Answer: bn= 150*3^(n-1)( bn is a quantity of bacteria in generation n)
Step-by-step explanation:
It looks like geometrical sequence, each next generation is three times greater than previous one. So the r of this sequence is 3.
The first generation has 150 representatives, so b1=150
The formula of geometrical sequence is bn=b1*r^(n-1)
(in our case bn is a quantity of bacteria in generation n)
so bn= 150*3^(n-1)( bn is a quantity of bacteria in generation n)
Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of xx that support your conclusion.
x = x + 3
The equation has ____.
(options are no solution, one solution, or infinite solutions)
A value of x that makes the equation false is ___, which when substituted into the equation and simplified makes the equation turn into ___ = ____.
Another value of x that makes the equation false is ___, which when substituted into the equation and simplified makes the equation turn into ___ = ___.
Answer:
There are no solutions.
The left side of the equation will always be three less than the right side of the equation since both sides have the same variable.
The population of the world grows exponentially at a rate of 1.1% per year.
Find the number of years it takes for the population to grow from 7 billion to 7.31 billion.
Give your answer correct to the nearest whole number.
Answer:
4
Step-by-step explanation:
Every year, the world grows by 1.1%. Converting to a decimal, we can divide by 100 to get 1.1% = 0.011. This means that the world grows by 0.011 exponentially each year. To put this into an expression, we can add 1 to our percentage to get 1.011. This represents 1 = 100% (the original population) and the growth of 1.1% = 0.011. We multiply the rate including the growth by the population to get the population after one year. After the first year, we have
population * 1.011 as the new population after one year. We do that for every year, so the second year's population is population*(1.011)*(1.011) and so on. If x represents the amount of years, then the population can be represented as
(original population)*1.011ˣ
Therefore, to get from 7 billion to 7.31 billion, we have
7 billion * 1.011ˣ = 7.31 billion
divide both sides by 7 billion to relatively isolate the x
1.011ˣ = 7.31/7
Another way of writing this is
log (base 1.011) (7.31/7) = x
≈ 3.96
Rounding to the nearest whole number, we get 4 as our answer
The number of years it takes for the population to grow from 7 billion to 7.31 billion is;
n = 4 years.
We are told that the population of the world grows exponentially by 1.1% per year. This is equivalent to growth of 0.011 per year exponentially.
Now, since the exponential rate is 0.011 per year, thus, if the original population is P, then after a year, the new population will be;
P_1 = 1.011¹ × P
After 2 years, it will be;
P_2 = 1.011² × P
Thus, if n represents the number of years after the initial population, then population after n years if original population is P is;
P_n = 1.011ⁿ × P
Now, we are told that the population grew from 7 billion to 7.31 billion.
Thus;
P = 7 billion
P = 7 billion P_n = 7.31 billion
Thus;
7 billion × 1.011ⁿ = 7.31 billion
divide both sides by 7 billion to get;
1.011ⁿ = 7.31/7
1.011ⁿ = 1.044285
n log 1.011 = log 1.044285
n = 0.018819/0.004751156
n ≈ 4 years
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Write and equation in point slope form:
Perpendicular to the line y=2x+6; passes through the point (0,9).
Answer:
y - 9 = -1/2 (x - 0)
Step-by-step explanation:
perpendicular slope = -1/2
y - 9 = -1/2 (x - 0)
PLZ HELPP
Q: Nitrates are organic compounds that are a main ingredient in fertilizers. When those fertilizers run off
into streams, the nitrates can have a toxic effect on
fish. An ecologist studying nitrate pollution in two
streams measures nitrate concentrations at 42 places on Stony Brook and 42 places on Mill Brook. The parallel dotplots display the data.
1. Explain what the dot above 12 in the Stony Brook graph represents.
By looking at the dot graph, we can see that the single dot above 12 in the Stony Brook graph, means that the ecologist find that in one of the 42 places measured in the Stony Brooks lake, the nitrate concentration was 12 mg/L
To understand this, first I want to give a brief explanation of how these graphs work.
You know that the ecologist did study the Nitrate pollution at 42 places in two lakes.
Each of these 42 places is represented with a dot in the corresponding graph. Now looking at the graph, the position of the dots represents the nitrate concentration (you can see it in the horizontal axis) on one of these 42 places (42 dots for 42 places).
So, having a single dot above 12 in the Stony Brook graph, means that the ecologist find that in one of the 42 places measured in the Stony Brooks lake, the nitrate concentration was of 12 mg/L
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A van moves with a constant speed of 116 km/h. How long will it take to travel a distance of 174 kilometers?
Answer:
1.5 hours / 90 minutes
Step-by-step explanation:
time = distance ÷ speed
A car accelerates from stationary state to X kmj-1 in 10 minutes. If the acceleration of the car is 300 km h-2, find the value of X.
Step-by-step explanation:
X = Acceleration × time
=300× (10/60)
=50km/h
What fraction is equal to -0.37?
A(-1, 3), B(2, 2), and C(3, -6). If the triangle is translated 5 units to the right, what are the coordinates of A'?
Answer:
(4,3)
Step-by-step explanation:
If the triangle ABC is moved 5 units to the right, the coordinates of A will be (4,3). We can find this by using the values already given for A. We are given (-1,3) which is A's current position. Since we are moving it to the right we are only looking at the first number. If we add 5 to -1 we get 4 which we put in the place of the -1 in the coordinates to get our answer.
hey please help i’ll give brain new question sorry
Answer:
12. This is because of the commutative property of addition.
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
Using the commutative property of addition
8+4 = 12
4+8 = 12
If QS bisects PQT, SQT=(8x- 25),PQT=(9x+34), and SQR=112, find each measure.
The values of the angles are;
x = 12°
m∠PQS = 71°
m∠PQT = 142°
m∠TQR = 41°
The reason the above values are correct is as follows:
Question: The part of the question that appears missing as obtained online is as follows;
The required angles: x, m∠PQS, m∠PQT, and m∠TQR
Please see attached drawing of the angles from the question
The given parameters are;
[tex]\overset{\longrightarrow}{QS}[/tex] bisects ∠PQT
m∠SQT = (8·x - 25)°
m∠PQT = (9·x + 34)°
m∠SQR = 112°
We have;
m∠PQT = m∠SQT + m∠PQS (Angle addition postulate)
m∠SQT ≅ m∠PQS (Angles formed by angle bisector are congruent)
m∠SQT = m∠PQS Definition of congruency
m∠PQT = 2 × m∠SQT
Therefore;
(9·x + 34)° = 2 × (8·x - 25)° = (16·x - 50)°
Collecting like terms gives;
(34 + 50)° = 16·x - 9·x = 7·x
7·x = 84°
x = 84°/7 = 12°
x = 12°
m∠SQT = (8·x - 25)°
Therefore;
m∠SQT = (8 × 12 - 25)° = 71°
m∠SQT = 71°
m∠PQT = 2 × m∠SQT
∴ m∠PQT = 2 × 71° = 142°
m∠PQT = 142°
m∠PQS = m∠SQT (Angles formed by the same bisector [tex]\overset{\longrightarrow}{QS}[/tex])
∴ m∠PQS = m∠SQT = 71°
m∠PQS = 71°
m∠SQR = m∠SQT + m∠TQR (Angle addition postulate)
m∠SQT = 71°
∴ m∠SQR = 112° = 71° + m∠TQR
m∠TQR = 112° - 71° = 41°
m∠TQR = 41°
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X/6 = 8 what is the answer
Answer:
x = 48
Step-by-step explanation:
Multiply both sides by 6
x = 6 * 8
x = 48
Check:
48/6 = 8
8 = 8
Answer:
[tex] \frac{x}{6} = 8 \\ \\ x = 8 \times 6 \\ \\ x = 48[/tex]
can someone please help me please
Max drove 185 miles on the Autobahn. He drove for 2 hours at 65 miles per hour, and then sped up to 110 miles per hour for the last part of his trip.
Solve this equation for t
to find out how many hours Max drove at 110 miles per hour.
185 = 65(2) + 110t
Answer:
Max drove half an hour at 110 miles per hour.
Step-by-step explanation:
185 = 65(2) + 110t
185 = 130 + 110t
-130 -130
---------------------------
55 = 110t
/110 /110
----------------------------
0.5 = t
I need help solving this.
16 - 2t + 5t +9
Answer:
give brainliest please I need it to level up
Step-by-step explanation:
16 - 2t + 5t + 9
16 + 9 -2t + 5t=0
25 + 3t =0
3t= -25
t= -8.3
2/9+1/3 thx for helping I need ASAP
Step-by-step explanation:
[tex] \frac{2}{9} + \frac{1}{3} \\ by \: taking \: out \: the \: lcm \: of \: 9 \: and \: 3 \: \\ we \: get \: 9\: as \: lcm \\ now \\ \frac{2 \times 1 + 1 \times 3}{9} \\ \frac{2 + 3}{9} \\ \frac{5}{9} [/tex]
15 L + 2% please help
Answer:
15.3 L
Step-by-step explanation:
1% of 15 is 15÷100=0.15
0.15×2=0.3, so 2% is 0.3
15+0.3=15.3
Two numbers are said to be -------- If they do not have common factor other than 1.
When two numbers have no common factors other than 1. In other words there is no value that you could divide them both by exactly (without any remainder). Relatively Prime is also called "coprime" or "mutually prime".
I think this help you Now thank you
The answer is Co-prime
Hope It Help
Find the area of the shape.
Either enter an exact answer in terms of π or use 3.143, point, 14 for π and enter your answer as a decimal
Answer:
84.861
Step-by-step explanation:
In the given figure, 1/4 part of Circle is missing
so, we have to find the area of 3/4 part of circle
Area of circle = πr²
Given, r = 6
Now, Area of 3/4 part of circle = (3/4)×πr²
= (3/4) × 3.143 × 6²
= 84.861
Please help me one question left
Answer:
thanks for points
Step-by-step explanation:
too easy boi
Fine the measurements. Are this correctly?
Answer:
1: 5 2: 13 3: sqr root of 15 4: 1 5: 1 6: 3
Step-by-step explanation:
Follow the formula a squared plus b squared equals c squared. C is always the longest side of the equation. So figure out your variables to fill in and in the end, square root your remaining answer.
which is the simplified form of the expression
please help!!
Answer:
A
Step-by-step explanation:
p^-8q^-20 * p^8q^-10
=q^-30
=1/q^30
SOMEONE HELP ME PLEASE AND SHOW WORK
Answer:
23
Step-by-step explanation:
9x-4=6x+5
3x-4=5
3x=9
x=3
plug in x
6(3)+5 = 23
If ∠ROQ and ∠ROS are complementary angles, then what is the value of x and m∠ROS?
A.
x = 28; m∠ROS = 60°
B.
x = 31; m∠ROS = 62°
C.
x = 62; m∠ROS = 31°
D.
x = 60; m∠ROS = 28°
Answer:
B. x = 31; m∠ROS = 62°
Step-by-step explanation:
Complementary angles add to 90
∠ROQ + ∠ROS = 90
28+2x = 90
Subtract 28 from each side
2x = 90-28
2x=62
Divide by 2
2x/2 = 62/2
x = 31
∠ROQ =28
∠ROS = 2x=2*31 = 62
Sophie bought snacks for her team's practice. She bought a bag of chips for $2.49 and
a 12-pack of juice bottles. The total cost before tax was $27.57. Write and solve an
equation which can be used to determine x, how much each bottle of juice costs?
Call a bottle of juice costs is x
$2.49 + 12x = $27.57
12x = $27.57 - $2.49
12x = $25.08
x = $25.08 / 12
x = $2.09
SO each bottle of juice costs $2.09.
Mark as Brainliest If the answer is helpful!
Verify the following (-23) { ( -5) + (19) } = ( -23) x -5 + (-23) x (19)
explanation needed fast pls
What is -0.1 as a fraction?
Answer:
-1/10
Step-by-step explanation:
after (.) we put zero in the denominator according to how many numbers are after .
-0.1= -1/10
hope this will help you
plz mark me as braniliest
ten times the sum of half a number and six is eight
Answer: x=585
Step-by-step explanation:
thats the answer
hey please help i’ll give brain
Answer:
[tex]7 \times 6 = 5 \: sixes + 2 \: sixes \\ 7 \times 6 = 30 + 12 \\ = 42 \\ \\ thank \: you[/tex]
Hi ;-)
[tex]7\cdot6=5 \ \text{sixes}+\boxed2 \ \text{sixes}\\\\=\boxed{30}+12\\\\=\boxed{42}[/tex]
a jar contains 65 pennies 27 nickels 30 dimes and 18 quarters a coin is randomly selected from the jar find each probability
The required probabilities are [tex]P(\text{pennies})=\dfrac{13}{28},P(\text{nickels})=\dfrac{27}{140},P(\text{dimes})=\dfrac{3}{14},P(\text{quarters})=\dfrac{9}{70}[/tex].
Given:
Pennies = 65
Nickels = 27
Dimes = 30
Quarters = 18
To find:
The probability of each.
Solution:
The probability formula:
[tex]\text{Probability}=\dfrac{\text{Favorable outcome}}{\text{Total outcomes}}[/tex]
Total number of coins:
[tex]65+27+30+18=140[/tex]
The probability of selecting Pennies is:
[tex]P(\text{pennies})=\dfrac{65}{140}[/tex]
[tex]P(\text{pennies})=\dfrac{13}{28}[/tex]
The probability of selecting nickels is:
[tex]P(\text{nickels})=\dfrac{27}{140}[/tex]
The probability of selecting dimes is:
[tex]P(\text{dimes})=\dfrac{30}{140}[/tex]
[tex]P(\text{dimes})=\dfrac{3}{14}[/tex]
The probability of selecting quarters is:
[tex]P(\text{quarters})=\dfrac{18}{140}[/tex]
[tex]P(\text{quarters})=\dfrac{9}{70}[/tex]
Therefore, the required probabilities are [tex]P(\text{pennies})=\dfrac{13}{28},P(\text{nickels})=\dfrac{27}{140},P(\text{dimes})=\dfrac{3}{14},P(\text{quarters})=\dfrac{9}{70}[/tex].
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Avery has three times as much money as Jackie. Jackie has $6 less than Samantha. Together they have $56. How much money does each have?
HEEEEELP
The money belongs to Jackie, Avery, and Samantha is $10, $30, and $16 respectively.
Given that,
Avery has three times as Jackie.
Also, Jackie has $6 lower than Samantha.
Together they have $56.
Based on the above information
Let us assume the Jackie be x
So, Avery should be 3x
Samantha should be x + 6
So, the equation should be
x + 3x + x + 6 = $56
5x = $56 - $6
5x = $50
x = $10
So, Jackie has $10
Avery has $30
And, Samantha has $16
Therefore we can conclude that the money belongs to Jackie, Avery, and Samantha is $10, $30, and $16 respectively.
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