Solution :
Transforming given equations :
[tex]1)\ P = 600( 1 + \dfrac{12}{100})^t\\\\2)\ P = 1000( 1 + \dfrac{3}{100})^t\\\\3)\ P = 200( 1 + \dfrac{8}{100})^t\\\\4)\ P = 900( 1 - \dfrac{10}{100})^t[/tex]
From above equations we can see that equation 1) has largest percentage growth rate and the percent growth rate is 12% .
Hence, this is the required solution.
Answer: (i), 12%
Step-by-step explanation:
Given
The Population of four towns is given
(i) [tex]P=600(1.12)^t[/tex] i.e.
[tex]\Rightarrow P=600(1+0.12)^t\\\Rightarrow P=600(1+12\%)^t[/tex]
rate=12%
(ii) [tex]P=1000(1.03)^t[/tex]
[tex]\Rightarrow P=1000(1+0.03)^t\\\Rightarrow P=1000(1+3\%)^t[/tex]
rate=3%
(iii) [tex]P=200(1.08)^t[/tex]
[tex]\Rightarrow P=300(1+0.08)^t\\\Rightarrow P=300(1+8\%)^t[/tex]
rate=8%
(iv) [tex]P=900(0.90)^t[/tex]
[tex]\Rightarrow P=900(1-0.10)^t\\\Rightarrow P=900(1-10\%)^t[/tex]
rate=10% fall
So, the largest growth rate is for town (i) i.e. 12%
A spinner is divided into 4 equal sections numbered 1 through 4. It is spun twice, and the numbers from each spin are added.
What is the probability that the sum is less than 6?
Answer:
4equal to plus 5 eul is to be 9
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 16 feet and a height of 19 feet. Container B has a diameter of 20 feet and a height of 15 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.
To the nearest tenth, what is the percent of Container B that is empty after the pumping is complete?
18.9% is the answer
Step-by-step explanation:
volume of a cylinder = πd²/4 x h
where d is diameter and h is height of cylinder.
thus
vol of A is
[tex]vol \: of \: a \: = \pi \times \frac{ {d}^{2} }{4} \times h \\ = \pi \times \frac{ {16}^{2} }{4} \times 19 \\ = \pi \times 4 \times 16 \times 19 \\ = 3818.24[/tex]
and
[tex]vol \: of \: b = \pi \times \frac{ {20}^{2} }{4} \times 15 \\ = \pi \times 5 \times 20 \times 15 \\ = 4710[/tex]
difference in vol of a and b is
[tex]diff \: = vol \: of \: b \: - vol \: of \: a \\ = 4710 - 3818.24 \\ = 891.76[/tex]
this volume will remain empty after container A is pumped into container B.
this volume as a percentage of total volume of B is
[tex]\% = \frac{diff \: vol}{total \: vol} \times 100 \\ = \frac{891.76}{4710} \times 100 \\ = 18.9\%[/tex]
A 16 ft ladder leans against the side of a house. The bottom of the ladder is 9 ft away from the side of the house. Find x, the angle of elevation of the ladder. Round your answer to the nearest tenth of a degree. (plz help listing BRAINLIST)
Answer:
55.8
Step-by-step explanation:
cos(x)=9/16
x=55.8
The angle of elevation of the ladder is approximately 60.5 degrees.
To find the angle of elevation (x) of the ladder, we can use trigonometry. The ladder, the side of the house, and the ground form a right triangle. The length of the ladder is the hypotenuse of the right triangle, and the distance from the bottom of the ladder to the house is one of the legs.
Using the tangent function:
tan(x) = opposite/adjacent
tan(x) = 16 ft / 9 ft
Now, solve for x:
x = arctan(16/9)
Using a calculator, we find
x ≈ 60.5 degrees
So, the angle of elevation of the ladder is approximately 60.5 degrees.
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The parent function f(x)=x^3 is transformed to g(x)=(x-1)^3+4. Which graph represents function g?
Choose the definition for the function. please help me
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Answer:
A
Step-by-step explanation:
It is usually sufficient to look at one section of the graph to answer a question like this. Often the best choice is the section that has a solid dot at the end of the curve. Here, that is the right section.
The left end of the right section is at x=-2, so that part of the function is defined for x ≥ -2. The line to the right has a positive slope, so the coefficient of x will be positive.
Only one answer choice has a positive x-coefficient for x ≥ -2.
[tex]\textbf{A. }\begin{cases}-x-2&\text{if }x<-2\\x+4&\text{if }x\ge-2\end{cases}[/tex]
Answer:
Step-by-step explanation:
This graph is made up of two different, separate line segments. In other words, it comes in two pieces which can be described as a pair of linear functions.
We call this a "piecewise linear" function. Choice A is the best one.
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``````````````````````````````````
Answer:
~~~~~~~~~~~~~~~~~~~~~~~~~.~~~~~~~~~~~~~~~~~~~~~~~~~
Step-by-step explanation:
In ΔFGH, the measure of ∠H=90°, FH = 8, OF = 17, and HG = 15. What ratio represents the sine of ∠G?
Answer:
[tex]\sin(G) = \frac{8}{17}[/tex]
Step-by-step explanation:
Given
[tex]\angle H = 90^o[/tex]
[tex]FH = 8[/tex]
[tex]GF = 17[/tex]
[tex]HG = 15[/tex]
See attachment for illustration
Required
The ratio of [tex]\sin(G)[/tex]
[tex]\sin(G)[/tex] is calculated as:
[tex]\sin(G) = \frac{Opposite}{Hypotenuse}[/tex]
From the attachment, we have:
[tex]\sin(G) = \frac{FH}{GF}[/tex]
This gives:
[tex]\sin(G) = \frac{8}{17}[/tex]
What percent of l0.2 gram of 32 mg
The percent of 10.2 gram of 32 mg is gotten to be; 31.875%
How to find the percentage?When we are trying to find the percentage with the expressions "if" and "of", we will use the formula;
is/of *100%
Now, we want to find the percentage of 10.2 gram of 32 mg. Thus, the percentage is expressed as;
10.2/32 * 100% = 31.875%
Thus, the percent of l0.2 gram of 32 mg is gotten to be 31.875%
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And then next time we will come back and
A person drives a car between the two places x and y. On his outward journey he consumes 8 km per liter of petrol, on his return journey he covers 12 km per liter. Find the average of his mileage assuming the distance between the two places to be 100
Type the correct answer in each box. Use numerals instead of words. if necessary, use / for the fraction bar(s).
Find the sum. Write your answer in simplest form.
Answer:
[tex]\frac{11}{12} - \frac{1}{3} = \frac{7}{12}[/tex]
Step-by-step explanation:
Given
See attachment for question
Required
Solve
We have:
[tex]\frac{11}{12} - \frac{1}{3}[/tex]
Take LCM and solve
[tex]\frac{11}{12} - \frac{1}{3} = \frac{11 - 4}{12}[/tex]
[tex]\frac{11}{12} - \frac{1}{3} = \frac{7}{12}[/tex]
Answer:
1
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Find the sum. Write your answer in simplest form.
Step-by-step explanation:
3y=150, what is the value of y-2
Answer:
y = 48
Step-by-step explanation:
Start with the given 3y = 150.
Solve this for y by dividing both sides by 3: y = 50
Then y - 2 = 50 - 2, or
y = 48
The value of y-2 is 48,
What is an equation?Two expressions connected by an equal sign makes an equation.
Given is an equation, 3y = 150
Solving for y,
3y = 150
y = 150 / 3
y = 50
therefore, y-2 = 50-2
= 48
Hence, the value of y-2 is 48,
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The weights (in ounces) of 28 tomatoes are listed below. 1.1 1.6 1.8 1.9 2.0 2.3 2.3 2.5 2.5 2.5 2.5 2.6 2.6 2.6 2.8 2.9 2.9 3.0 3.1 3.1 3.1 3.3 3.4 3.5 3.5 3.6 3.9 4.9 What is the five number summary?
Answer:
2.6 2.6 2.8 2.9 2.9
Step-by-step explanation:
used median for the five numbers.
Are (2, 5) and (5, 2) the same location? Why or why not?
Answer:
They are not in the same location
Step-by-step explanation:
Well because we have x axis and y axis, x always has to go first. In (2, 5) 2 is first and has to start from the x axis and 5 is the y axis. And the (5,2) is the opposite and the places would be in totally different places on the coordinate plane.
Answer: No
Step-by-step explanation: The order of coordinates for a given point is very important. For example, (2, 5) and (5, 2) represent two very different points on a coordinate system, as shown in the picture below.
A given point, such as (2, 5), is often reffered to as
an ordered pair because the order of coordinates is very important.
find the area for brainlest
Answer:
A = 30 units²
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b = 12 and h = 5 , then
A = [tex]\frac{1}{2}[/tex] × 12 × 5 = 6 × 5 = 30 units²
A is set of positive multiples of 5 less than 23
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Answer:
{5, 10, 15, 20}
Step-by-step explanation:
Multiples of 5 are of the form 5n, where n is an integer. The ones of interest will satisfy ...
0 < 5n < 23
0 < n < 4.6
That is, the multiples of 5 we want are for values of n that are 1 through 4. The set is ...
5 × {1, 2, 3, 4} = {5, 10, 15, 20}
A universal set U consists of elements. If sets A, B, and C are proper subsets of U and n(U), n(A B)n(A C)n(B C), n(A B C), and n(A B C), determine each of the following.
a. n(AUB)
b. n(A'UC)
c. n(AnB)'
Answer:
[tex]n(A\ u\ B) = 10[/tex]
[tex]n(A'\ u\ C) = 10[/tex]
[tex]n(A\ n\ B)' = 6[/tex]
Step-by-step explanation:
Given
[tex]n(U) = 12[/tex]
[tex]n(A\ n\ B) =n(A\ n\ C) = n(B\ n\ C) =6[/tex]
[tex]n(A\ n\ B\ n\ C)=4[/tex]
[tex]n(A\ u\ B\ u\ C)=10[/tex]
Required
Solve a, b and c
There are several ways to solve this; the best is by using Venn diagram (see attachment for diagram)
Solving (a):
[tex]n(A\ u\ B)[/tex]
This is calculated as:
[tex]n(A\ u\ B) = n(A) + n(B) - n(A\ n\ B)[/tex]
From the attachment
[tex]n(A) = 0+2+4+2 = 8[/tex]
[tex]n(B) = 0+2+4+2 = 8[/tex]
[tex]n(A\ n\ B) = 4 +2 = 6[/tex]
So:
[tex]n(A\ u\ B) = 8 + 8 - 6[/tex]
[tex]n(A\ u\ B) = 10[/tex]
Solving (b):
[tex]n(A'\ u\ C)[/tex]
This is calculated as:
[tex]n(A'\ u\ C) = n(A') + n(C) -n(A'\ n\ C)[/tex]
From the attachment
[tex]n(A) = n(U) - n(A) = 12 - 8 = 4[/tex]
[tex]n(C) = 0+2+4+2 = 8[/tex]
[tex]n(A'\ n\ C) = 2[/tex]
So:
[tex]n(A'\ u\ C) = 4 + 8 - 2[/tex]
[tex]n(A'\ u\ C) = 10[/tex]
Solving (c):
[tex]n(A\ n\ B)'[/tex]
This is calculated as:
[tex]n(A\ n\ B)' = n(U) - n(A\ n\ B)[/tex]
[tex]n(A\ n\ B)' = 12- 6[/tex]
[tex]n(A\ n\ B)' = 6[/tex]
find the y-intercept for the parabola
defined by this same equation:
y = 2x2 – 8x + 5
Answer:
y=5
y int
x=0
y=2(0)^2-8(0)+5
y=5
note everything multiplied by 0 is 0
please answer !!! quickly thank you!
Answer:
B) this line has zero slope.
Step-by-step explanation:
it doesn't increase or decrease. it is a constant; zero
Answer:
This line has zero slope.
Step-by-step explanation:
The slope of the line doesn't change it just stays straight.
Which graph shows the solution set of the inequality 2.9(x+8) <26.1?
O
+++
-10
-5
0
5
10
-10
-5
0
5
10
O
-10
-5
0
5
5
10
-10
-5
5
5
10
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Answer:
D
Step-by-step explanation:
The inequality symbol is < (not ≤), which means the end point of the graph will be an open circle.
After dividing by the coefficient of x, you have an inequality of the form ...
x +( ) < ( )
which means the solution will be left of the (open circle) end point of the graph. Only one graph has that form.
__
If you actually work through the numbers, you get ...
x +8 < 9 . . . . . . divide both sides by 2.9
x < 1 . . . . . . . . . subtract 8 from both sides
Help troll or report Help plsssss
Answer:
11. (a) 3/4+1/2=5/4
(b) 4/5= 8/10 , 16/20
12. 8 children don't like choc ice cream
Step-by-step explanation:
11. 3/4 +2/4=5/4(change 1/2 by making it the same as the one next to it)
12. 3/5 of 20 = 12
20-12=8
Which graph represents the function f(x) = –x2 + 5?
Answer:
Step-by-step explanation:
The graph of f(x) = –x^2 + 5 is that of an upside-down parabola with vertex (0, 5) and x-intercepts (-√5, 0) and (+√5, 0). Plot the vertex (0, 5) and then draw a smooth curve through it and through the x-intercepts.
The function f(x) = -x2+5 is thus represented by the quadratic functions in the first graph.
what is quadratic functions ?A quadratic function has the formula f(x) = ax2 + bx + c, with a, b, and c being integers and a not equal to zero. Parabolas can have openings that are upward or downward, different "widths" or "steepnesses," but they all share the same fundamental "U" shape.
here calculation
The function provided is f(x) = -x2+5
.... (1) (1)
We must locate the function's graph.
The quadratic function's vertex form is f(x)= a(x-h)2 + k.... (2)
When we compare (1) and (2), we obtain
h=0 , k=5
It denotes that the function's vertex is (0,5).
The values list is
x y
-2 1
-1 4
0 5
1 4
2 1
Place all ordered pairings on a coordinate plane, and then use a free-hand curve to link them.
The function f(x) = -x2+5 is thus represented by the quadratic functions in the first graph.
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In a recent survey, 75% of the community favored building a police substation in their neighborhood. If 14 citizen are chosen at random, find the probability that exactly 8 of them favor the building of the police substation.
.
Answer:
/ROB.UX ME 1,000,000,000
Step-by-step explanation:
Answer:
.073398
Step-by-step explanation:
It's easiest to use a binomial distribution here
We have...
14C8*.75⁸*(1-.75)⁶= .073398
What are the roots of the equation x2 + 16x + 73 = 0 in simplest a + bi form?
Answer:
-8+2i and -8+2i
Step-by-step explanation:
here simply we'll use general formula
x= (-b +or - √ b^2-4ac)/2a
my question is in the document
Which graph represents the solution set for the inequality 1xs 18?
2
+++
0 1 2
3 4 5 6 7 8 9 10
>
+++
0 6 12 18 24 30 36 42 48 54 60
+
0 1 2 3 4 5 6 7 8 9 10
0 6 12 18 24 30 36 42 48 54 60
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Answer:
D
Step-by-step explanation:
Multiplying the inequality by 2 will eliminate the fraction and give you ...
x ≤ 36
The "or equal to" part of the symbol means the end dot will be solid. The "less than" part of the symbol means the graph is shaded to the left of the end dot, which is at x=36. This description matches the graph shown below.
CALCULATORS COST $125.00 FOR 25 CALCULATORS. WHAT IS THE COST PER CALCULATOR?
Answer: $5 per calculator
Step-by-step explanation: divide 125 and 25
Answer:
5$
Step-by-step explanation:
Given:
25 calculators cost 125.00
So:
_______ DIvide the cost of calculators by the number of calculators, and we get 5$
If can someone help me.
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Answer:
Tim is correct. 5/8 > 1/2
Step-by-step explanation:
By taking 5/8 of the lasagna, Tim will be taking more than half (4/8) of it. No remaining share can be larger. Any remaining share will be 3/8 or less, so will be smaller than a 5/8 share.
Tim's 5/8 share is the largest.
Can you help me in question 30?!
Answer: 24
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
Volume is length times width times height so you just have to multiply 3 by 4 by 2 to get 24.
The time it takes to build a house (T), varies directly with the floor area (A), and inversely with the number of workers (W). What is the equation that models this situation?
Answer:
T = k * (A/W)
Step-by-step explanation: