The function to represent the growth of the bacteria overtime in your science experiment is:
[tex]y = 70(3^x)[/tex]
Solution:
Given that,
Suppose you are performing an experiment in science class in which you start with 70 bacteria and the amount of bacteria triples every hour
Let,
y is the number of bacteria at time x
x is the number of hour(time)
As per the given information,
You start your experiment with 70 bacteria,and the bacteria triples in every hour
Therefore,
At end of 1 hour,
y = 70 x 3 = 210
At the end of 2 hours,
[tex]y = 210 \times 3 = 630\\\\Which\ can\ also\ be\ written\ as\\\\y = 70 \times 3^2 = 70 \times 9 = 630[/tex]
At the end of 3 hours,
[tex]y = 630 \times 3 =1890 \\\\Which\ can\ also\ be\ written\ as\\\\y = 70 \times 3^3 = 70 \times 27 = 1890[/tex]
Thus at end of "x" hours we will have,
[tex]y = 70 \times 3^x\\\\y = 70(3^x)[/tex]
Thus the function to represent the growth of the bacteria overtime in your science experiment
2) Solve the System of Equations using Substitution. (5 points) -3x+2y=12 x=2y-8
Answer:
x= -2 and y= 3
Step-by-step explanation:
since x = 2y -8, substitute this in the first equation
Thus, -3(2y-8) + 2y =12
-6y+24+2y=12
-6y+2y=12-24
-4y=-12
y=3
put the value of y in the second equation,
x=2y-8
x=2(3)-8
x=6-8
x=-2
So, x=-2. y=3
Answer:
(x, y) = (-2, 3)
Step-by-step explanation:
You want the solution to the system of equations ...
-3x +2y = 12x = 2y -8SubstitutionUsing the second equation, we can add 8 to get an expression for 2y:
x +8 = 2y
Substituting this into the first equation gives ...
-3x +(x +8) = 12
-2x = 4 . . . . . . . . . simplify, subtract 8
x = -2 . . . . . . . . divide by -2
-2 +8 = 2y . . . . substitute for x in the rearranged equation 2
y = 6/2 = 3 . . . . . . simplify, divide by 2
The solution is (x, y) = (-2, 3).
Simplify the expression 3^-8 × 3^4.
Answer:
Step-by-step explanation:
3^-8 × 3^4
Following the indices rule
a^y × a^z = a^(y+z)
:- = 3^(-8+4)
= 3^-4
= 1/3⁴
= 1/81
what equation is equivalent to y=2x+3 ?
Answer:
x+x +1+2= y
Step-by-step explanation:
in equilateral ABC what does y equal
Answer:
y = 75°, and I'm pretty sure this sheet is incorrect
Step-by-step explanation:
The interior angles of a triangle always add up to 180, and in an equilateral triangle, all 3 angles are congruent. (180/3 = 60)
[tex]m\angle A= 60\textdegree= 6x[/tex]
Therefore, [tex]x=10\textdegree[/tex]
[tex]\triangle DAE[/tex] is an isosceles triangle, as [tex]\angle B[/tex] [tex]\cong[/tex] [tex]\angle C[/tex], the sides opposite to them are also congruent; [tex]\overline{\rm AE}\cong\overline{\rm AD}[/tex] and in turn, [tex]m\angle ADE \cong m\angle AED: m\angle ADE = m\angle AED = y[/tex]
If [tex]m\angle DAE = 3x = 30\textdegree[/tex], then [tex]y = (180-30)/2 =150 /2 = 75\textdegree[/tex]
Chas builds a circular pen for his dog. The radius
of the pen is 9 feet. How much fencing did Chas
use for the pen?
A 28.26 feet
C 63.585 feet
B 56.52 feet
D 254.34 feet
Do you need to
the circumfere
or the area of
circle?
Skye chose A as the correct answer. How did she get that answer?
Answer:
when ever they say fencing it is perimeter i will send rhe rest later
she did 2×pie (3.14 according to the question )×radius (9)
Answer:
The correct answer is 56.52 feet
Step-by-step explanation:
(I know the question is supposed to be about how skye got the answer but if you wanted to know the real answer im here for you).
Tahmar knows the formula for simple interest is l=prt where I represent the simple interest on an amount of money p for t years at r rate she transforms the equation to isloate p : p using this formula what is the amount of money p that will generate $20 at a 5% interest rate over 5 years
Answer:
$80
Step-by-step explanation:
The formula for p is ...
p = I/(rt)
Filling in the given values, we get ...
p = $20/(0.05·5) = $80
The amount that will generate the desired interest is $80.
Tanya needs to earn another $100 to buy a new cell phone . She works 5 days this week. How much money will she have to earn each day in order to be able to buy the phone?
which is the product of 7/9 and 6? answer it
The product of multiplying 7/9 and 6 is 42/9, which can also be expressed as the mixed number 4 and 2/3.
Explanation:Finding the product of two numbers in mathematics is a fundamental concept which involves multiplying the numbers together.
In the specific case of multiplying a fraction by a whole number, like 7/9 and 6, the process is straightforward.
To calculate 7/9 multiplied by 6, you can think of the whole number 6 as a fraction with a denominator of 1, which would make the problem 7/9 x 6/1.
When multiplying fractions, you simply multiply the numerators together and then multiply the denominators together. In this instance, the multiplication would look like (7 x 6) for the numerator and (9 x 1) for the denominator.
That simplifies to 42 over 9, which can be further simplified or left as an improper fraction depending on the context of the problem or the instructor's directions.
In the case of 42/9, which is already simplified, we can conclude that the product of 7/9 and 6 is 42/9, or 4 and 2/3 when written as a mixed number.
What is the diameter of a cylinder that has a volume of 237 cubic units and a height of 3 units? Show your calculations.
Answer:
The Diameter of the cylinder is 10.29 units
Step-by-step explanation:
Given:
Volume of the Cylinder = 237 cubic units
Height of the Cylinder = 3 units
To Find :
Diameter = ?
Solution:
The Volume of the cylinder = [tex]\pi r^2 h[/tex]
where
r is the radius
h is the height
On substituting the values
[tex]237 = \pi (r)^2 (3)[/tex]
[tex]\frac{237}{ 3 \pi} = r^2[/tex]
[tex]\frac{79}{\pi} = r^2[/tex]
[tex]25.146 = r^2[/tex]
r = 5.014 units
Noe the diameter is = 2r = 2( 5.014) = 10.29 units
PLEASE ANSWER
What is the slope of the graph?
Answer:
The slope is 5/3
Step-by-step explanation:
In order to find the slope from a graph, you have to use the method called "rise over run". You do this by looking at the point (0,-1). and going up on the y axis and counting until its on the SAME y axis for the next point which is at (3,4). If you count from -1 to 4, you'll get 5, which is the rise number. Next you have to solve the "run" number. Now that we already have our rise number start from (0,4) and count how many ticks/counts it takes to move the x axis to the point (3,4). It takes 3 counts. Since it's called rise/run. You put 5 at the top, and 3 at the bottom.
[tex]\frac{5}{3}[/tex]
Hope this helps :)
Factor completely x3 + 7x2 − 2x − 14.
(x − 7)(x2 − 2)
(x + 7)(x2 + 2)
(x + 7)(x2 − 2)
(x − 7)(x2 + 2)
The factor of the provided polynomial after the factorization process are similar to option C, (x+7)(x²-2)
How to find the factor of polynomial?The factor of a polynomial is the terms in linear or equation form, which are when multiplied together, give the original polynomial equation as result.
Find these factors by taking out the common factors.
The given polynomial equation in the problem is,
x³+7x²-2x -14
The above equation has the unknown variable x and the highest power of this unknown variable is 3.
Take out the highest common factor x², which can divide each term of the first two terms of equation (x³, 7x²). Thus,
x²(x+7)-2x-14
Take out the highest common factor -2 from the second two terms as,
x²(x+7)-2(x+7)
Now take out the common group (x+7) as,
(x+7)(x²-2)
Hence, the factor of the provided polynomial after the factorization process are similar to option C, which is
(x+7) (x²-2)
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HURRY
If you try to solve a linear system by the substitution method and get the result 0 = 8, what does this mean?
A. The system has one solution, (0, 8).
B.The system has one solution, (8, 0).
C.The system has no solutions.
D.the system has an infinite number of solutions.
Answer:
C
Step-by-step explanation:
0 = 8 is a false statement which means the system has no solutions
The 0 = 8 shows the system has no solutions.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
we have 0= 8.
First whenever we get 0 = 0 in this case the solution will infinite many solution.
and, if we get the quantities on both side are equal then it have unique solution.
Lastly, if we have non equal quantity on both side of equal like 0= 8 then it does not have any solution.
Hence, 0 = 8 shows the system has no solutions.
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What conjecture can you make about the number of regions created by n unique diameters ?
Answer:
2n
Step-by-step explanation:
Look at the photo below for the details.
:)
Diameter of circle is known as greatest chord of the circle.
Number of regions created by n unique diameter is 2n.
Diameter of circle is two times of its radius.
By 1 diameter, two region is created in circle
By 2 diameter, 4 region is created in circle.
By 3 diameter , 6 region is created in circle.
Therefore, by n unique diameters, 2n regions is created in circle.
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I need someone to explain this to me. I don’t understand it at all. :(
4. Calculate the distance Kris walks in 8 days
if she walks 7/8mile each day.
Answer:
I have two ideas on how to solve the question for anyone that befit you you choose I hope it helps
but I prefer the second one.
Kris walks a total of 7 miles over the course of 8 days by multiplying the daily walking distance of 7/8 mile by 8 days.
To calculate the total distance Kris walks in 8 days, where she walks 7/8 mile each day, we need to perform a multiplication of the daily distance by the number of days.
The calculation will be:
7/8 mile/day * 8 days = 7 miles.This is because each 7/8 gets multiplied by 8, effectively cancelling out the denominator of 8, resulting in 7 whole miles.
Therefore, Kris walks a total of 7 miles over the course of 8 days.
7. A person walks at a speed of 1.5 m/s for 35 seconds. How far has the person walked?
Answer:
52.5 meters
Step-by-step explanation:
1.5 times 35 would equal 52.5 meters.
Answer:
52.5 meters
Step-by-step explanation:
1.5 * 35
Which facts could be applied to simplify this expression? Select three options.
(Negative 5 x minus 3 y) minus (negative x minus 3 z)
To subtract like terms, subtract the coefficients, not the variables.
Like terms are terms that contain the same variable, raised to the same power.
The simplified expression is Negative 6 x minus 3 y + 3 z.
The simplified expression is Negative 4 x minus 3 y + 3 z.
Negative (negative x) is equivalent to Negative x, so Negative 5 x minus x = negative 6 x.
Answer:
A, B, and D
Step-by-step explanation:
To subtract like terms, you're supposed to subtract the coefficients, so Option 1 is correct. The statement like terms are terms that contain the same variable, raised to the same power, is true, so Option 2 is correct. The simplified expression is -4 - 3y + 3z, so Option 3 is wrong and Option 4 is correct. Option 5, -(-x) = -x is wrong, so Option 5 is not correct. Therefore, the answers are Options 1, 2, and 4 (or A, B, and D).
Hope this helps! I got it right on Edgen.
Answer:
a b d
Step-by-step explanation:
Forty-seven percent of fish in a river are catfish. Imagine scooping out a simple random sample of 25 fish from the river and observing the sample proportion of catfish. What is the standard deviation of the sampling distribution? Determine whether the 10% condition is met.
The standard deviation is 0.0998. The 10% condition is not met because there are less than 250 fish in the river.
The standard deviation is 0.0998. The 10% condition is met because it is very likely there are more than 250 fish in the river.
The standard deviation is 0.9002. The 10% condition is met because it is very likely there are more than 250 fish in the river.
The standard deviation is 0.9002. The 10% condition is not met because there are less than 250 fish in the river.
We are unable to determine the standard deviation because we do not know the sample mean. The 10% condition is met because it is very likely there are more than 250 fish in the river.
Answer: The standard deviation is 0.0998. The 10% condition is met because it is very likely there are more than 250 fish in the river.
Step-by-step explanation:
The standard deviation of the sampling distribution = [tex]\sqrt{\dfrac{p(1-p)}{n}}[/tex] , where p= population proportion and n = sample size.
Let p be the proportion of fish in a river are catfish.
As per given , we have
p= 0.47
n= 25
The, the standard deviation of the sampling distribution will be [tex]\sqrt{\dfrac{0.47(1-0.47)}{25}}[/tex]
[tex]=\sqrt{0.009964}\approx0.0998[/tex]
The 10% condition : Sample sizes should be no more than 10% of the population.
But a river can have more than 250 fish [where 10% of 250 =25 (sample size)]
i.e. The 10% condition is met because it is very likely there are more than 250 fish in the river.
So the correct answer is "The standard deviation is 0.0998. The 10% condition is met because it is very likely there are more than 250 fish in the river."
Answer:
The standard deviation is 0.0998. The 10% condition is met because it is very likely there are more than 250 catfish in the river.
Step-by-step explanation:
I got it right on the quiz
tom and jerry have to stuff and seal 63 envelopes for a new marketing campaign. jerry can stuff and seal 15 envelopes in 2 minutes. tom can do 3 envelopes per minutes . how long would it take them if they work together ?
Answer:
5
Step-by-step explanation:
The time taken to stuff and seal 63 envelopes by both Tom and Jerry will be 6 minutes.
Given the Parameters :
Jerry's rate = 15/2 = 7.5 envelopes per minute Tom's rate = 3 envelopes per minuteCombined rate :
Jerry's rate + Tom's rate 7.5 + 3 = 10.5 envelopes per minuteTime taken if they work together :
Total number of envelopes = 63 Total time taken = total number envelopes ÷ combined rate Total time taken = (63 ÷ 10.5) = 6 minutesTherefore, the time taken of they both worked together will be 6 minutes
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Given that the Probability of a chance event is a number between zero and one that expresses the likelihood of the event occurring, choose all that are correct.
•0 indicates a certain event
•0.25 indicates an unlikely event
•0.75 indicates a likely event
•1 indicates an impossible event
•0.5 indicates equally likely to occur or not occur.
Please help if you can, thank you! ✨
Answer:
The correct statements are:
• Second statement: 0.25 indicates an unlikely event
• Third statement: 0.75 indicates a likely event
• Last statement: 0.5 indicates equally likely to occur or not occur.
Explanation:
Since the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring, you can translate it into:
A zero probability (0) means that the event is impossible, it will never happen. For example, the probability that when you roll a 6-sided die (with numbers 1 to 6) you get an irrational number is 0, meaning that it will never occur.A one probability (1) means that the event will occur with certainty. For instance, the changes to roll an even or odd number when you roll a 6-sided die is 100%You migth split the likelihood in some notorius outcomes:
0: impossible (the event will never happen)Close to zero (about 0 - 0.3): unlikely (the chances are small)0.5: even (equal chances of happening and not happening)Close to 1 (about 0.7 - 1): likely (the changes are large)1: certain (it is 100% sure that the event will happen)That means that:
first statement, 0 indicates a certain event, is incorrect.0.25 indicates an unlikely event (second statement is correct)0.75 indicates a likely event (third statement is correct)third statement is incorrect (1 does not indicate an impossible event, but a certain event)0.5 indicates equally likely to occur or not occur (fith statement is correct).The correct statements are:
0.25 indicates an unlikely event0.75 indicates a likely event0.5 indicates equally likely to occur or not occur.What are the correct statements?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
If probability is 0.5, there are equal chances that the event might occur or would not occur. If probability is less than 0,5, it is unlikely the even t would occur and if it is greater than 0.5, it is likely the event would occur.
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Is 65% greater than 5/8
Answer:
Yes it is. 65 as a decimal is .65, 5/8 is .625, so 65% is greater
Step-by-step explanation:
the answer to your question is yes
NEED HELP ASAP
Simplify each expression. The simplified expression should have no exponents. (I will give you the highest amount of points)
Sorry there is a few questions. I missed a day at school and need to catch up
9)
- 12xy/7x⁴ × 21x⁵y²/4y = - 9x²y²
10)
- 3x⁵/x¹³ × 2x¹⁰y/15y² = -2x²/5y
11)
4xy¹¹/x⁷y⁶ × 6x⁸y/8x³ = 3y⁶/x
12)
y¹⁰/2x³ × 20x¹⁴/xy⁶ = 10x¹⁰y⁴
13)
5x⁻²/3x × 2y³/x¹⁰ = 10y³/3x¹³
14)
(5xy/8x⁻¹y²)² × 26y³/5x²y⁵ =
= 25x⁴/64y² × 26/5x²y²
= 65x²/32y⁴
Round to the place value of underlined digit
64,999
Help please (easy) *attachment below*
Answer:
x = 17.
Step-by-step explanation:
We know that the two angles are supplementary (equal 180) as they are found on a straight line. Therefore,
(5x - 18) + (4x + 45) = 180.
9x + 27 = 180.
9x = 153.
x = 17.
Which are perfect cubes?
8
21
27
125
126
1,000
1,331
1,332
HELP ASAP ):
Answer:
8 ; 27 ; 125 ; 1000 ; 1331
Step-by-step explanation:
8 = 2³
27 = 3³
125 = 5³
1000 = 10³
1331 = 11³
Answer:
8, 27, 125, 1000, 1331.
Step-by-step explanation:
2^3 = 8
3^3 = 27
5^3 = 125
10^3 = 1000
11^3 = 1331
how to solve math word problems
Answer:
You have to know how to interperet a problem
Step-by-step explanation:
god gave you a brain use it
The reading on a car speedometer has 1.6% maximum error the speed limit on the road is 65 miles per hour
A) the speedometer reads 64 miles per hour is it possible that the cat is going over the speed limit
B) the speedometer reads 64 miles per hour is the car definitely going over the speed limit
Answer:
For A) it is possible that the speed the cat is going over the speed limit
For B) The statement is false as if the error is negative, the speed of the car will be less than the speed limit.
Step-by-step explanation:
Data provided in the question:
Maximum error on a car speedometer = 1.6% = 0.016
Maximum Speed limit on the road = 65 miles per hour
Now,
The error will be ± 1.6%
Now,
When the speedometer reads 64 miles per hour
The possible speed of the car can be
64 miles per hour + Error
= 64 + [0.016 × 64]
= 64 + 1.024
= 65.024 miles per hour
or
The speed can be
64 miles per hour - Error
= 64 - [0.016 × 64]
= 64 - 1.024
= 62.976 miles per hour
Hence,
For A) it is possible that the speed the cat is going over the speed limit
For B) The statement is false as if the error is negative, the speed of the car will be less than the speed limit.
You were looking at a map with a scale 1inch =40 miles if two towns are separated on the map by 6 inches what is the actual distance between them
Answer:
240 miles
Step-by-step explanation:
The actual distance between two towns, which are separated by 6 inches on a map with a scale of 1 inch to 40 miles, is 240 miles.
Explanation:The subject of this question is Mathematics, specifically focusing on understanding how map scales work. In this case, the map scale is 1 inch equals 40 miles. This means, for every inch on the map, it represents 40 miles in actual distance.
To find out the real distance between two towns that are separated by 6 inches on the map, you multiply the map scale distance (40 miles) by the number of inches (6).
Which is, 6 inches x 40 miles = 240 miles.
So, the actual distance between the two towns is 240 miles.
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Translate to an algebraic expression the sum of a and 8
Answer:
umm give me more examples
Step-by-step explanation:
Answer:
x=8+a
Step-by-step explanation:
sum of a and 8
x=a+8
when they say the sum of you add an equal sign
and when they said of a and 8 it means that whatever the sum is its equal to a+8
since the sum wasn't mentioned the sum will be known as a variable
lets put x as the variable
Use an equation to find the value of k
so that the line that passes through the given points has the given slope.
(−2,k), (2,0); m=−1
k=
[tex]\boxed{k=4}[/tex]
Explanation:We know that the slope of a line is given by:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ Where: \\ \\ (x_{1},y_{1}) \ and \ (x_{2},y_{2}) \ are \ points \ that \ lie \ on \ the \ line \\ \\ \\ Here: \\ \\ (x_{1},y_{1})=(-2,k) \\ \\ (x_{2},y_{2})=(2,0) \\ \\ m=-1 \\ \\ \\ -1=\frac{0-k}{2-(-2)} \\ \\ -1=\frac{-k}{4} \\ \\ -k=4(-1) \\ \\ \boxed{k=4}[/tex]
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