In 2004, the population of butterflies in West Fremont is 60,000, and growing at a rate of 1.4% each year. Determine the year when the population will reach 240,000.
Answer:
99.713 years
Step-by-step explanation:
In year 2103, the population will reach 240,000
Here,
The population of butterflies in West Fremont is 60,000.
And, growing at a rate of 1.4% each year.
How to find interest?
Use compound interest formula [tex]A = P (1 + \frac{r}{100} )^n[/tex] to find interest.
Like in financial interest we have, [tex]A = P (1 + \frac{r}{100} )^n[/tex]
We have;
[tex]240000 = 60000 (1 + \frac{r}{100} )^n\\(1 + \frac{r}{100} )^n = \frac{24}{6} \\(1 + \frac{r}{100} )^n =4\\[/tex]
[tex]n ln (\frac{101.4}{100}) = ln (4)\\ n = \frac{ln 4}{ln 101.4 - ln 100}\\ n = 99.713[/tex]
Hence,
Year = 2004 + 99
So, In year 2103, the population will reach 240,000
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here is the screenshot for anyone who is willing to help me
Answer:
1. 6,000
2. 7,000-4,000=3,000
3. 0
4. 15
5, 6/8 7/8
6. greater than
7. equal to
8. 520,685
9. the 5
10a. 3210
10b. 2346
--------------------
1. 7,000
2. all of them
3. two
4. 3
5. 2
6. b
7a. 3 b. 2
8. 14/30
9. 3/8
10. N=175
Step-by-step explanation:
Which ratios form a proportion?
A) 4/10 and 10/25
B) 4/9 and 9/4
C) 3/5 and 9/25
D) 4/11 and 6/13
Help me. Please due today
Answer:
2). As x-> -∞, f(x)->∞
As x-> ∞, f(x)-> -∞
5). As x-> -∞, f(x)-> -∞
As x-> ∞, f(x)-> ∞
3). As x-> -∞, f(x)-> -∞
As x-> ∞, f(x)-> ∞
6). As x-> -∞, f(x)-> ∞
As x-> ∞, f(x)-> ∞
Step-by-step explanation:
I just watched a quick video so you can't completely trust me, but i tried my best. Hopefully someone more trustworthy for this comes in.
You work for a waste removal company. The trailer of one of your dump trucks is 10 feet wide, 15 feet long, and 6.5 feet high. If a ton of debris equals 200 cubic feet, how many trucks are needed to cart away 45 tons of debris from a demolition site?
Answer:
10
Step-by-step explanation:
Each trailer of each truck can cart away (10)(15)(6.5) = 975 cubic feet of debris.
To cart 45 tons of debris i.e. 200 x 45 = 9000 cubic feet of debris away, we need
9000/975 = 9.23 trucks.
Since you need at least 9.23 trucks, and you cannot have a decimal number of trucks, 10 trucks are needed to cart away 45 tons of debris from a demolition site.
Which of the following graphs represents the line that passes through (-2, -3) and has a slope of
Answer: A
Step-by-step explanation:
The answer is choice A since it has the rise and run of 2/3.
there are red, green and blue sweets in a bag, the ratio is 1:4:7 there 120 green sweets.how many sweets in total.
Answer:
Step-by-step explanation:
1:4:7
1+4+7=12
120+12+10
Answer:
Step-by-step explanation:
first divide 120/4 = 30
so everything needs to be multiplied by 30
new ratio is 30:120:210
add them together
30 + 120 + 210 = 360
hope this helps <3
If x/y=6 y/w=4 and x=36 , what is the value of w?
Answer:
w = 1.5
Step-by-step explanation:
if x equals 36 you have to figure out what 36 divided by equals 6 and thats 6 so y=6 then you have to take 6 and figure out what divided by it equals four and that is going to be 1.5
Answer:
w=3/2
Step-by-step explanation:
x/y=6 here x=36
then, 36/y=6
6y=36
y=36/6
y=6
here y/w=4
6/w=4
6=4w
w=6/4
w=3/2
Graham is folding a piece of paper to make an origami figure. Each time he folds the paper, the thickness of the paper is doubled. The paper starts out flat, with a thickness of 3 millimeters.
A. Write a list of six ordered pairs showing the output as the thickness of the paper when the input is the number of times it is folded. Explain how you came up with your ordered pairs.
B. Is this relation a function? Explain why or why not using the ordered pairs you came up with in Part A.
Answer:
A. Graph attached
B. It's a function. One input has only one output, it passed the vertical line test.
Step-by-step explanation:
a₀ = 3 a₁ = 6 = 3 x 2¹ a₂ = 6 x 2 = 3 x 2² ..... aₙ = 3 x 2ⁿ
answer graph attached
A list of ordered pairs may or may not represent a function.
The six ordered pairs are: [tex]\mathbf{(x,y) = \{(0,3),(1,6),(2,12),(3,24),(4,48),(5,96)\}}[/tex].The ordered pair is a function.(a) The ordered pair
Let x represent the number of folds, and y represent the thickness.
So, the first ordered pair is:
[tex]\mathbf{(x,y) = (0,3)}[/tex]
When x increases by 1, the value of y gets doubled.
So, the six ordered pairs are:
[tex]\mathbf{(x,y) = \{(0,3),(1,6),(2,12),(3,24),(4,48),(5,96)\}}[/tex]
(b) Is the ordered pair, a function
In (a), we have:
Every x value has a different corresponding y value.
This means that the ordered pair is a function.
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Multiply. Express your answer as a decimal. 1/2 x 15
Answer:
7 1/2
Step-by-step explanation:
convert mixed numbers to fractions to get 1/2 and 15/1
then, multiply the two to get 15/2
then simplify for the answer 7 1/2
answer 7.5
Step-by-step explanation:
convert the fraction to a decimal by dividing the numerator by the denominator
5. A triangle is shown.
5x
5x - 219
3x + 45
This
triangle has the same perimeter as an equilateral triangle with a side length of 3x + 58. What is the value
of x?
A. 87
B. 0
C. 23.2
D. 109.5
The set of whole numbers includes zero, but the natural numbers do not.
OA. True
OB. False
SUBMIT
Answer: True
The set of whole numbers is {0, 1, 2, 3, 4, 5, ...}
The set of natural numbers is {1, 2, 3, 4, 5, ...}
Both sets describe numbers that are positive and without any fractional or decimal component. The only difference is that 0 is included in the first set, but exclude from the second. If you want to include negative whole numbers as well, then you'd use the set of integers.
The given statement is true.
What is number?A number is an arithmetic value used to represent quantity. Hence, a number is a mathematical concept used to count, measure, and label. Thus, numbers form the basis of mathematics.
The statement given is says that, the set of whole numbers includes zero, but the natural numbers do not.
So, if we see the definition of both types of numbers, we can say that the whole numbers are the natural starting from 0, and the natural numbers are the one which includes only counting numbers used in our daily life.
Hence, the given statement is true.
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A resale stores having a sale on DVDs and cds. DVDs cost $7 and CDs cost $4. on one day, the store made $211 from DVD and CD sales and so the total of 40 times. Write a system of equations then solve to find how many DVDs and CDs were sold show both the equations and the solution
Answer:
Step-by-step explanation:
7 x 20
4 x 17
What is a decimal that is equivalent to the fraction 7/10
Answer: 0.7
Step-by-step explanation:
Answer:
0.7 is the decimal
Help
D
Dmsjzjzjzjjzzxhxhxhxhxhxh
Answer:
18
Step-by-step explanation:
[tex]{82 { }^{2} } - 80 {}^{2} = 324 \\ \sqrt{324 } = 18[/tex]
please answer a through d
Answer:
See explanation below.
Step-by-step explanation:
Given: 100 lbs on Earth is 16.6 lbs on the moon.
a. The independent variable is weight. The gravity of the Moon and the gravity of the Earth are constant. Weight can change, but gravity is a constant.
b. An equation that relates the weight of someone on the Moon who travels to the Earth:
100 / 16.6 = 6.02. Take the Moon weight and multiply by 6.02:
Moon Weight * 6.02 = Earth Weight.
Proof:
16.6 * 6.024 = 99.99 - approximately 100 lbs Earth weight.
c. A 185 lb astronaut on Earth would weigh:
16.6 / 100 = .166. Take the Earth weight and multiply by .166:
185 * .166 = 30 lbs on the Moon.
d. A person who weighs 50 lbs on the Moon:
50 * 6.024 = 301.2 lbs on Earth.
Hope this helps! Have a good day and year! :)
PLZ HELP!! Select the correct answer.
It would take Charlene and Gina 18 minutes to organize Charlene's comic book collection if they work together. If Gina works alone, it would take her 15 minutes long than it would take Charlene working alone.
When x represents the number of minutes it takes Charlene to organize the comic book collection working alone, the situation is represented by this equation: 1/x +1/x+15=1/18
Which value is a solution of the rational equation that must be discarded because of the context?
A x=0 B. x=-9 C. x=-15 D. X=-30
Answer:
the answer is x=-9
Step-by-step explanation:
The value of a solution of the rational equation that must discard and nullify the context of the equation is -9
Word problems in mathematics require crucial understanding because they are used to solve a real-life scenario. It entails the gathering of all information necessary to arrive at the solution.
From the information given:
It will take Charlene and Gina 18 minutes to organize comic books Gina will use = 15 minutes if Gina works alonewhere x represents the number of minutes
The equation representing the above information is given as:
[tex]\mathbf{\mathbf{\dfrac{1}{x}+ \dfrac{1}{x+15}= \dfrac{1}{18}}}[/tex]
The objective of this question is to determine the value in which it will discard and nullify the context of the above equation.
In that case, the number must be a number in which when substituted into the above equation will result in having the same value on the left-hand side and the right-hand side.
From the given option, the number that results in that is -9
[tex]\mathbf{\mathbf{\dfrac{1}{-9}+ \dfrac{1}{-9+15}= \dfrac{1}{18}}}[/tex]
[tex]\mathbf{\mathbf{0.05555555556= 0.05555555556}}[/tex]
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Find the LCM of 12 and 27 using prime factorizations
Step-by-step explanation:
Prime Factorization of 12
2 12
2 6
3 3
1
Prime factors of 12 are 2,3. Prime factorization of 12 in exponential form is:
12 = 22×31
Prime Factorization of 27
3 27
3 9
3 3
1
Prime factors of 27 are 3. Prime factorization of 27 in exponential form is:
27 = 33
Now multiplying the highest exponent prime factors to calculate the LCM of 12 and 27.
LCM(12,27) = 22×33
LCM(12,27) = 108
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1, 2, 3, 4, 6, 12
Factors of 27
List of positive integer factors of 27 that divides 27 without a remainder.
1, 3, 9, 27
Least Common Multiple of 12 and 27 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12 and 27, than apply into the LCM equation.
GCF(12,27) = 3
LCM(12,27) = ( 12 × 27) / 3
LCM(12,27) = 324 / 3
LCM(12,27) = 108
Least Common Multiple of 12 and 27 by Listing Multiples
Multiples of 12
12, 24, 36, 48, 60, 72, 84, 96,108
Multiples of 27
27, 54, 81,108
Find the smallest number that is on all of the lists. We have it in bold above.
∴ Least Common Multiple of 12 and 27 is 108
Properties of LCM 12 and 27
(i) The LCM of 27 and 12 is associative
LCM of 12 and 27 = LCM of 27 and 12
Frequently Asked Questions on LCM of 12 and 27
1. What is the LCM of 12 and 27?
Answer: LCM of 12 and 27 is 108.
2. What are the Factors of 12?
Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.
3. What are the Factors of 27?
Answer: Factors of 27 are 1, 3, 9, 27. There are 4 integers that are factors of 27. The greatest factor of 27 is 27.
4. How to Find the LCM of 12 and 27?
Answer:
Least Common Multiple of 12 and 27 = 108
Step 1: Find the prime factorization of 12
12 = 2 x 2 x 3
Step 2: Find the prime factorization of 27
27 = 3 x 3 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 108 = 2 x 2 x 3 x 3 x 3
Step 4: Therefore, the least common multiple of 12 and 27 is 108.
The LCM (least common multiple) of 12 and 27 using prime factorizations would be 108.
Used the concept of least common multiple that states,
The Least common multiple of two or more numbers is the smallest number that is a multiple of two or more numbers.
Given that the two numbers are 12 and 27.
Hence, the prime factorizations of 12 and 27 are,
12 = 2 × 2 × 3
27 = 3 × 3 × 3
So, the LCM of 12 and 27 is,
2 × 2 × 3 × 3 × 3
= 108
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Which numbers are solutions to the equation 30 = r2? Select all that apply. X = 15 x = 30 X = 900 X = -15 T- 30 Ox= = -900
Answer:x=15
Step-by-step explanation:
What is the percent change when your savings increases from $50 to $85?
Answer:
70%
Step-by-step explanation:
Calculating Percent Increase
Example 1: Jackson’s intern job at a software company paid $15.42 an hour. He graduated from college and accepted a full-time position from the same company for a larger wage of $35.52 an hour. What is Jackson’s percent increase in pay?
Solution: Using the handy-dandy Percent Change Calculator, dropping the two amounts into it quickly returns a percent pay increase of 130.35%. Here’s how the calculator found the percent increase. We assign the older value to variable A and the newer value to variable B. Units, in this case the dollars, are always stripped or canceled out in percent change problems since we’re looking for increases or decreases in percentage. So in the first part of the equation we take 35.52 and subtract 15.42 from it and get 20.10. Then we divide that amount by the original older value and get 1.3035. Now we must convert that number to a percent by multiplying it by 100. That gives us a percent increase answer of 130.35%. Formula Completed: [(35.52-15.42)/15.42) x 100] = 130.35%
True Value Hardware ordered 112 rakes. When True Value received the order, 46 rakes were missing. What percent of the order did True Value receive? (round to the nearest 100th)
Answer:
true value received 58.93% or the order.
What is an
equation of the line that passes through the points (-4, 4) and (8,1)?
Answer:
-1/4x + 3
Step-by-step explanation:
Answer:
y=-1/4x + 3
Step-by-step explanation:
i just got it right
PLEASE HELP PLEASE Which of the following expressions could be used to represent "three less than half a number"?
1/3 - 3 n
3 n - 1/2
3 - 1/2n
1/2 n - 3
Answer:
1/3
Step-by-step explanation:
because it was right
Line B passes through the points (5, 10) and (0,0). What is the slope of the line perpendicular to line
B?
Answer:
-1/2 is the answer
Step-by-step explanation:
Laura randomly pulled a marble from a bag and then replaced it.
• After 60 trials, she had pulled the color blue 25% of the trials.
• She had pulled red 15% of the trials.
• The remaining trials she pulled green.
How many times could Laura be expected to pull a green marble after 300 trials?
O A. 150
OB. 120
O C. 180
OD. 100
Answer: C. 180 times
Step-by-step explanation:
From the 60 trials, the percentage of times Laura picked a green marble was:
= 100% - Percentage of times blue and red were picked
= 100% - 25% - 15%
= 60%
If these results were repeated with 300 trials, the number of times Laura would be expected to pick green would be:
= 60% * 300
= 180 times
What is the value of x in the figure shown below?
С
4.7
D
42°
3.5
3.5
30
B
А A
4.7
=
Answer:
30 degrees
Step-by-step explanation:
It's a pateelogram so oppate angles are equal so
x = 30 degrees
Hope this helps :)
The measure of x is 30 degree.
What are parallel line?The fundamental characteristics listed below make it simple to recognise parallel lines.
Straight lines that are always the same distance apart from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.As, we know that the Property of Parallel line are:
Corresponding angle are Equal.
Alternate interior Angles are Congruent.
Vertical angles are Congruent.
As, per the figure we can see that
AB || CD
So, by Alternate Interior Angle
<DCB = <CBA
x = 30
Thus, the measure of x is 30 degree.
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My sister need help!!!
Answer:
nice hand writing
Step-by-step explanation:
Evaluate the expression below
72+ 5 (3 4) - 62
Answer: 3/4
Step-by-step explanation:
Please help me answer this with the correct answer :)
Explain your answer
I will give braisnlt :)
Answer: Choice A) If Amber and Jorge each sell 5 trees in one week, they will earn the same amount
The amount they earn is $200 each.
========================================================
Explanation:
Let's form the equation for the amount Amber earns.
She starts off at $150, and then we add on 10x dollars. The 10x is because she earns 10 dollars per tree, and we have x be the number of trees sold.
Overall we can say her equation is y = 150+10x
This is the same as y = 10x+150
----------
Since Jorge's equation is y = 25x + 75, we can apply substitution to solve for x
y = 10x+150
25x+75 = 10x+150 .... replace y with 25x+75
25x+75-10x = 150 ... subtract 10x from both sides
15x+75 = 150
15x = 150-75 ... subtract 75 from both sides
15x = 75
x = 75/15 .... divide both sides by 15
x = 5
If they sell 5 trees per week, then Amber and Jorge earns the same amount of money.
That amount earned is
Amber: y = 10x+150 = 10*5+150 = 50+150 = 200 dollars
Jorge: y = 25x+75 = 25*5+75 = 125+75 = 200 dollars
Both earn $200 per week from selling 5 trees for that week. This helps confirm we have the right answer.
us
The legend on a map states that 1 inch
is 600 miles. If you measure 5 inches
on the map, how many miles would
the actual distance be?
Answer:
3,000
Step-by-step explanation:
one inch is equal to 600 miles, 5 × 600 = 3,000
Answer:
3,000
Step-by-step explanation:
600 times 5= 3,000
I hope this helps :)
