Use the information below to answer questions 34-35 The volume of water in the lake is 150,000 Kilolitres. The volume kept decreasing at the rate of 45% every monthly through evaporation and a river outlet. 34. How long will it take before there is only 15,000 Kilolitres left in the lake? A. 4.5 months B. 6 months C. 300 months D. 75 months
how many more months will if take the lake to dry up the same descrese rate?
Answers
If the volume of the river is 150000 kilolitres and 45% is evaporating every month then after 4.5 months there will be 15000 kilolitres and it will take approximately 42 months to completely dry up.
Given that the volume of the river is 150000 kilolitres and the water is decreasing at a rate of 45%.
We are required to find the number of months after which the water left in the river will be 15000 kilolitres and the number of months after which the river will be completely dried up.
The amount of water left after n years can be written as:
=150000*\((1-0.45)^{n}\)
When the volume will be 15000 kilolitres.
15000=150000*\((0.55)^{n}\)
0.1=\((0.55)^{n}\)
\((0.55)^{4.5}\)=\((0.55)^{n}\)
By comparing both sides we will get n=4.5.
Now put the amount of volume be 0.
0=150000*\((0.55)^{n}\)
\((0.55)^{42}\)=\((0.55)^{n}\)
By equating both sides we will get n=42. We know that 0.55 to the power anything will not give 0 but we have taken nearest value to 0.
Thus the lake will take 42 months to completely dried up.
Hence if the volume of the river is 150000 kilolitres and 45% is evaporating every month then after 4.5 months there will be 15000 kilolitres and it will take approximately 42 months to completely dry up.
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Related Questions
Sara wants to make dinner for herself the recipe she will use calls for 13 1/2 ounces of chopped nuts however the recipe feeds 6 people how many ounces of chopped nuts does Sara need for one serving
Answers
Sara need 9/4 ounces of chopped nuts
How to calculate the number of chopped nuts that sara needs?Sara wants to make dinner for herself
The recipe she will use calls for 13 1/2 ounces
The recipe feeds 6 people
The number of ounces of chopped nuts that Sara needs can be calculated as follows
13 1/2
= 27/2 ÷ 6
= 27/2 × 1/6
= 27/12
= 9/4
Hence Sara needs 9/4 ounces of chopped nuts for one serving
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Enter the number that belongs in the green box
Answers
The angle measure that belongs in the green box is given as follows:
70.67º.
What is the law of sines?We consider a triangle with side lengths and angles related as follows, as is the case for this problem:
Side length of a is opposite to angle A.Side length of b is opposite to angle B.Side length of c is opposite to angle C.Then the lengths and the sines of the angles are related as follows:
sin(A)/a = sin(B)/b = sin(C)/c.
The relation for this problem is given as follows:
sin(x)/12 = sin(76º)/12.34
Applying cross multiplication, the missing angle measure is given as follows:
sin(x) = 12 x sine of 76 degrees/12.34
sin(x) = 0.9436.
x = arcsin(0.9436)
x = 70.67º.
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contracts for two construction jobs are randomly assigned to one or more of three firms, a, b, and c. the joint distribution of y1, the number of contracts awarded to firm a, and y2, the number of contracts awarded to firm b, is given by the entries in the following table. y1 y2 0 1 2 0 1 9 2 9 1 9 1 2 9 2 9 0 2 1 9 0 0 find cov(y1, y2). (round your answer to three decimal places.) cov(y1, y2)
Answers
The value of covariance cov(y1, y2) is -0.222
y1
y2 0 1 2 Total
0 1/9 2/9 1/9 4/9
1 2/9 2/9 0 4/9
2 1/9 0 0 1/9
Total 4/9 4/9 1/9 1
marginal distribution of y2:
y2 P(y2) y2P(y2) y2^2P(y2)
0 4/9 0.0000 0.0000
1 4/9 0.4444 0.4444
2 1/9 0.2222 0.4444
total 1 0.66667 0.88889
E(y2) = 0.6667
E(y2^2) = 0.8889
Var(y2) = E(y2^2)-(E(y2))^2=0.4444
marginal distribution of y1
y1 P(y1) y1P(y1) y1^2P(y1)
0 4/9 0.0000 0.0000
1 4/9 0.4444 0.4444
2 1/9 0.2222 0.4444
total 1.00 0.6667 0.8889
E(y1) = 0.6667
E(y1^2) = 0.8889
Var(y1)= σy = E(y1^2)-(E(y1))^2 = 0.4444
E(XY) =∑xyP(x,y)=0.2222
Cov(y1,y2) = -0.222
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For which of the following increasing functions f does (f-1)'(20) = 1/5
A f(x)= x + 5
B f(x) = x^3 + 5x + 20
C f(x) = x^5 + 5x + 14
D f(x)= e^x+ 5x + 19
Answers
Answer:
D f(x)= e^x+ 5x + 19
Step-by-step explanation:
D f(x)= e^x+ 5x + 19
We want to see for which one of the given functions, the inverse derivate evaluated in x = 20 is equal to 1/5.
The correct option is B: f(x) = x^3 + 5x + 20
Remember that two functions f(x) and g(x) are inverses if:
f( g(x)) = g( f(x))) = x
And for the inverse derivate of a function, we have the rule:
\(\frac{d}{dx} [f^{-1}(f(x))] = \frac{1}{f'(x)}\)
So first we need to find for what value of x each function is equal to 20, and then we need to see if the derivate of the function evaluated in that same value of x is equal to 5.
For example, for the first option we have:
A: f(x) = x + 5
We find the x-value such that the function is equal to 20.
f(15) = 15 + 5 = 20
We derivate the function.
f'(x) = 1
We evaluate the function in the x-value we got above.
f'(15) = 1
This is not the correct option, as this is not 5.
Now we need to do that for all the given options.
The only correct option will be the second one:
B: f(x) = x^3 + 5x + 20
First we find the x-value such that this is equal to 20
f(0) = 0^3 + 5*0 + 20 = 20
Then the x-value is x = 0.
Now we find the derivate of f(x).
f'(x) = 3*x^2 + 5
Now we evaluate that in the x-value we got before:
f'(0) = 3*0^2 + 5 = 5
As wanted, this is equal to 5.
Then we have:
\(\frac{d}{dx} [ f^{-1}( f(0))] = \frac{1}{f'(0)} \\\\\frac{d}{dx} [ f^{-1}(20)] = \frac{1}{5}\)
As wanted.
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Hexagon DEFGHI is translated on the coordinate plane below to create hexagon D′E′F′G′H′I′: Hexagon DEFGHI and Hexagon D prime E prime F prime G prime H prime I prime on the coordinate plane with ordered pairs at D 2, 5, at E 5, 5, at F 6, 3, at G 5, 1, at H 2, 1, at I 1, 3, at D prime negative 6, negative 2, at E prime negative 3, negative 2, at F prime negative 2, negative 4, at G prime negative 3, negative 6, at H prime negative 6, negative 6, at I prime negative 7, negative 4
Answers
Answer: To find the image of a figure under a translation, you need to apply the same translation to every point in the figure.
In this case, the image of hexagon DEFGHI is hexagon D′E′F′G′H′I′. To find the image of each point, you can apply the translation that maps point D to point D′.
For example, to find the image of point E under the translation, you can apply the same translation that maps point D to point D′:
Point D is located at (2, 5).
Point D′ is located at (-6, -2).
The translation that maps point D to point D′ is a translation 6 units to the left and 2 units down.
To find the image of point E under this translation, you can apply the same translation to point E:
Point E is located at (5, 5).
The image of point E is located at (5 - 6, 5 - 2) = (-1, 3).
You can follow the same process to find the images of the other points under the translation.
Alternatively, you can use the coordinates of point D and point D′ to find the translation vector that describes the translation. The translation vector is a displacement that describes the change in position of a point under the translation.
In this case, the translation vector is given by the displacement from point D to point D′:
Point D is located at (2, 5).
Point D′ is located at (-6, -2).
The translation vector is given by the displacement (-6 - 2, -2 - 5) = (-8, -7).
To find the image of any point under the translation, you can add the translation vector to the coordinates of the point. For example, to find the image of point E under the translation, you can add the translation vector to the coordinates of point E:
Point E is located at (5, 5).
The translation vector is (-8, -7).
The image of point E is located at (5 - 8, 5 - 7) = (-3, -2).
You can follow the same process to find the images of the other points under the translation.
Step-by-step explanation:
How do you solve these angles again?
Answers
Answer:
(2x+2)
=98
(x+34)
=82
Step-by-step explanation:
a straight line adds up to 180
(2x+2)+(x+34)=180
x+2+x+34=180
(2x+x)+(2+34)=180(Combine Like Terms)
3x+36=180
3x+36=180
Step 2: Subtract 36 from both sides.
3x+36−36=180−36
3x=144
Step 3: Divide both sides by 3.
3x/3=144/3
x=48
Now you have your x just substitute it in
(2x+2)
=98
(x+34)
=82
If answers not right i am sorry but i tried
Select the correct answer.
What is the solution for x in the equation?
-3x + 7x − 8 = 34 + 9x − 2
A.
B.
C.
D.
Answers
Answer:
-8
Step-by-step explanation:
-3x + 7x - 8 = 34 + 9x - 2
-3x + 7x - 9x = 34 - 2 + 8
-5x = 40|: (-5)
x = -8
\({ \bf{ \underbrace{ The\:value\:of\:x\:is\:-8.}}}\)
\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)
\( - 3x + 7x - 8 = 34 + 9x - 2 \\ ⇢ 4x - 9x = 32 + 8 \\ ⇢ - 5x = 40 \\ ⇢ x = \frac{40}{ - 5} \\ ⇢ x = - 8\)
\({ \bf{ \underbrace{To\:verify :}}}\)
\( - 3x + 7x - 8 = 34 + 9x - 2 \\ ⇢ - 3 \times - 8 + 7 \times - 8 - 8 = 34 + 9 \times - 8 - 2 \\ ⇢24 - 56 - 8 = 34 - 72 - 2 \\ ⇢24 - 64 = 34 - 74 \\ ⇢ - 40 = - 40 \\ ⇢L.H.S.=R. H. S\)
Hence verified. ✔
\(\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}\)
Don’t judge
Heeeweeeeeeeeeeelllllllllllp
Answers
Jackson wrote different patterns for the rule subtract 5 select all the patterns he could have written
Answers
When Jackson wrote different patterns for the rule "subtract 5", the patterns that he could have written include
A. 27, 22, 17, 12, 7
D. 100, 95, 90, 85, 80
What is the expression regarding the pattern?It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. In this case, when Jackson wrote different patterns for the rule "subtract 5", the patterns that he could have written include 27, 22, 17, 12, 7 and 100, 95, 90, 85, 80. In this cases, there are difference of 5.
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Complete question
Jackson wrote different patterns for the rule "subtract 5". Select all of the patterns that he could have written.
27, 22, 17, 12, 7
5, 10, 15, 20, 25
55, 50, 35, 30, 25
100, 95, 90, 85, 80
75, 65, 55, 45, 35
which sides form a right triangle
Answers
Answer:
c
Do i get brainliest lol
what is the probability of A is 0.8, what is the probability of B is 0.45, what is the probability of either A and B is 0.30?
Answers
Answer:
you need to be more clearStep-by-step explanation:
i am confused
2(3r+7)−(2+r)
I need the answer
Answers
Hey there,
Answer:
k(a + b) = ka + kb
2(3r + 7) - (2+ r)
= 2*3r + 2*7 - (2 + r)
= 6r + 14 - (2 + r)
= 6r + 14 - 2 - r
= 6r - r + 14 - 2
= 5r + 12
;)✅
The price of an item has been reduced by 2.09 The original price was 99.15 What is the price now?
Answers
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The current price of the item is 97.06
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Original price of an item = 99.15
The price has been reduced by 2.09.
The current price.
= 99.15 - 2.09
= 97.06
Thus,
The current price of the item is 97.06
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Which of the following is closest to the square root of 12
Answers
Answer:
3.46410161514
is the square root of 12 so whatever is closest to that.
Step-by-step explanation:
The given figure is a right triangular prism.
In the prism:
• DF = 22 in.
• EG = 11 in.
• Volume of the prism = 1936 cubic in.
What is the length of AD?'
Use the given information to complete the worksheet.
Thank you!
Answers
The length of side AD is,
⇒ AD = 16
We have to given that;
The given figure is a right triangular prism.
In the prism:
• DF = 22 in.
• EG = 11 in.
• Volume of the prism = 1936 cubic in.
Since, Volume of right triangular prism is,
V = 1/2 (bh) x L
Substitute all the values we get;
V = 1/2 (22 × 11) × AD
1936 = 121 × AD
AD = 16
Thus, The length of side AD is, 16
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I am unsure how to do this, please help!
Answers
The original number in the given question solved by algebra is 39/7.
What is Algebra?
Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
The number is divided 5 times by 7 more than that number.
Let the number be x
Then,
x+7/5x = 8
x+7=40x
7=39x
x=39/7
Therefore, by algebra the answer will be 39/7.
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1. Solve
1/2 + p = -3
what is p
Answers
p=-7/2
Hope it help
please help w this i don’t get it :(
Answers
Answer:80°
This is the answer i think hope this helps you
a triangle has angles measuring 45°, 55°, and 80°. it is dilated by a scale factor of 2. what are the angle measures, in order from least to greatest, of the dilated image? enter the correct answers in the boxes.
Answers
Answer:
\(45\)°, \(55\)°, and \(80\)°
Step-by-step explanation:
Dilations preserve angle measures, regardless of the scale factor. Therefore, the angle measures of the image will be the same of that of the pre-image, so our answer is still \(45\)°, \(55\)°, and \(80\)°. Hope this helps!
3. A company makes a profit of $60 per software program and $45 per video game. The company can produce at most 300 software programs and at most 200 video games per week. Total production cannot exceed 400 items per week. How many items of each kind should be produced per week in order to maximize the profit? Use linear programming to solve. Show all your work. Answer:
Answers
Answer:
Step-by-step explanation:
This problem is a maximization problem
the objective is to maximize profit
let software program be x
and video program be y
the objective function is
60x+45y>P-------1
constrains
300x+200y<400------2
we can further reduce the expressions
3x+2y<4-----2
Simplify.
Rewrite the expression in the form x^n
x^5/x^2
Answers
Answer:
\( {x}^{3} \)
Step-by-step explanation:
\( \frac{ {x}^{5} }{ {x}^{2} } = \frac{ {x}^{3} \times {x}^{2} }{ {x}^{2} } = {x}^{3} \)
I hope I helped you^_^
solve x and y for 5x−y=44−3=−3x−y=−12
Answers
The values of the variables are;
x = 7
y = -9
How to solve for the variablesFrom the information given, we have that;
5x−y=44
−3x−y=−12
Using the elimination method of solving simultaneous equations
Subtract equation (2) from equation (1), we get;
5x - y - (-3x - y) = 44 - (-12)
Now, expand the bracket
5x - y+ 3x + y = 56
collect the like terms
5x + 3x = 56
add the terms
8x = 56
Make 'x' the subject of formula
x= 7
Now, substitute the value of x in equation (2)
-3x - y = -12
-3(7) - y = -12
expand the bracket
-21 - y= - 12
collect like terms
-y = 9
y = -9
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please i’ll fail if i don’t get this right. please i’ll give brainlyist The current temperature of 15°F below zero is 18°F below the high temperature of the day. What is the high temperature for the
day?
OA. 5°F
ов. 33°F
OC. 3°F
OD. 33°F
Answers
Answer:
I think its C
Step-by-step explanation:
Determine the largest power of 10 that is a factor of the following numbers (equivalently, the number of terminal 0's, using ordinary base 10 representation):(a) 50!.
(b) 1000!.
Answers
The largest power of 10 that is a factor of 1000! is 5^249, or 10^249.
(a) To find the largest power of 10 that is a factor of 50!, we need to count the number of factors of 5 in 50! since each factor of 5 contributes at least one factor of 10.
There are 10 multiples of 5 in 50!, namely 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. Each of these contributes one factor of 5. There are also 2 multiples of 25 (25 and 50), each of which contributes an additional factor of 5. Therefore, the total number of factors of 5 in 50! is 10 + 2 = 12.
Since each factor of 10 contains one factor of 5 and one factor of 2, we also need to count the number of factors of 2. It is clear that there are more factors of 2 than factors of 5, so we only need to count the factors of 5. Therefore, the largest power of 10 that is a factor of 50! is 5^12, or 10^12.
(b) To find the largest power of 10 that is a factor of 1000!, we follow the same reasoning as in part (a). The number of factors of 5 in 1000! is:
⌊1000/5⌋ + ⌊1000/25⌋ + ⌊1000/125⌋ + ⌊1000/625⌋ = 200 + 40 + 8 + 1 = 249
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All the students in the sixth grade either purchased their lunch or bought their lunch from home on Monday. 24% of the students purchased their lunch. 190 students bought their lunch from home. How many students are in the sixth grade?
Answers
There are 250 students in the sixth grade.
How to find number of students?First, let's define some variables:
The total number of sixth-grade students is called "x."
The number of students who purchased their lunches will be referred to as "p."
The number of students who brought their lunch from home will be referred to as "h."
We know that from the problem statement that
p + h = x (since all students either purchased their lunch or brought their lunch from home)
p = 0.24x (since 24% of the students purchased their lunch)
h = 190 (since 190 students brought their lunch from home)
We can use these equations to solve for x:
p + h = x
0.24x + 190 = x (substituting in the value of p and h from the other equations)
0.76x = 190 (subtracting 0.24x from both sides)
x = 250 (dividing both sides by 0.76)
Therefore, there are 250 students in the sixth grade.
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What is the product?
3x³(2x² +4x+1)
O 2x +4Xô + xô
O
6x¹0+12x5+3x5
O 6x² + 12x6 +5
O 3x5+2x² + 4x+1
Answers
Answer:
6x⁵+12x⁴+3x³
Step-by-step explanation:
3x³(2x² + 4x + 1) = 3x³ × (2x² + 4x + 1)
therefore
3x³(2x² + 4x + 1) =
(3x³ × 2x²) + (3x³ × 4x) + (3x³ × 1)
*NOTE: for the brackets the multiplication law of indices is applied, i.e:
nª × n^b = n^a+b therefore
x³ × x² = x^3+2 = x⁵
x³ × x = x^3+1 = x⁴
x³ × x⁰ = x^3+0 = x³
*Note the quoeficents multiple each other, i.e:
3 × 2 = 6
3 × 4 = 12
3 × 1 = 3
so:
= 6x⁵ + 12x⁴ + 3x³
No bots answer fast plz 1. (4x + 8) + (7x + 3) =
Answers
………………………………….
Answer: 11x+11
Step-by-step explanation:
hope this helped u in any way
estimate. Which difference is greater? 1) 11/20 - 1/10. 2) 11/12 - 3/10. 3) The estimated differences are equal
Answers
Answer:
Option 2) is greater. 11/12-3/10
Answer:
2.) 11/12 - 3/10
Step-by-step explanation:
1.) 36/60
2.) 37/60
25/18 as a mixed number
Plsss help me
Answers
Step-by-step explanation:
7
1 ---
18
hope it helps !
Can someone please provide a step-by-step explanation for the answer?
If the universe of discourse is the real numbers, give the truth value of each of the
following propositions:
(a) ∀x∃y(x = y²)
(b) ∀x∃y(x² = y)
(c) ∃x∀y(xy = 0)
(d) ∀x∃y(x + y = 1)
Answers
The Propositions are resulting
(a) ∀x∃y(x = y²) is False
(b) ∀x∃y(x² = y) is True.
(c) ∃x∀y(xy = 0) is True.
(d) ∀x∃y(x + y = 1) is True.
(a) ∀x∃y(x = y²)
This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.
If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.
For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².
Therefore, the proposition (a) is false.
(b) ∀x∃y(x² = y)
For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.
For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.
Therefore, the proposition (b) is true.
(c) ∃x∀y(xy = 0)
The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.
Therefore, the proposition (c) is true.
(d) ∀x∃y(x + y = 1)
To determine the truth value, we need to check if this statement holds true for every value of x.
If we take any value of x, we can find a corresponding value of y that satisfies the equation.
For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.
Therefore, the proposition (d) is true.
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