Answer:
6 years
Step-by-step explanation:
Given
[tex]Initial\ Investment = 150[/tex]
[tex]Ratio = double[/tex]
Required
When will it get to 4000
This question illustrates a geometric progression and will be solved using:
[tex]T_n = ar^{n-1}[/tex]
In this case;
[tex]T_n = 4000[/tex]
[tex]r = double = 2[/tex]
[tex]a = 150[/tex]
So, we're to solve for n
[tex]4000 = 150 * 2^{n - 1}[/tex]
Divide through by 150
[tex]\frac{4000}{150} = 2^{n-1}[/tex]
[tex]26.67= 2^{n-1}[/tex]
Take Log of both sides
[tex]Log26.67= Log2^{n-1}[/tex]
Apply law of logarithm
[tex]Log26.67= ({n-1})Log2[/tex]
Take Log values
[tex]1.42602301569 = (n - 1) * 0.30102999566[/tex]
Make n - 1 the subject
[tex]n - 1 = \frac{1.42602301569}{0.30102999566}[/tex]
[tex]n - 1 = 4.73714591984[/tex]
Add 2 to both sides
[tex]n = 1 + 4.73714591984[/tex]
[tex]n = 5.73714591984[/tex]
[tex]n = 6[/tex] (Approximated)
Hence, it'll take 6 years
help please!
find the value of x so that the figures have the same perimeter
Answer: 7
Step-by-step explanation: For the first figure, 7 + 3 = 10, so the perimeter would be 10 + 10 + 7 + 7, which equals Perimeter = 34. For the other figure, 7 - 4 = 3, so 3 + 14 + 14 + 3 = 34, also. Hope this helps!
Phil has drawn some house plans in which the lounge room will be 9.5 m long when it is built. This length has been drawn as 19cm on the house plan. What scale did Phil use for his house plans?
Answer:
1:50 scale
Step-by-step explanation:
9.5m * 100 = 950cm
950/19 = 50
Which step can you use to solve the equation t - 8= -3?
O Add 8 to each side of the equation.
Subtract 8 from each side of the equation.
O Multiply each side of the equation by 8.
O Divide each side of the equation by 8.
Solve the equation t-8=
3.
the sqaure root of 130 falls between which consecutive numbers
The figure below shows how Ali spends his time in a day. Calculate the number of hours Ali
spends on playing.
Answer:
75°C = 5h
Step-by-step explanation :
1. Make sure your mind is fresh and that you understand each step before reading
2. 24 hours is equal to 360°C
3. so now lets break up the hours. We can do this by choosing a simple degree that was given in the diagram. For example "Watching tv".
Tip : when choosing one of the degrees , ( i mean one of the choices like watching tv, playing and sleeping) , try choosing the simplest one , which has a simple number and a multiple of 360.
so now you want to know how many hours is 60 equal to .
= 360 ÷ 60 = 60 (this is to make sure the number is a multiple and will not be a decimal )
= 24 ÷ 6 = 4
this means Ali spend 4 hours watching tv
and by doubling that you get 60°C = 4h
the amount of time he slept 120°C = 8h
and you keep playing with the numbers like that
so for playing
60°C = 4h
divide by 4 15°C = 1h
× by 5 75°C = 5h
this means ali spends 5h playing , 8h sleeping, 4h watching tv and 7 h studding
In how many ways can four people sit around a circular table? Seating arrangements are considered different only if at least one person has at least one different neighbor.
Answer:
(x-1)!
Step-by-step explanation:
lets say you want to sit x people around a table you would do x!. but since it doesn't count if you rotate the table you have to divide it by x, so the answer is x!/x = (x-1)!
Olga tried to solve an equation step by step.
1/4 (1/3k+9)=6
1/3k=15
k=5
Find Olga's mistake.
Which is an example of deductive reasoning?
Answer:
In deductive reasoning, if the given facts are true and you apply the correct logic, then the conclusion must be true.
Step-by-step explanation:
Answer:
All even numbers are divisible by 2. The number 18 is even, so it is divisible by 2.
Step-by-step explanation:
Help me plz I don't know how to this I don't understand!!!
The answer is B.
In order for this chart to be true, each x and y pair must be proportional to the other ones. (in other words, each row of x and y should increase the same amount as the other ones.)
look at the first row. we can write this as 3/5 (x over y). then look at the third and fourth row. 6/10 = 3/5, and 9/15 = 3/5, so the pairs are proportional.
If a triangle is an equilateral triangle, then the triangle has exactly three 60°
angles. △ABC is an equilateral triangle?
Step-by-step explanation:
In an equilateral triangle, all the three sides are equal as well as all the angles are equal. Let the angles be x.
We know that the sum of angles of a triangle is equal to 180 degrees. It means that,
x+x+x=180
3x=180
x=60°
Hence, if a triangle is an equilateral triangle, then the triangle has exactly three 60° angles. Hence, △ABC is an equilateral triangle
81 minus 39
And can you explain how plz?. Lol i meed it asapp
Answer:
42Step-by-step explanation:
[tex]81-39\\\\\mathrm{Line\:up\:the\:numbers}\\\begin{matrix}\space\space&8&1\\ -&3&9\end{matrix}\\\mathrm{In\:the\:bolded\:column,\:subtract\:the\:second\:digit\:from\:the\:first}\\\begin{matrix}\space\space&8&\textbf{1}\\ -&3&\textbf{9}\end{matrix}\\\\\mathrm{The\:bottom\:number\:is\:larger\:than\:the\:upper\:number.\:\:Try\:to\:'borrow'\:a\:digit\:from\:the\:left.}\\\\\mathrm{Borrow\:}1\mathrm{\:from\:}8\mathrm{.\:\:The\:remainder\:is\:}7\\[/tex][tex]\begin{matrix}\space\space&\textbf{7}&10\\ \space\space&\textbf{\linethrough{8}}&1\\ -&\textbf{3}&9\end{matrix}\\\\\mathrm{Add\:}1\mathrm{\:ten\:to\:}1:\quad \:10+1=11\\\begin{matrix}\space\space&7&\textbf{11}\\ \space\space&\linethrough{8}&\textbf{\linethrough{1}}\\ -&3&\textbf{9}\end{matrix}\\\\\mathrm{In\:the\:bolded\:column,\:subtract\:the\:second\:digit\:from\:the\:first}:\quad \:11-9=2\\[/tex]
[tex]\frac{\begin{matrix}\space\space&7&\textbf{11}\\ \space\space&\linethrough{8}&\textbf{\linethrough{1}}\\ -&3&\textbf{9}\end{matrix}}{\begin{matrix}\space\space&\space\space&\textbf{2}\end{matrix}}\\\mathrm{In\:the\:bolded\:column,\:subtract\:the\:second\:digit\:from\:the\:first}:\quad \:7-3=4\\\\\frac{\begin{matrix}\space\space&\textbf{7}&11\\ \space\space&\textbf{\linethrough{8}}&\linethrough{1}\\ -&\textbf{3}&9\end{matrix}}{\begin{matrix}\space\space&\textbf{4}&2\end{matrix}}[/tex]
HELP PLS IF U DONT KNOW CEASE IT DONT ANSWER ONLY ACCEPTING VARIFIED ANSWERS !!!!!!
Answer:
31%
Step-by-step explanation:
use the formula :
P(A&B) / P(B)
meaning :
probability that a student graduates while on fin aid / student on fin aid
= 1879/6101
=1879/6101 *100
= 30.798....
= 31%
Sophie drove 162 miles in 3 hours. How fast did she drive in hours per mile
Answer:
54 Miles Per Hour
Step-by-step explanation:
162/3
please help help help
Answer:
I'm fairly sure its 4.93 grams.
Step-by-step explanation:
you take the origional water of 45.1ml and the new 52.3ml, and find the difference, which in this case is 7.2ml.
the density formula is D=M/V
D= Density
M=Mass
V=Volume
so it would be
D= 35.49/7.2
which is 4.93.
again this is just from what I remember of science class.
Answer: 4.93g/cm^3
Step-by-step explanation:
Formula for Density: D = mass / volume
We know that the mass of the unknown object is 35.49g
Mass = 35.49g
To find the volume
Initial water level: 45.1 mL
Final water level: 52.3mL
52.3cm^3 - 45.1cm^3 = 7.2cm^3
Volume = 7.2cm^3
Density = 35.49g/7.2^3
Density =
if Kyle's terrarium had a volume of 64 ft3 ,what would the edge length be?
Answer:
4 ft
Step-by-step explanation:
Volume of a cube = [tex]x^{3}[/tex] (where x equals the side/edge length)
V = [tex]x^{3}[/tex]
64 = [tex]x^{3}[/tex]
64 divided by 3 = 4 ft
What is the simplified expression for 5ab+9ab-ab? 0 12ad O 13ab 0 15ad O 16ab
Answer:
13ab
Step-by-step explanation:
5ab+9ab = 14ab. 14ab-1ab=13ab.
Good luck
12 POINTS I NEED SOMEONES HELP BEFORE THIS DAY FINISHES
A town has a population of 2000 and grows at 4% every year. Write an
equation to represent the scenario
Answer:
2000+ (2000× .04x)
Step-by-step explanation:
2000 people plus the percent that it grows, found by multiplying .04 (4%) by the original number. the x is the number of years
HELPPPPPPPPPPPPPPPPPPPPPPPP
Answer: can i help wat is a tip
Which expression does NOT have a Greatest Common Factor?
Answer:
4x^2-9
Step-by-step explanation:
i just took the quiz
This is about greatest Common factor (G.C.F) thus Option C and Option D does not have a greatest common factor.
What is Greatest common factor?The Greatest common factor between 2 or more numbers is simply the greatest factor that is common to all the numbers.
Option A; 2x² -18
Factors of 2 are 1, 2
Factors or 18 are; 1, 2, 3, 6, 9, 18
In this option we can see that 2 is the only common factor between all the numbers.
Thus, the GCF = 2 So this has a GCF
Option B: 3x² + 12x + 6
Factors of 3 are 1, 3
Factors of 6 are 1, 3. 6
Factors or 12 are; 1, 2, 3, 4, 6, 12
The highest common factor is 3 Thus, this has GCF.
Option C; 4x² - 9
The factors of 9 are; 1, 3, 9
The factors of 4 are; 1, 2, 4
Since there is no highest common factor here as 1 is not considered to be a highest common factor even though it is a factor.
Option D; 6x² + 2x² + 5x
The factors of 9 are; 1, 3, 9
The factors of 4 are; 1, 2, 4
Since there is no highest common factor here as 1 is not considered to be a highest common factor even though it is a factor.
To Read more about the concept at;
brainly.com/question/17799077
#SPJ2
help i need help i can't figure this out
Answer: A) 23
Step-by-step explanation:
3^2 + ( 6 - 2 ) ⋅ 4 -6/3
3^2 + 4 ⋅ 4 -6/3
9 + 4 ⋅ 4 -6/3
9 + 16 -6/3
25 - 6/3
75/3 -6/3 = 69/3
69/3 = 23
Answer:
23
Step-by-step explanation:
3^2 + (6 - 2) x 4 - 6/3
3^2 + 4 x 4 - 6/3
9 + 16 - 6/3
25 - 6/3
6/3 = 2
25 - 2 = 23
For the pair of functions, find (f o g)(x) and (gof)(x).
f(x) = -2x2, g(x) = x + 4
A. (fog)(x) = -2x^2– 8x^2; (gof)(x) = -2x^3 - 8x^2
B. (fºg)(x) = -2x^2– 16x - 32; (g = f)(x) = -2x^2+ 4
C. (fog)(x) = -2x^2 + 4; (g e f)(x) = -2x^2- 16x - 32
D. (fog)(x) = -2x^2- 32; (go 3)(x) = -2x^2 + 4
I need help with this Algebra
Answer:
Step-by-step explanation:
f(-3) = 3(-3)^3 + 5 = 3(-27) + 5 = -81 + 5 = -76
g(4) = -4(4) - 1 = -16 - 1 = -17
Which function is most likely graphed on the coordinate plane below? f(x) = 3x – 11 f(x) = –4x + 12 f(x) = 4x + 13 f(x) = –5x – 19
Answer:
D
Step-by-step explanation:
It's D on Enginuity
The graph of the function in the coordinate plane is f(x) = –5x – 19.
What is a Graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
As per the given diagram:
The x intercept of the line = -ve
The y intercept of the line = -ve
For f(x) = 3x - 11
x intercept = +ve
y intercept = -ve
Hence, not possible
For f(x) = -4x + 12
x intercept = +ve
y intercept = +ve
Hence, not possible
For f(x) = 4x + 13
x intercept = -ve
y intercept = +ve
Hence, not possible
For f(x) = -5x - 19
x intercept = -ve
y intercept = -ve
Hence, possible
The function plotted on the coordinate plane is f(x) = –5x – 19.
To learn more on Graphs, click:
brainly.com/question/17267403
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When translating a number to the scientific notion (ex: 0.000157), do you count the zero to the left of the decimal point? Like would the scientific notion of 0.000157 be 1.57 x 10^-4 ? If you could explain how scientific notion works that be great. thanks
Answer:
You do not count the zero to the left of the decimal
Step-by-step explanation:
That zero is just a placeholder as there is nothing to the left of the decimal, you could also write the number as .000157
Your answer is correct, 0.000157 is 1.57x10^-4
Scientific notation is just expressing numbers in their exponential form. The power/exponent is found by counting how many times the decimal has moved to the right or the left.
A farmer applies different fertilizer to his wheat crops to see which will make his plants grow the highest.
What is the independent variable?
Answer:
highest )hope this helps :)
Step-by-step explanation:
Answer:
The crop
Step-by-step explanation:
As the type of fertilizer changes it can not be the independent variable. Since nothing else (except the farmer) is referenced we can deduct that the crop is the independent variable.
83.63 - 2.89 × (4.9 - 2.9)2 A. 72.07 B. 50.43 C. 1,046.56 D. 49.31 Please help
Answer:
A would be the anwser
Step-by-step explanation:
Answer: A. 72.07
Step-by-step explanation: Plato
563x367
use scratch paper to help you
Answer: 206621
Step-by-step explanation:
563x367=206621, so 563x7=3941, 563x60=33780, and finally 563x300=168900. Add them all up, 3941 + 33780 + 168900 = 206621.
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Describe and correct the error a student made when starting to solve the equation 8 ^ (x + 3) = 2 ^ (2x - 5) 8 ^ (x + 3) = 2 ^ (2x - 5) (2 ^ 3) ^ (x + 3) = 2 ^ (2x - 5) 2 ^ (3x + 3) = 2 ^ (2x - 5) Choose the correct answer below A. The student should have divided both sides by 2 ^ 2 to simplify the expression B. The student did not convert 8 to the correct power of 2 C. The student did not distribute 3 in * (2 ^ 3) ^ (x + 3) x + 3 D.The student should have expressed the initial rational exponent as the sum of two rational exponents ..
Answer:
C. is the correct option
C. The student did not distribute 3 in * (2 ^ 3) ^ (x + 3) x + 3
and x = - 14
Step-by-step explanation:
8 ^ (x + 3) = 2 ^ (2x - 5)
Here is how the student solved the equation
8 ^ (x + 3) = 2 ^ (2x - 5)
8 ^ (x + 3) = 2 ^ (2x - 5)
(2 ^ 3) ^ (x + 3) = 2 ^ (2x - 5)
2 ^ (3x + 3) = 2 ^ (2x - 5) ----- This is where the student made the error.
The student did not distribute 3 in * (2 ^ 3) ^ (x + 3).
This is how to solve the equation
8 ^ (x + 3) = 2 ^ (2x - 5)
8 ^ (x + 3) = 2 ^ (2x - 5)
(2 ^ 3) ^ (x + 3) = 2 ^ (2x - 5)
Then, we will 3 distribute in (2 ^ 3) ^ (x + 3), so that we get
2 ^ (3x +9) = 2 ^ (2x -5)
Since the bases on both sides of the equation are equal, we can equate the powers so that we get
(3x +9) = (2x -5)
Then we will collect like terms
3x - 2x = -5 -9
∴ x = -14
This solution could be better written in this format
[tex]8^{x+3} = 2^{2x-5} \\2^{3} ^{(x+3)} = 2^{2x-5}\\2^{(3x+9)} = 2^{2x-5}\\{(3x+9)} = {2x-5} \\3x-2x= -5-9\\x = -14[/tex]
The product of 7 and j is 91
j = 13
Step-by-step explanation:7×j = 91
j = 91 : 7
j = 13
what is the answer to
10 + (-4)
Answer:
6
Step-by-step explanation:
Note the rules for signs directly next to each other:
If there is two positive signs, the result will be positive.
If there is one positive and one negative sign, the result will be negative.
If there is two negative signs, the result will be positive.
In this case, there is a positive and a negative sign. You are, therefore, subtracting 10 with 4:
10 + (-4) = 10 - 4 = 6
6 is your answer.
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