Given :-
Passing marks in an exam is 40% .Seema gets 130 marks and fails by 2 marks.To find :-
The maximum marks for the exam .Solution :-
According to the Question ,
[tex]\dashrightarrow[/tex] Passing marks = 40% .
[tex]\dashrightarrow[/tex] Seema's marks = 130 .
Let us take the maximum marks be x . Then ,
[tex]\dashrightarrow[/tex] Passing marks = 130 + 2
[tex]\dashrightarrow[/tex] Passing marks = 132
And , by question ,
[tex]\dashrightarrow[/tex] 40x/100 = 132
[tex]\dashrightarrow[/tex] x = 132 * 100/40
[tex]\dashrightarrow[/tex] x = 330
Hence the maximum marks for the exam is 330.
Given :
Passing marks in the examination = 40% . Marks obtained by Seema = 130 .So, Let us assume the maximum marks as x .
Also,
Passing marks = 132 [ ∵ Seema got 130 marks and she failed by 2 marks ]
According to the question :
[tex] \\ \tt : \implies\dfrac{40x}{100} = 132 \\ \\ \tt : \implies\dfrac{4 \cancel{0}x}{10 \cancel{0}} = 132 \\ \\ \: \: \: \tt \: : \implies 4x = 132 \times 10 \\ \\ \tt : \implies \: 4x = 1320 \\ \\ \tt : \implies \: x = \frac{1320}{4} \\ \\ \tt : \implies \: x = 330 \: \: \\ [/tex]
Hence, The total marks is 330 .
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.
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
Write 15.5 as a fraction in the simplest form and as a decimal
Give the number and type of solutions of the equation.
Answer:
B. 2 non-real solutionsStep-by-step explanation:
Compare the left and right side of the given equation in terms of the lines they represent:
x² is a parabola with non-negative value- 3x - 7 is a line with negative slope and negative y-interceptTheir intersection seems not possible. Lets graph and confirm.
See attached below.
It means there are no real solutions. Correct answer choice is B
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
write the tangent of ∠T as a fraction
Answer:
[tex]\tan \angle T = \dfrac{SR}{TS} = \dfrac 43[/tex]
Step-by-step explanation:
is (1, 3) a solution to the system of equations
8x + y = 11
12x + 2y = 18
Answer:
(1, 3) a solution to the system of equations
8x + y = 11
12x + 2y = 18
Step-by-step explanation:
ay están todos los deberes de la semana pasada gunnorni
Answer:
x=1 and y=3
Step-by-step explanation:
yes x=1 and y=3 is the solution for the equation.just by making y in the first equation subject of the formula and replacing in the second equation.
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
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
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]
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 )
Help please!!!!!!!!!!!!!
Answer:
Hm? Is there meant to be a file, if so I can’t see it. :((
Step-by-step explanation:
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
-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.
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:
Please help me with this question.
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
Can someone help me with this plis
Answer:
it is c
Step-by-step explanation:
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.
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 mosquito flies at a speed of 40.2 meters per minute.
At this rate, how many meters can it fly in 5 minutes?
PLZ HELP
Answer:
201
Step-by-step explanation:
40.2*5=201
201 meters per minute
Find the value of √1600×8²+√4225
Step-by-step explanation:
√1600×8²+√4225
40 x 64 + 65
= 2625
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 < ∞
Help please, 9th grade math.
Answer:
table k
Step-by-step explanation:
4:3 ratio
How i can answer this question
60m
How?
5m × 3m × 4m
5m × 3m = 15m
15m × 4m = 60m
Therefore
the answer is 60
a statue of abraham lincoln casts a 9-foot shadow at the same time the white house casts 48-foot shadow . if the white house is 70 feet tall , how tall is the statue of abraham lincoln
Step-by-step explanation:
let's ignore the question, if the statue can cast an isolated shadow based on its location ...
2 objects and their shadows create 2 similar right-angled triangles.
that means all angles are the same, and the side lengths of one triangle correlate to the corresponding side lengths of the other triangle via the same factor.
so,
48 × f = 9
f = 9/48 = 3/16
therefore, the height of the statue is
70 × f = 70 × 3/16 = 210/16 = 13.125 ft
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
Need help NOW on HS geometry
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.
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