Mutations happen at a steady rate.
True
False
4(x + 3) + 2x = 6(x + 2)
Answer:
answer is 0
Step-by-step explanation:
g The population of Little Townville in 2005 was 13,625 people. In 2009 the population grew to 15,325 people. Assume that this trend is linear and the population has been growing like this since 2000. a. Write a function for the population, P, in terms of the number of years since 2000, ????. (6 points) b. What is the slope of the function and what does it represent in the context of the problem. Include units. (5 points) c. What is the vertical intercept of the function and what does it represent? Include units (5 points) d. What do you believe the population was in 2015?
Answer:
a) [tex]P(t) = 11500 + 425t[/tex]
b) The slope is of 425 people, which is by how much the population increases each year.
c) The vertical intercept is of 11500 people, and it represents the population of Little Townville in the year 2000.
d) 17,875 people.
Step-by-step explanation:
A linear function that measures population after t years has the following format:
[tex]P(t) = P(0) + at[/tex]
In which P(0) is the vertical intercept, which represents the initial population, and a is the slope, which represents the yearly population.
a. Write a function for the population, P, in terms of the number of years since 2000.
The first step is finding the slope.
Finding the slope:
The slope is the change in the output divided by the change in the input, during a period of time.
The population of Little Townville in 2005 was 13,625 people. In 2009 the population grew to 15,325 people.
This means that in 2009 - 2005 = 4 years, the population increased by 15325 - 13625 = 1700.
So the slope is
[tex]a = \frac{1700}{4} = 425[/tex]
So
[tex]P(t) = P(0) + 425t[/tex]
Finding the initial population:
We want to find P(0), which is the population in 2000. The population of Little Townville in 2005 was 13,625 people, which means that [tex]P(5) = 13625[/tex]. So
[tex]P(t) = P(0) + 425t[/tex]
[tex]13625 = P(0) + 425*5[/tex]
[tex]P(0) = 13625 - 425*5[/tex]
[tex]P(0) = 11500[/tex]
So
[tex]P(t) = 11500 + 425t[/tex]
b. What is the slope of the function and what does it represent in the context of the problem. Include units.
The slope is of 425 people, which is by how much the population increases each year.
c. What is the vertical intercept of the function and what does it represent? Include units
The vertical intercept is of 11500 people, and it represents the population of Little Townville in the year 2000.
d. What do you believe the population was in 2015?
2015 is 2015 - 2000 = 15 years after 2000, so this is P(15).
[tex]P(15) = 11500 + 425*15 = 17875[/tex]
17,875 people.
A person who is standing on a ledge throws a rock into the air. The rock reaches a maximum height of 676 feet
above the ground after 1.5 seconds.
If the rock hits the ground below the ledge 8 seconds after it is thrown, which quadratic function can be used to find
the height of the rock above the ground t seconds after it is thrown?
Answer:
The quadratic equation is [tex]h(t) = -318.22t^2 + 954.67t + 12728.89[/tex]
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta= b^{2} - 4ac[/tex]
Quadratic equation:
[tex]ax^2 + bx + c = 0[/tex]
The rock reaches a maximum height of 676 feet above the ground after 1.5 seconds.
This means that:
[tex]-\frac{b}{2a} = 1.5[/tex]
[tex]y_{v} = -\frac{b^2-4ac}{4a} = 676[/tex]
If the rock hits the ground below the ledge 8 seconds after it is thrown
This means that:
[tex]64a + 8b + c = 0[/tex]
Relation of b and a:
[tex]-\frac{b}{2a} = 1.5[/tex]
This means that:
[tex]b = -3a[/tex]
Relationship of c and a:
[tex]64a + 8b + c = 0[/tex]
[tex]64a - 24a + c = 0[/tex]
[tex]c = -40a[/tex]
Finding a:
[tex]y_{v} = -\frac{(-3a)^2-4a(-40a)}{4a} = 676[/tex]
[tex]9a^2+160a = -2704a[/tex]
[tex]9a^2 + 2864a = 0[/tex]
[tex]a(9a + 2864) = 0[/tex]
Since it is a quadratic equation, a cannot be 0.
[tex]9a + 2864 = 0[/tex]
[tex]9a = -2864[/tex]
[tex]a = -\frac{2864}{9}[/tex]
[tex]a = -318.22[/tex]
Finding b and c:
[tex]b = -3a = -3(-318.22) = 954.67[/tex]
[tex]c = -40a = -40(-318.22) = 12728.89[/tex]
The quadratic equation is given by:
[tex]h(t) = -318.22t^2 + 954.67t + 12728.89[/tex]
The quadratic equation is [tex]h(t) = -318.22t^2 + 954.67t + 12728.89[/tex]
Select the correct answer.
The equation of a line is y = -3x – 2. What are the slope and the y-intercept of the line?
A.
slope = -3 and y-intercept = 2
B.
slope = 3 and y-intercept = -2
C.
slope = 3 and y-intercept = 2
D.
slope = -3 and y-intercept = -2
Answer:
The answer is D slope = -3 y-intercept = -2
Step-by-step explanation:
Answer
D.
Step-by-step explanation:
The first part of the equation is -3 and the second part is -2. The number attached to the variable is the "slope" and the number coming after the variable is the y intercept.
25/35 and 10/14 simplified
Answer:
(25/5)/(35/5)
=> 5/7
(10/2)/(14/2)
=> 5/7
Hence both of the numbers simplify to 5/7
Hope it helps
negative 5x plus 4y equals 3 i need x and y please
Answer:
x = 9
y = 12
Step-by-step explanation:
-5x + 4y = 3
x = 2y - 15
Manipulate the equations such that the coefficients of two variables are additive inverses
-5x + 4y = 3
x = 2y - 15
Inverse operations
-> 4y - 3 = 5x
-> 2y - 15 = x (*(-5))
->4y - 3 = 5x
-> -10y + 75 = -5x
Now add the equations to eliminate a variable,
4y - 3 = 5x
-10y + 75 = -5x
-6y + 72 = 0
Inverse operations
-6y + 72 = 0
72 = 6y
/6 /6
12 = y
Back solve to find (x)
2y - 15 = x
2(12) - 15 = x
24 - 15 = x
9 = x
Suppose you have a tablet with a capacity of gigabytes. For a plain text book, one byte typically corresponds to one character and an average page consists of 2000 characters. Assume all gigabytes are used for plain text books.
a. How many pages of text can the tablet hold?
b. How many 500 page books can the tablet hold?
Answer:
tablet can hold 500000 pages of text .
tablet can hold 1000 books of 500 pages
Help asaaaaaap guys
Answer:
-3.5,-3,-2 1/2,-2,2.5
Step-by-step explanation:
Least. Greatest
-3.5, -3, -2 1/2, -2, 2.5
Find angle picture below.
Answer:
Angle M = 63
Angle N = 96
Step-by-step explanation:
By exterior angle of triangle:
Angle M + Angle N = 159
(4y+3)+(6y+6)=159
y = 15
Angle M = 4y + 3 = 4(15) + 3 = 63
Angle N = 6y + 6 = 6(15) + 6 = 96
Question 16
If n = 6, what is the value of 9n – 4?
Α.
11
B.
50
С
52
D
54
Answer is Option B) 50
9(6)-4
54-4
50
The Brady & Matthew Camera Company has just come out with their newest professional quality digital camera, the ToughPix1. The company is selling this camera only through its new mobile app at a profit of per camera. This purchase comes with a guarantee that, barring gross negligence, if the camera breaks in the first two years after purchase, Brady & Matthew will replace it free of charge. Replacing a camera in this way costs the company . Suppose for each ToughPix1 there is a chance that it will need to be replaced exactly once, a chance that it will need to be replaced exactly twice, and a chance that it will not need to be replaced.
Answer:
a chance that it will not need to be replaced
Step-by-step explanation:
PLEASE HURRY I WILL MARK BRAINIEST
The new wing of an art
museum has 3 times
as many windows as
the old wing. Together,
both wings have
32 windows. How many
windows are in
the new wing?
Answer: 24
Step-by-step explanation:
32/4 = 8
3 * 8 = 24
24 + 8 = 32
There are 24 windows in the new wing.
Hope this helped! :)
ILL GIVE 50 POINTS AND BRAINLIEST!!!
A business assistant must leave more than $50 in the supply account. There is $175 in the account. The assistant needs to order x boxes of pens that cost $6.50 each.
What is the maximum number of boxes of pens the business assistant can buy? Please show your math work and justify your answer.
Anybody know how to do lowest terms and can teach me how to get the answer to lowest terms questions?
Answer:
Step-by-step explanation:
6/9+x=7/10
x=7/10-6/9
when adding fractions both denominators must be equal, we’ll make them 90
x=(7/10)(9/9)-(6/9)(10/10)
x=63/90-60/90
x=3/90, the greatest divisor of 3 and 90 is 3 so divide both the numerator and denominator by 3
x=(3/3)/(90/3)
x=1/30
prove that:
[tex] |x \: y \: z \\ {x \: {y \\ {z \\ yz \: zx \: xy = (y - z) \: (z - x) \: (x - y) \: (xy + yz + zx)}^{2} }^{2} }^{2} | [/tex]
Answer:
???
Step-by-step explanation:
moris code?
Answer:
c, none of the above
Step-by-step explanation:
khan
The frequency table shows the scores from rolling a dice.
Score
Frequency
Answer:
The median is 3.5
Step-by-step explanation:
We want to find the median of the set of values.
First, we need to write the set in ascending order.
We get:
1 five times
2 three times
3 five times
4 two times
5 seven times
6 four times
The median will be the midle value (for example in a set of 5 elements, the middle element is the third one) of this set, then the first part is to write the set, we get:
{1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6}
In this set we have
5 + 3 + 5+ 2 +7 + 4= 26 values
So we will not have a middle value, we need to take the mean of the two middle values (the 13th value and the 14th value)
We can see in the set above that these values are:
3 and 4.
Then we want to take the mean between 3 and 4.
We get:
M = (3 + 4)/2 = 3.5
The median of this set is 3.5
Please help me with this work
Answer:
1. (5y) = 35
2. (6y) = 1
3. (4y) = 2
4. (11y) = 15
5. 18, 24, 42, 60
The number of miles Henry rides his bike in 10 days is 60miles
Step-by-step explanation:
A city planner is studying the need for affordable housing in the city's Urban Planning Department. He learned from the census of all 75,342 households in the city that the median family income is $65,000, with an average of 2.9 persons-per-household, and 88% live in a single household unit. Previously, the planner had surveyed a group of 400 randomly selected households in the city. The surveyed households had a median family income of $52,000, an average of 3.2 persons per household, and 80% lived in a single household unit. 2
(a) For city planner's survey, identify the population and the sample,
Population: (Choose one)
Sample: (Choose one)
(b) Choose whether each number described below is a parameter or a statistic for the city planner's survey,
Number Parameter Statistic
The 80% of the group of randomly selected households that live in a single household unit
The average of 2.9 personer household of all the households in the city The $65,000 median family income of all the households in the city At a TV assembling facility, the Quality Assurance (QA) department tested a random selection of 600 TV's assembled in March.
Answer:
Population = 75,342 households
Sample = 400 randomly selected households
The percentage who live in a single household unit = Parameter
The average of 2.9 person per household of all households in the city = parameter
The $65,000 median family income of all the households in the city = Parameter
Step-by-step explanation:
The population refers to all the entire elements, observations or subject which fits into a particular study. In the scenario above, the entire household in the city of study. That is, the 75,342 households.
The sample is the subset of the population which is a smaller set of observation meant to be representative of the larger population. The sample here is the 400 randomly selected households.
Parameter differs from statistics in that numerical estimates or calculations obtained from the population is called the parameter while the numerical characteristics derived from the sample is called statistic.
In this exercise we have to use the knowledge of probability to calculate the chances of choosing a TV approved by the quality control, so:
400 randomly selected households
So, based on the information given in the statement, we have:
Population = 75,342 householdsSample = 400 randomly selected householdsSome parameters for this equation are:
The percentage who live in a single household unit The average of 2.9 person per household of all households in the cityThe $65,000 median family income of all the households in the cityThe inhabitants of a place refers to all the complete essential feature, attention or subject that fits into the study. In the sequence of events above, the complete household fashionable the city of study. That is, the 75,342 households.
The sample exist the subset of the inhabitants of a place that exist a tinier set of comment on something scrutinized intend expected representative of the best inhabitants of a place. The sample in this place happen the 400 carelessly picked households.
See more about statistics at brainly.com/question/10951564
The probability of choosing a green sweet at random from the bag is 1/12.
Please see the picture, I need to answer that question.
Answer:
2 times became that's correct
Which is the value of the rational expression 6-x/x+5 when x=2
Answer:
4/7
Step-by-step explanation:
6-x/x+5 let us take x=2
6-2/2+5=4/7
A cereal box says that it now contains 25% more cereal. If it originally had 12 ounces of cereal, how much does it have now?
Answer:
15
Step-by-step explanation:
Answer:
21 ounces.Step-by-step explanation:
This is percentage increase.In order to find that, we simply do:
(100+25)% = 125%
100% = 12 ounces
125% = ?
12*125/100 = 9 ounces
Add it up to the original amount:
12+9 = 21 ounces
factorize by splitting the middle term 6x-11x+4
Answer: (2x - 1)(3x - 4)
(split -11x as -8x and -3x)
Step-by-step explanation:
I am assuming that it is actually 6x^2 - 11x + 4
To find out how to split the middle term: The two numbers should multiply to a*c (6*4 = 24) and add to b (-11)
-8, -3 works
(6x^2 - 8x) + (-3x + 4)
2x(3x - 4) + -1(3x - 4)
(2x - 1)(3x - 4)
a toy company is going to issue new ID codes to its employees.Each codes will have one letter followed by five digits. The digits 2 and 6 will not be used. So, there are 26 letters and 8 digits that will be used. Assume that the digits can be repeated.. How many employee ID codes can be generated
Answer:
851,968
Step-by-step explanation:
26*8*8*8*8*8= 851,968
From the combination of codes, 851,968 employee ID codes can be generated.
Given,
Employee ID codes can be generated.
Each code will have one letter followed by five digits. The digits 2 and 6 will not be used. So, there are 26 letters and 8 digits that will be used.
The number of employee codes to be determined.
In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In a combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.
Required number of codes = 26 * 8 * 8 * 8 * 8 * 8
= 851,968
Thus, from the combination of codes, 851,968 employee ID codes can be generated.
Learn more about permutations and combinations here: https://brainly.com/question/2295036
#SPJ2
What is the solution of x = 2 + StartRoot x minus 2 EndRoot?
Answer:
x= 2 or x=3
Step-by-step explanation:
Both satisfy the equation. I hope this helped.
Answer:
x=2 or x=3
Step-by-step explanation:
just took the test it is C
2^x=1/128 solve the equation
Answer:
x = − 7
Step-by-step explanation:
y = 4.5*x^2-9*x+8.5;4.5;-9;8.5
-(((-9)^2-(4*4.5*8.5))/(4*4.5))
-(-9/(2*4.5))
4.5*0^2-(0*9)+8.5
(7*x^5-(5*x^7))^(1/2)+1/((7*x^5-(5*x^7))^(1/2))
is 2/6 rational or irrational
Answer:
Rational
Step-by-step explanation:
A rational number is any integer, fraction, terminating decimal, or repeating decimal.
good luck, i hope this helps :)
A total of 472 tickets were sold. They were either adult tickets or student tickets. The number of student tickets were 3 times tge number of adult tickets sold. How many adult tickets were sold?
Answer:
adult tickets = 118
student tickets = 354
Step-by-step explanation:
a = number of adult tickets
s = number of student tickets
a + s = 472
3a = s
substitute for s
a + 3a = 472
reduce
4a = 472
divide by 4
4a/4 = 472/4
a = 118
s = 354
Use least common multiple or greatest common divisor to solve the problem.
Three clocks chime every 15 minutes, 39 minutes, and 65 minutes,
respectively. If the three clocks chime together, how much time must pass
before they will chime together again?
Answer:
Step-by-step explanation:
3) 15,39,65
_________
5 )5,13,65
--------------
13 )1,13,13
----------------
| 1,1,1
L.C.M.=3×5×13=195
They will chime together after 195 minutes.
24 - 3x Evaluate each expression if x = 5
Answer:
9
Step-by-step explanation:
24 - 3(5)
24 - 15
9
good luck, i hope this helps :)