex] ÷ [tex]\frac{1}{2}[/tex] = - [tex]\frac{1}{2}[/tex]
[tex]x_{7}[/tex] = 0
( x , y ) : ( - 8 , - 4 ), ( - 4 , - 2 ), ( 2 , 1 ), ( 1 , [tex]\frac{1}{2}[/tex] ), ( [tex]\frac{2}{3}[/tex] , [tex]\frac{1}{3}[/tex] ), ( - [tex]\frac{1}{2}[/tex] , - [tex]\frac{1}{4}[/tex] ), ( 0 , 0 )
Please solve this question
Answer:
46?
Step-by-step explanation:
23*2=46
Answer:
37.31 cm
Step-by-step explanation:
∡ AB = 180 - 148 = 32° = ∡ DE
∡ CD = 360 - ∡ AE - ∡ AB - ∡ BC - ∡ DE = 360 - 148 - 32 - 87 - 32 =61°
∡ CE = 61 + 32 = 93°
arc length = 2[tex]\pi[/tex]r [tex]\frac{angle}{360}[/tex] = 2×3.14×23×[tex]\frac{93}{360}\\[/tex] = 37.31 cm
Can someone help me?
Answer:
I figure you could simplify it by multiplying both sides by 6, resulting in -31+23=-30+18-1+5
-8=-8
Step-by-step explanation:
The population of a pigeons in a city is 100 and is growing exponentially at 20% per year. Write a function to represent the population of pigeons after
t
t years, where the monthly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per month, to the nearest hundredth of a percent
Answer:
p(t) = 100×1.0153^(12t)1.53% per monthStep-by-step explanation:
In general, the function will be written ...
p(t) = (initial value)×(growth factor)^t
where t is in units comparable to those applicable to the growth factor. The growth factor is found from ...
growth factor = 1 + growth rate
Here, the growth rate is given as 20% per year, so the growth factor per year is ...
1 +20% = 1.20
The initial value is given as 100, so we can write the exponential function as ...
p(t) = 100×1.20^t
__
The time period units for t are supposed to be years, but we want to find the growth rate for a month. We can do that by recognizing there are 12 months in a year. In the above equation, we can use (1/12)(12t) in place of t, then figure the growth factor (and growth rate) per month.
p(t) = 100×(1.20^(1/12))^( 12t)
p(t) = 100×1.0153^(12t) . . . . population exponential function
This shows the monthly growth factor is 1.0153, so the monthly rate of change (growth rate) is ...
1.0153 -1 = 0.0153 = 1.53% . . . . monthly rate of change
Answers:
Function is [tex]P(t) = 100(1.0153)^{12t}\\\\[/tex]Monthly growth rate is roughly 1.53%=====================================================
Explanation:
The population starts at 100 pigeons. After a year, the population goes up by 20%, meaning the population goes up by 20. It lands on 120 after a full year (100+20 = 120).
Dividing the "before" and "after" population amounts gets us 120/100 = 1.20
If we didn't worry about the monthly rate, and only cared about the annual rate of growth, then the population function would be
[tex]P(t) = 100(1.20)^t[/tex]
where t is the number of years and P(t) is the population for that year number. Notice how the 1.20 is the base of the exponential to quickly tell the reader the annual rate of growth. We read off the .20 portion and that converts to 20% after moving the decimal 2 spots to the right.
If we were to plug t = 0 into that function, then we'd get P(0) = 100. Inputting t = 1 leads to P(1) = 120. This helps confirm we have the correct annual growth rate function.
---------------------
Unfortunately, your teacher doesn't want the annual growth rate function. Instead, they want you to write a function where the reader can easily pick out the monthly rate of change without having to do any math. This is due to the instructions that "the monthly rate of change can be found from a constant in the function". Let m be this constant.
Since t is the number of years, this means t = 1/12 represents 1/12 of a year, aka 1 month. If you were to compute P(1/12), then you should get roughly 101.530947049973
Divide this amount over the initial population to find m.
m = 101.530947049973/100 = 1.01530947049973
So we get m = 1.0153 after rounding to four decimal places.
The number m is in the form 1+x. Solving 1+x = m will lead to x = 0.0153 to indicate a monthly rate of change is roughly 1.53% since we move the decimal point 2 spots to the right to go from 0.0153 to 1.53%
The pigeon population is increasing by roughly 1.53% each month.
This is why computing this m value leads to the reader able to spot the monthly rate of change without having to resort to a calculator. All they have to do is read the digits to the right of the decimal point and convert that to percentage form.
---------------------
An alternative way to compute this value is to use this formula
m = (1+r)^(1/12)
We'll plug in the annual rate r = 0.20 to get:
m = (1+r)^(1/12)
m = (1+0.20)^(1/12)
m = 1.01530947049973
m = 1.0153
We get the same approximate value as earlier.
---------------------
Whichever method you use, you should get roughly m = 1.0153
We're given that A = 100 is the initial population
So we'll then be able to form this function
[tex]P(t) = A*(m)^{12t}\\\\P(t) = 100(1.0153)^{12t}\\\\[/tex]
This represents the monthly growth of the population where t is in years. Note that after something like t = 3 years, we have 12t = 12*3 = 36 months pass by. So that's why the 12t is in the exponent rather than simply t.
Once again, for comparison we have...
[tex]P(t) = 100(1.20)^{t}\\\\[/tex] for annual growth[tex]P(t) = 100(1.0153)^{12t}\\\\[/tex] for monthly growthEach function has t represent the number of years. The difference is the base of each exponential to tell us the respective annual or monthly growth rate. Also, the exponent up top must be adjusted depending on which you go for.
---------------------
You may be wondering: "what if the exponent in the monthly growth rate function wasn't 12t?". Let's find out. We'll assume the monthly growth rate function is [tex]P(t) = 100(1.0153)^{t}\\\\[/tex] and show that an error happens.
If we plugged in something like t = 1, we should get P(t) = 120 like mentioned earlier.
[tex]P(t) = 100(1.0153)^{t}\\\\P(1) = 100(1.0153)^{1}\\\\P(1) = 100(1.0153)\\\\P(1) = 101.53\\\\[/tex]
That value of 101.53 is the approximate population number after 1 month, rather than 1 year. Making the exponent 12t will fix the issue.
A storage container leaks water at a rate of 15 gallons every 30 days.
What is the unit rate in gallons per week?
Enter your answer as a mixed number in simplest form in the box.
Answer:
i think 3.5 gallons per week
[tex]3 \frac{1}{2} [/tex]
Step-by-step explanation:
15 gallons every 30 days
x gallons per weeks (7 days)
15×7 = 30x
105 = 30x
105/30 = x
3.5 = x
answer as a mixed number in simplest form = 3 1/2
Answer: The answer is 3 1/2
Step-by-step explanation:
I took the quiz and did 100% :)
-X + 2y= -3 and -8x — 3y= -5
Answer:
x=1, y=-1. (1, -1).
Step-by-step explanation:
-x+2y=-3
-8x-3y=-5
----------------
-8(-x+2y)=-8(-3)
-8x-3y=-5
------------------------
8x-16y=24
-8x-3y=-5
-----------------
-19y=19
y=19/-19
y=-1
-x+2(-1)=-3
-x-2=-3
-x=-3+2
-x=-1
x=1
(1, -1)
Answer:
x = 1, y = -1
or as an ordered pair, (1, -1).
Step-by-step explanation:
-x + 2y = -3
-8x — 3y = -5
Multiply first equation by -8:
8x - 16y = 24
Add this equation to the second equation:
-19y = 19
y = -1.
Plug y = -1 into the second equation:
-8x - 3(-1) = -5
-8x + 3 = -5
-8x = -8
x = 1.
a-y= b+y/a make y subject
Answer:
y = [tex]\frac{a^2-ab}{a+1}[/tex]
Step-by-step explanation:
a - y = b + [tex]\frac{y}{a}[/tex] ( multiply through by a to clear the fraction )
a² - ay = ab + y ( subtract y from both sides )
a² - ay - y = ab ( subtract a² from both sides )
- ay - y = ab - a² ← factor out y from each term on the left side
y(- a - 1) = ab - a² ( divide both sides by - a - 1 )
y = [tex]\frac{ab-a^2}{-a-1}[/tex] ( multiply numerator/ denominator by - 1 )
y = [tex]\frac{a^2-ab}{a+1}[/tex]
Find the 62nd term of the arithmetic sequence
15, 13, 11, ...
Answer:
[tex]a_{62}=-107[/tex]
Step-by-step explanation:
This is an arithmetic sequence:
[tex]a_n=a_1+(n-1)d[/tex]
where d is the common difference and n is the index of any given term.
The common difference of the given sequence is -2:
[tex]13-15=-2\\11-13=-2[/tex]
Using the first term and the common difference, you can write the equation for this sequence:
[tex]a_n=15+(n-1)(-2)[/tex]
And using that equation, you can find the 62nd term:
[tex]a_{62}=15+(62-1)(-2)\\a_{62}=15+(61)(-2)\\a_{62}=15-122\\a_{62}=-107[/tex]
1. Rosie orders dessert at the cafe. The total bill is $50. She tips the waiter 10%.
How much money does the waiter get?
Answer:
5
Step-by-step explanation:
this means it'll be $55
Write 15.5 as a fraction in the simplest form and as a decimal
Find the value of √1600×8²+√4225
Step-by-step explanation:
√1600×8²+√4225
40 x 64 + 65
= 2625
The weight of an object on moon is 1/6 of its weight on Earth. If weight of an object on Earth is 18/5 kg, what would be its weight on moon? Please help me!!!!
Answer:
3/5 kgStep-by-step explanation:
The weight of an object on Moon is 6 times smaller than same on Earth.
If it weights 18/5 kg on Earth then its weight on Moon is:
18/5 * 1/6 = 3/5 kgAnswer:
Solution given:
weight of moon=1/6 th of Earth
If weight of Earth is 18/5 kg
weight of moon=?
we have
weight of moon: 1/6 of weight of Earth
=1/6*18/5
=3/5kg
Its weight on moon is 3/5 kg
i need help with this question (3x56-7+76)/99=
Answer:
x^56+23/33
Step-by-step explanation:
The has the power of 56
Simplify please...Simplify Simplify
Answer:
See images.
Step-by-step explanation:
For these kinds of problems, get a common denominator. Put everything over that common denominator and add or subtract the terms in the numerator. Combine like terms. See images.
Answer:
Here are the answers.
Step-by-step explanation:
Please help Tysm!! <3
Answer:
68 homes
Step-by-step explanation:
1. First, let's set up a proportional relating the home to the # of hours.
[tex]\frac{17}{49} = \frac{x}{196}[/tex]2. Now, let's see if we can divide 196 by 49. If so, the quotient we get is the number we multiply 17 by to get x.
[tex]196/49 = 4[/tex] This means that we multiply 17 by 4 to get x.[tex]17 * 4 = 68[/tex]Therefore, the answer is 68 homes.
Which quantity of fruit contains an amount of vitamin C closest to the combined
amount of vitamin C in 50 g grams of acerola cherries and 150 g grams of
kiwifruit?
A. 2,000 g grams of black currants
B. 800 g grams of guava
C. 1,800 g grams of pineapple
D. 600 g grams of strawberries
Answer:
c would be the closest due to the total amount of vitamin c in the objects.
The quantity of fruit which contains an amount of vitamin C closest to the combined content is: C. 1,800 g grams of pineapple.
How to calculate the amount of vitamin.In this exercise, we would determine the amount of vitamin C that is present in a combination of 50 grams of acerola cherries and 150 grams of kiwifruit.
For acerola cherries:
100 grams of acerola cherries = 1678 mg.
50 grams of acerola cherries = X mg.
Cross-mutiplying, we have:
X = 83,900/100 = 839 mg.
For kiwifruit:
100 grams of kiwifruit = 105 mg.
150 grams of kiwifruit = Y mg.
Cross-mutiplying, we have:
Y = 15,750/100 = 157.5 mg.
Combine vitamins = 157.5 + 839 = 996.5 mg.
Based on intuition, we would choose 1,800 grams of pineapple.
100 grams of pineapple = 56 mg
1,800 grams of pineapple = Z mg.
Cross-mutiplying, we have:
Z = 100,800/100 = 1008 mg.
Thus, 996.5 mg of vitamin C is closest to 1008 mg.
Note: If you do the above computations for other quantities of fruit, you'll get a value far from 996.5 mg.
Read more on vitamins here: https://brainly.com/question/9348916
Which set of numbers are ordered from least to greatest?
O A. 7,1-41, -7,0,-131, 3
B. -31, -7,0,3,7, 1-4]
C. -7,-131,0,3, 4,7
D. 7.1-41,3,0.-131, -7
How i can answer this question
60m
How?
5m × 3m × 4m
5m × 3m = 15m
15m × 4m = 60m
Therefore
the answer is 60
Overnight the low temperature dropped to-6 degrees Fahrenheit. If the temperature during the was 11 degrees Fahrenheit, what was the difference between the high and low temperatures?
Answer:
17 degrees F
Step-by-step explanation:
11 - (-6) = 17
Subtracting a negative is the same as adding.
Draw the polygon with the given vertices in a coordinate plane.
(3,2),(4,7),(6,0)
I will give you brainlist if you draw it out too
PLEASE TYPE IN THE COORDINATES
Answer:
Step-by-step explanation:
13. This body system regulates body activities using homones. Slow response, tong lasting
A. Respiratory
C. Skeletal
B. Muscular
D. Endocrine
Answer:
hi
Step-by-step explanation:
Two forces X = 50N and Y = 60 N are acting on a wooden block and it moves to the left as
shown below in figure.
The force which causes motion is ?
what is the domain of the function
Answer:
(a) -∞ < x < ∞
Step-by-step explanation:
Unlike the square root function, the cube root function is defined for all values of its argument. Here, x can take on any value and the function will be defined for that value.
-∞ < x < ∞
For 18-20, factor each of the following and show work.
18. 5x^4 - 25x
19. 4x^2 - 9
20. x^2+8x+12
Step-by-step explanation:
20. x^2+8x+12
x^2 + 6x +2x + 12
X(X+6) + 2(X+6)
(X+2) (X+6)
18. 5x^4 - 25x
5x(x^3-5)
19. 4x^2 - 9
4x^2/4 -9/4 = 0/4
x^2 = 9/4
X=√9/4
Suppose two bicyclists start at the same location.
The first bicyclist rides due north and the other rides
due west. Find the distance in miles that the first
bicyclist rode if they are 3/2 miles apart after riding
for 1 hour at the same speed.
Answer:
Step-by-step explanation:
See attachment.
If both cyclists travel for the same time and speed, they will have travelled the same distance. Since one is headed north and the other east, we can see that the distance between them in one hour is the hypotenuse of a right triangle. Each leg has distance x. We can say x^2 + x^2 = (3[tex]\sqrt{2}[/tex])^2
2x^2 =1 8
x^2 = 9
x = 3
They both rode 3 miles.
Can you please help me
Answer: Attached.
Step-by-step explanation:
Either solve the equations directly, or graph them and look for the point of intersection.
How I can apply the distribute property to this question?
Answer:
6(4c+6d+3)
Step-by-step explanation:
First, find the greatest common factor, which is 6, in this case.
24/6=4
36/6=6
18/6=3
6(4c+6d+3)
-hope it helps
A grocery store sells steak for $6.10 per pound. What would be the cost of 2 3/5 lb. of steak?
Answer:
$15.86
Step-by-step explanation:
Make 2 3/5 improper fraction (5 times 2 and add 3 equals 13)
13/5 times 6.1 ( or 6 1/10 or 61/10)
equals 793/50
divide
answer is 15.86
3c+2=20
c
ok anwer this
Answer:
3c =20-2
3c = 18
c = 18÷3
=6
Answer:
Here is Your answer
Step-by-step explanation:
Hope u Like it
C = 2/17
Plz Mark me As Brainiest
Find the area of each figure
Answer:
54
Step-by-step explanation:
.5*9*12
16x2 + 81y2 + 32x + 648y + 16 = 0 write instandard form