The population of a slowly growing bacterial colony after t hours is given by
p(t) = 4t² + 27t + 150. Find the growth rate after 2 hours.
bacteria/hour
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A function is an expression that defines a relationship between an independent variable and a dependent variable.
The number of bacteria colonies after 2 hours is 220.
What is a function?It is an expression that defines a relationship between an independent variable and a dependent variable.
We have,
P(t) = 4t² + 27t + 150
Where t = time
P(t) = population of a slowly growing bacteria colony after a particular time
The growth rate after 2 hours:
P(2) = 4 x (2)² + 27 x 2 + 150
P (2) = 16 + 54 + 150
P (2) = 220
Thus the number of bacteria colonies after 2 hours is 220.
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If you put $1,000 in a savings account that yields an 7% annual rate of interest that is compounded weekly,
a
how much would that be worth in 25 weeks (round to the nearest dollar)?
(Select the best choice below.)
O A. $1,040
O B. $1,034
O C. $1,043
OD. $1,025
Please show work! Thank you
Answer:
Answer B- 1034
7% annual rate is 70. divide by 52 (total amount of weeks in a year) =1.35. 1.35 × 25=33.75 rounded up 34. 1000+34=1034
Find the equation of a line that passes through the points (1,-2) and (3,-4). Express your final answer in slope-intercept form.
[tex]\text{Given that,}\\\\(x_1,y_1) = (1,-2)~~ \text{and}~~ (x_2,y_2) = (3,-4)\\\\\text{Slope,}~ m= \dfrac{y_2-y_1}{x_2 -x_1} = \dfrac{-4+2}{3-1} = -\dfrac 22 = -1\\\\\text{Equation with given points,}\\\\y-y_1 = m(x-x_1)\\\\\implies y +2 = -1(x-1)\\\\\implies y = -x+1 -2\\\\\implies y = -x-1\\\\\text{This is the slope-intercept form(y =mx+b).}[/tex]
Answer:
y=-x-1
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-4-(-2))/(3-1)
m=(-4+2)/2
m=-2/2
m=-1
y-y1=m(x-x1)
y-(-2)=-1(x-1)
y+2=-x+1
y=-x+1-2
y=-x-1
what is an equation of the line that passes through points (4,-8) (-4,2)?
Answer:The equation of the line that passes through the points (–12, –8) and (–17, –16) is y + 16 = 8/5(x + 17). slope = (-16 + 8)/(-17 + 12) = -8/-5 = 8/5 y + 16 = 8/5(x + 17)
Step-by-step explanation:
2x-3y=7 and y=3x-7 how do you solve this using subsitution
[tex]2x-3y = 7~~~....(i)\\\\y = 3x -7~~~....(ii)\\\\\\\text{Substitute}~ y = 3x -7~ \text{in equation (i):}\\\\\\2x-3(3x-7) = 7\\\\\implies 2x -9x + 21 =7\\\\\implies -7x = 7 -21\\\\\implies -7x = -14\\\\\implies x = \dfrac{-14}{-7} = 2\\\\\\\text{Substitute x = 2 in equation (ii):}\\\\y=3(2) -7 = 6 -7 = -1\\\\\\\text{Hence (x,y) =(2,-1)}[/tex]
For the following problem, y varies directly as x If y = 34 when x = 4 , find y when x is 3.
Answer:
Step-by-step explanation: plug in 3 for X and then solve
Give me 5 stars
Adam bought a fish aquarium worth $3,000 in the first week of the year. Its value depreciates by 3% per week. What will the value of the fish aquarium be after 5 weeks?
=0.75 times 3000=2250
In a basketball game, Archie made 3/5 of his shots. Which numbered choice has a value that is the same as the ratio Archie made in his game?
Answer:
0.6
Step-by-step explanation:
3/5=0.6
Name a number that has the same absolute value as 23
Answer: A number with the same absolute value of 23 is -23.
Explanation: The absolute value of a number is how far it is from zero, and the absolute value of a number is always positive, unless the number is 0, in which case the absolute value is neutral, and the absolute value is 0.
Examples: 6 is 6 away from zero, so the absolute value of 6 is 6.
−6 is 6 away from zero, so the absolute value of −6 is 6.
The number that has the same absolute as 23 is -23.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
An absolute number x is denoted by |x|
If x = -x,
|-x| = x
Now,
|23| = 23
|-23| = 23
So,
-23 has the same absolute value as 23.
Thus,
-23 is the number.
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Which graph represents (x,y)(x,y)left parenthesis, x, comma, y, right parenthesis-pairs that make the equation y = 2xy=2xy, equals, 2, x true?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
(Choice B)
B
(Choice C)
C
Step-by-step explanation:
The graph has a slope of 0.5 and a y-intercept of 5
The equation is given as:
A linear equation is represented as:
Where m represents the slope, and c represents the y-intercept
So, by comparison:
m = 0.5
c = 5
This means that:
The slope is 0.5, and the y-intercept is 5
Hence, the graph of has a slope of 0.5, and a y-intercept of 5
See attachment for the graph of
A
i know its a because the other kids'answer is wrong.
Find the Product of 7/9of27
7 x 27 189
= -------------------
9 x 1 9
pls help it is 7th grade math
[tex]39+\dfrac 15 w \\\\=39+\dfrac 15 \left(-\dfrac 12 \right)\\\\\\=39 - \dfrac 1{10}\\\\\\=\dfrac{389}{10}\\\\\\=38\dfrac{9}{10}[/tex]
Travis has hired Charlie and Dora to plant flowers. Dora can plant 150 flowers in the same time it takes Charlie to plant 120 flowers, which can be shown using the following relationship where d and c are the respective rates at which Dora and Charlie can plant flowers:
150 over d equals 120 over c
Also, Dora can plant 18 flowers more per day than Charlie.
How many flowers can Charlie plant per day?
Answer:
72
Step-by-step explanation:
If the rates d and c are flowers per day, we have ...
150/d = 120/c
d -c = 18
__
Multiplying the first equation by cd/30, we have ...
5c = 4d
Multiplying the second equation by 4 gives ...
4d -4c = 72
Adding these equations together, we get ...
5c +4d -4c = 4d +72
Simplifying and subtracting 4d leaves ...
c = 72
Charlie can plant 72 flowers per day.
What is the answer ??
Answer:
first of all take LCM OF THE denominator and solve it as shown
PLEASE HELP ME WITH GEOMETRY
What composition of rigid motions maps STR to MNP?
Answer:
first option
Translate seven left followed by mirror over y = 2
Step-by-step explanation:
The solution is Option A.
The translation of triangle MNP to triangle STR is a translation of 7 units to the right and a reflection along R = 2
How does the transformation of a function happen?
The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the triangle be represented as MNP
Now , the transformed triangle be STR
Now , the translation is given as
Step 1 :
The coordinates of triangle is MNP
M = M (-5 , 2 )
N = N ( - 8 , 5 )
P = P ( -2 , 4 )
Now , the translation of 7 units to the right will result in
M' = M' ( 2 , 2 )
N' = N' ( -1 , 5 )
P' = P' ( 5 , 4 )
Step 2 :
The coordinates of the translated triangle M'N'P' is
M' = M' ( 2 , 2 )
N' = N' ( -1 , 5 )
P' = P' ( 5 , 4 )
Now , on reflection of triangle M'N'P' by R = 2 , we get
S = S ( 2 , 2 )
T = T ( -1 , -1 )
R = R ( 5 , 0 )
Hence , the translation of triangle MNP to triangle STR is a translation of 7 units to the right and a reflection along the R = 2
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B(14, 12)
A(-5,-2)
A. Find the midpoint of Segment AB
A certain music club charges an annual membership fee of $99, in return, its members will be able to buy and download songs at a very low cost of 10 cents each. If Tyna spent a total of $149.30 including the membership fee, how many songs did she buy?
A) 99+10x=149.30
B) 99-10x=149.30
C) 99-0.1x=149.30
D) 0.1x+99=149.30
Answer:
D). 0.1x+99=149.30
How many songs Tyna Bought:
503 songs
Step-by-step explanation:
Since the membership fee is 99 you don't have to pay for it again
(Until next year that is)
Now it states that every download cost 10 cents or $0.1
So we don't know how many she will buy so we can replace that unknown value with x
So the equation is
0.1x+99=149.30
To solve this you first subtract 99 on both sides:
Which will result in
0.1x=50.3
Divide 0.1 on both sides
So Tyna bought 503 songs
(HOLY THAT IS A LOT OF SONGS)
Hope this Helps!
After a party there is 3/4 of a pizza left. You split it evenly between you and 3 friends. What fraction of a pizza does everyone get?
Answer:
3/16
Step-by-step explanation:
3/4÷4=3/16
Since there are 4 people, not 3, divide the remaining pizza by 4.
What is ten times as great as 450?
Answer: The answer is 4,500.
Explanation: 450 x 10 = 4,500.
Ten times as great as 450 is 4500.
We need to find what is ten times as great as 450.
What is multiplication?When we multiply two numbers, the answer is called product. The number of objects in each group is called multiplicand, and the number of such equal groups is called the multiplier.
Multiplication step:
Multiply the multiplicand by each of the numbers of the multiplier, moving from right to left. The units of the product are written below the line.The tens place of each product is added to the next product.Now, ten times as great as 450=10×450=4500
Therefore, ten times as great as 450 is 4500.
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Question Two :
A discrete random variable X has negative binomial distribution,
with 6 successes required each with probability of success 0.4
Determine the value of ...
a) ...E(X).
b) ... Var( X)
c) ... P ( X = 12).
Using the negative binomial distribution, it is found that:
a) [tex]E(X) = 15[/tex]
b) [tex]Var(X) = 6.67[/tex]
c) [tex]P(X = 12) = 0.0883[/tex]
Negative binomial distribution:
It is the number of trials until q successes of a binomial variable, with p probability of success.
The expected value is:
[tex]E(X) = \frac{q}{p}[/tex]
The variance is:
[tex]Var(X) = \frac{pq}{(1 - p)^2}[/tex]
The probability mass function is:
[tex]P(X = x) = C_{x+q-1,q-1}(1 - p)^xp^q[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, the parameters are: [tex]q = 6, p = 0.4[/tex].
Item a:
[tex]E(X) = \frac{6}{0.4} = 15[/tex]
Item b:
[tex]Var(X) = \frac{6(0.4)}{(1 - 0.4)^2} = 6.67[/tex]
Item c:
[tex]P(X = 12) = C_{17,5}(0.6)^12(0.4)^6 = 0.0883[/tex]
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Zachary is going out with his friends to see
a movie and shop. He has $32 and the
movie will cost $7.25. Write and solve an
inequality to find how much money
Zachary can spend shopping.
Answer:
7.25 + S ≤ 32
Step-by-step explanation:
Our initial value is 7.25, and that is to watch the movie. Next, the absolute max he can spend is 32, or he would have negative money, which he cannot have. Therefore, we use the ≤ sign and point it as 32, to show that it must be less than or equal to our total of 32. Then, we can represent the money they spend on shopping with s
Has a slope of -2/5 and goes through (-10,-1)
Answer:
Below in bold.
Step-by-step explanation:
Using the point-slope form of a straight line equation:
y - y1 = m(x - x1)
y - (-1)) = -2/5(x - -10)
y + 1 = -2/5(x + 10)
y + 1 = -2/5x - 4
y = -2/5x - 5.
In standard form this is:
2x + 5y = -25.
The next two systems do NOT have opposite like terms
Answer:
x = 10
y = 6
Step-by-step explanation:
Multiply second equation with -1 and then add it up with first equation
(-1)*(6x - 7y) = 18
-6x + 7y = -18
6x - 6y - 6x + 7y = 24 - 18 add like terms
y = 6 to find the value of x use this information
6x - 6y = 24 replace y with 6
6x - 6*6 = 24
6x - 36 = 24 add 36 to both sides
6x = 60 divide both sides by 6
x = 10
Write 1.96 as a percent and as a fraction,
lost on this a little
Answer:
the answer would be 7/5
Step-by-step explanation:
2 of them would already make a whole, and if you add another one, it's going to be more than just one pitcher of lemonade.
1 meter is equal to 100 centimeters or 1,000 millimeters. How many millimeters are in 2 meters, 17 millimeters?
Answer:
2,017
Step-by-step explanation: 2 meters= 2,000
So, 2,000+17= 2,017
2017 millimeters are in 2 meters, 17 millimeters as per the given unit conversion rate.
What is Unit conversion?A statement of the connection between units that are used to alter the units of a measured quantity without affecting the value is called a conversion factor. A conversion ratio (or unit factor), if the numerator and denominator have the same value represented in various units, always equals one (1).
Given, 1 meter is equal to 100 centimeters or 1,000 millimeters.
To calculate the total number of millimeters in 2 meters, 17 millimeters.
Since,
millimeters in 1 meter = 1000
Thus,
millimeters in 2 meter = 2000
millimeters in 2 meters, 17 millimeters = 2017
Therefore, there is 2017 mm in 2meteres, 17 mm as per the given unit conversion.
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Evaluate the expression when x = 8 and y = 1.
x2y
Answer:
1/8
Step-by-step explanation:
I took the test this is it
evaluate f(2) and lim f(x) where f(x)=5x^3+3x+1
I’m unsure why I keep getting this wrong
Answer:
the answer is 5
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carryonlearing
Answer:
26/25x^2+25x or x=0,x=-1
Step-by-step explanation:
Let f(x)=x* + 14x and g(x) = 6 - X. Find the domain off f + g. Determine the domain of f + g.
[tex]\begin{cases} f(x) = x^4+14x\\ g(x) = 6-x \end{cases}\qquad \qquad h(x) = f(x) + g(x) \\\\\\ h(x) = (x^4+14x)+(6-x)\implies h(x) = x^4+14x-x+6 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill h(x) = x^4+13x+6~\hfill[/tex]
now, if we graph h(x), Check the picture below, we can see that horizontally the line keeps on moving towards the left, going going and going towards -infinity, and it also keeps on moving towards the right, going going and going towards +infinity, and since the horizontal area used by the function is the domain of it, the domain for h(x) will be (-∞ , +∞).