Answer:
About 53022 bacteria present.
Step-by-step explanation:
We can use the continuous growth formula:
[tex]\displaystyle P = A e^{kt}[/tex]
Where k is some constant.
With an initial population of 5000, it grew to 6500 after two hours.
In other words, P = 6500 when A = 5000 and t = 2:
[tex]\displaystyle (6500) = (5000)e^{k(2)}[/tex]
Solve for k:
[tex]\displaystyle \begin{aligned} 6500 & = 5000e^{2k} \\ \\ e^{2k} & = \frac{6500}{5000} = \frac{13}{10} \\ \\ \ln\left(e^{2k}\right) & = \ln\left(\frac{13}{10}\right) \\ \\ 2k & = \ln\frac{13}{10} \\ \\ k & = \frac{1}{2}\ln\frac{13}{10}\end{aligned}[/tex]
Therefore, our equation is:
[tex]\displaystyle P = \bigg{5000e}^{\dfrac{1}{2}\ln\dfrac{13}{10}t[/tex]
After 18 hours, t = 18. Hence:
[tex]\displaystyle \begin{aligned} P(18) & = \bigg{5000e}^{\dfrac{1}{2}\ln\dfrac{13}{10}(18)} \\ \\ & \approx 53022\end{aligned}[/tex]
Therefore, after 18 hours, there will be about 53022 bacteria present.
Evaluate without using a mathematical table
1000(√0.0128÷200)
Answer:
0.5656854249
Step-by-step explanation:
1000(0.0128/200)
1000(0.11314/200)
1000(0.0005656854)
=0.5656854249
The height of the rectangle and the triangle are the same. The base of the triangle is half the base of the rectangle.
What is the area of the composite figure?
A. 225
B. 300
C. 375
D. 450
Step by step explanation: The last answer i wrote was wrong, so i retook the quiz and got 100% and this was right.
Answer:
.C ,375
I HOPE THIS helps i just know i got connect shons
The inequality 6 -fx < x - 9 is equivalent to
Answer:
f<−1+15/x
Step-by-step explanation:
5-16 Find the general indefinite integral.
15. [tex]\int \frac{1-\sin ^{3} t}{\sin ^{2} t} d t[/tex]
Simplify the integrand
[tex]\dfrac{1-\sin^2(t)}{\sin^2(t)} = \dfrac{\cos^2(t)}{\sin^2(t)} = \cot^2(t)[/tex]
Recall the derivative of csc(t),
[tex]\dfrac d{dt} \csc(t) = -\cot^2(t)[/tex]
It follows that
[tex]\displaystyle \int \frac{1-\sin^2(t)}{\sin^2(t)} \, dt = \int \cot^2(t) \, dt = \boxed{-\csc(t) + C}[/tex]
In AWXY, the measure of ZY=90°, XW = 5, YX = 4, and WY = 3. What ratio
represents the cotangent of ZX?
X
5
4.
Y
W
3
Given:
In Δ[tex]WXY,m < Y=90^o,WY=3,XW=5[/tex] and [tex]YX=4[/tex].
To find:
The ratio represents the cosine of ∠[tex]W[/tex].
Solution:
In Δ[tex]WXY,m < Y=90^o[/tex]. It means the opposite side of angle Y, i.e., XW is the hypotenuse of the triangle.
In a right angle triangle,
[tex]cos0=\frac{Base}{Hypotenuse}[/tex]
In the given triangle,
[tex]cosW=\frac{XY}{YW}[/tex]
[tex]cosW=\frac{3}{5}[/tex]
Therefore, the required cosine ratio is [tex]\frac{3}{5}[/tex].
Determine if x + 3 is a factor of -3x^3+6x^2+6x+9 How do you know
Answer:
x+3 is not a factor
Step-by-step explanation:
A graphing calculator shows the expression has a zero at x=3 and no other real zeros. If x+3 were a factor, there would be a zero at x = -3.
x+3 is not a factor of the expression.
_____
You can check to see if x+3 is a factor by evaluating the expression for x=-3. If (x+3) is a factor, x=-3 will make the function be zero.
3(-x³ +2x² +2x +3) = 3(((-x +2)x +2)x +3) = 3(((-(-3)+2)(-3) +2)(-3) +3)
= 3((-15+2)(-3) +3) = 3(39 +3) = 126 ≠ 0
The expression evaluates to 126 at x=-3, so x+3 is NOT a factor.
2. Find m angle 1
73
88
60
80
Answer:
88°
Step-by-step explanation:
RULES:
angles on a straight line add up to 180 degreesangles in a triangle add up to 180 degreesso.
because of rule 1, we do 180-120 to get 60, to get that right corner angle. Now, we know 2 angles. So, (because of rule 2), we can do 60+32 = 92, and 180-92 = 88
So, 1 = 88
Hope this helps! If it doesn't make sense, feel free to ask me to explain it further.
- profparis
Help me pls I am not sure about this
Answer: the answer is c which is 61 ¾ inches .
Step-by-step explanation: what I did that I made 62 ½ minus ¾ and it gave 61 ¾ inches, to know how many inches did she grew at the beginning of the year . I hope my answer is correct . Please give brainliest . Thanks .
I hunder percent agree.
I too hunder percent agree
Factor out the greatest common factor from the following polynomial.
3 2
15a + 3a + 1
In the figure below, parallelogram STXY is congruent to parallelogram UTWV.
If mTXY = 118°, what is mXTW?
A.
62°
B.
60°
C.
56°
D.
124°
Answer:
The correct answer is C.56.
Hope this helps you czn!!!!
Please Mark me as Brainleast!!!!!!!!
Please show your work, tysm :D
~giving brainliest!~
Answer:
. 0625
Step-by-step explanation:
1/2^4
or
1/16
just doing half life
Can you please help ni
Answer:
0.0833... inches longer or 1/12
Step-by-step explanation:
7/12=0.583
1/2 but multiplied by 6 is 6/12
so 7/12-6/12=1/12 longer or 0.0833-
HELP PLEASEEEE
The table below shows the
values for the function y = f(x).
The answers are:
Second option, evaluating x=-1
[tex]g(-1)=-2[/tex]
Fifth option, evaluating x=6
[tex]g(6)=\frac{3}{2}[/tex]
Why?We are given a table that shows the values for the given function (f(x), and we are asked to find the solution of an equivalent function (g(x)).
We have that:
[tex]g(x)=\frac{1}{2}f(x)[/tex]
Now, evaluating we have:
For x=-3
[tex]g(-3)=\frac{1}{2}f(-3)=\frac{1}{2}*5=2.5[/tex]
We have the values (-3,2.5) so, it's not part of the solutions to the function g(x).
For x=-1
[tex]g(-1)=\frac{1}{2}f(-3)=\frac{1}{2}*-4=-2[/tex]
We have the values (-1,-2) so, it's part of the solutions to the function g(x).
For x=0
[tex]g(0)=\frac{1}{2}f(0)=\frac{1}{2}*2=1[/tex]
We have the values (0,1) so, it's not part of the solutions to the function g(x).
For x=5
[tex]g(5)=\frac{1}{2}f(5)=\frac{1}{2}*-8=-4[/tex]
We have the values (5,-8) so, it's not part of the solutions to the function g(x).
For x=6
[tex]g(6)=\frac{1}{2}f(6)=\frac{1}{2} *3=\frac{3}{2}[/tex]
We have the values [tex](6,\frac{3}{2})[/tex] so, it's part of the solutions to the function g(x).
Hence, we have that the answers are:
Second option, evaluating x=-1
[tex]g(-1)=-2[/tex]
Fifth option, evaluating x=6
[tex]g(6)=\frac{3}{2}[/tex]
Have a nice day!
Pls pls pls pls help po
Answer:
1. you will multiply base times height:
16m * 12m = 192 sq m
2. same steps but just multiply it by two because its "twice as long"
18 cm * 6 cm = 108 * 2= 216
3. now for this one sice we are finding the base we will have to divide the 432 by 18 = 24
4. same steps like in question 1:
12 * 5 = 60
5. same steps like in question 1:
7 * 10 = 70
Step-by-step explanation:
hope this helps and have a great day!! :)
Please help on math.
Answer:
255cm²
Explanation:
To find the area of the triangle we must us a formula which is base x height ÷ 2 divide. So on the left side it is 17 cm and on the right without the triangle it is 10 so the triangle is 7cm tall. Next on the bottom without the triangle it is 22 and with it is 12 so the base is 10 now we multiply them which will be 70 then divide it by 2 which is 35cm².
And dont forget the squared!!
NO LINKS!!
Fill in the chart. (Round to the nearest penny)
=============================================================
Explanation:
If the money is compounded semiannually at a rate of 8%, then this means the multiplier (common ratio) is b = 1+r/n = 1+0.08/2 = 1.04
r = 0.08 = 8% annual interest raten = 2 = compounding twice a year, aka semiannually, aka every 6 months.In short, b = 1.04 is our growth multiplier. It says that the money is growing by 4% each 6 month period. Each time x goes up by 1, y increases by 4%. The starting amount is a = 2100 dollars.
We go from the template of [tex]y = ab^x[/tex] to [tex]y = 2100(1.04)^x[/tex]
Use that equation to fill out the table. For instance, if x = 2 then,
[tex]y = 2100(1.04)^x\\\\y = 2100(1.04)^2\\\\y = 2100(1.0816)\\\\y = 2271.36\\\\[/tex]
Meaning that after 2 semiannual periods (aka 2*6 = 12 months = 1 year), we'd have $2,271.36 in the account.
Repeat this for the other x values mentioned to get the table shown below. To fill out the final column of the first row, you'll look at the very bottom of the table in the previous column. Four semiannual periods is equal to 2 years.
--------------
These steps are repeated for the second row of the table.
This time the growth multiplier is b = 1 + r/n = 1 + 0.14/12 = 1.0116667 approximately. The starting amount is a = 700
So that's how we go from [tex]y = ab^x[/tex] to [tex]y = 700(1.0116667)^x[/tex]
Like before, you'd plug in the various x values to find their paired y counterparts.
Example:
Plug in x = 18
[tex]y = 700(1.0116667)^x\\\\y = 700(1.0116667)^{18}\\\\y = 700(1.2321801)\\\\y = 862.52607\\\\y = 862.53\\\\[/tex]
The values are approximate. After 18 months, aka 18/12 = 1.5 years = 1 yr + 6 months, we'd have about $862.53 in the account.
The width of a golden rectangle is 15 feet. Find the perimeter of the rectangle to the nearest foot
39 feet
64 feet
79 feet
72 feet
96 feet
In a golden rectangle, the sides of the rectangle are as per the golden ratio. The perimeter of the golden rectangle with a width of 15 feet is 79 feet.
What is a golden rectangle?In a golden rectangle, the sides of the rectangle are as per the golden ratio. The rectangle is given the name rectangle because of the fact that the ratio is the golden number 1.618.
In a golden rectangle, the sides of the rectangle are as per the golden ratio. Since the width of the rectangle is 15 feet, therefore, the length of the rectangle will be 1.618 times the width,
Length of the rectangle = 1.618 × 15 feet = 24.27 feet
Now, the perimeter of the rectangle can be written as,
[tex]\rm \text{Perimeter of the rectangle} = 2(Length+ Width) \\\\\text{Perimeter of the rectangle} = 2(24.27+15)\\\\\text{Perimeter of the rectangle} = 78.54 \approx 79\ feet[/tex]
Hence, the perimeter of the golden rectangle with a width of 15 feet is 79 feet.
Learn more about Golden Rectangle:
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After learning so much about how art and culture are connected, it is time to explore different cultural pieces of art.
I WILL GIVE BRAINLIST
For this activity, you will search online and find a piece of art from four different cultures. You will need to copy or screenshot the four pieces of art that you decide on, and insert them into your written assignment.
You may choose any type of art from any culture that you like, but please keep in mind the appropriateness of your choices.
One you have selected your four pieces of art, you will answer several questions about each one and briefly discuss the piece.
Questions and points to discuss for each piece of art:
What culture is your piece of art from?
Why did you choose this piece?
What does this piece tell you about the culture?
Think daily life, food, celebrations and rituals, nature, and overall lifestyle.
How is this piece of art different from the rest of your choices?
Answer:
What culture is your piece of art from?
Italian Renaissance
Why did you choose this piece?
Beacuse its a beautiful piece of artwork made by one of my favorite artist.
Step-by-step explanation:
Joseph walks 10 times around the track at a rate of x laps per hour. She runs eight times around the track of a rate of 3X laps per hour. Write and simplify an expression for the total time it takes him to go around the track 18 times
The expression for the total time is:
T = (324/34x).
How to get the expression?He does 18 laps in total.
8 laps at a rate of 3x10 laps at a rate of x.The average rate for the whole 18 laps is the average of the rates (taking in account the number of laps made with each) so we get:
average rate = (8/18)*3x + (10/18)*x = (34x/18)
This means that he does (34x/18) laps per hour.
Then, the time needed to do 18 laps is:
T = (18/(34x/18)) = (324/34x).
If you want to learn more about rates:
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What is the power set of s={1,2,3,4,5}
The power set P(X) of a finite set X is the set of all possible subsets of X. If X has n elements, then it has a total of 2ⁿ subsets.
For the set S = {1, 2, 3, 4, 5}, we have
• subsets with cardinality 0:
{ } (the empty set)
• subsets with cardinality 1:
{1}, {2}, {3}, {4}, {5}
• subsets with card. 2:
{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}, {3, 4}, {3, 4}, {4, 5}
• subsets with card. 3:
{1, 2, 3}, {1, 2, 4}, {1, 2, 5}, {1, 3, 4}, {1, 3, 5}, {1, 4, 5}, {2, 3, 4}, {2, 3, 5}, {2, 4, 5}, {3, 4, 5}
• subsets with card. 4:
{1, 2, 3, 4}, {1, 2, 3, 5}, {1, 2, 4, 5}, {1, 3, 4, 5}, {2, 3, 4, 5}
• subsets with card. 5:
{1, 2, 3, 4, 5}
Then P(S) is the set containing all of these sets,
{{}, {1}, {2}, {3}, …, {1, 2, 3, 4, 5}}
The mean per capita consumption of milk per year is 144 liters with a variance of 484. If a sample of 183 people is randomly selected, what is the probability that the sample mean would be less than 146.58 liters? Round your answer to four decimal places.
Answer:
12144
Step-by-step explanation11213123:
find the least common denominator for thes two ratioal expression -1/y 2/5yfind the least common denominator for thes two ratioal expression -1/y 2/5y
Answer: it is -1, because y has no more complete prime factors
Step-by-step explanation:
Sal and Zack built a scale model of the Texas Capitol using a scale in which 2 inches represents 8 feet. The height of the Texas Capitol is 312 feet.
Problem
What is the height of the scale model in inches?
=
An apple costs twice as much as a banana.
Using the equations 2a + 4b = 2.00 and
a=2b, where a is the cost of one apple
and b is the cost of one banana, what are
a and b?
zat 45:28
=
A a= $0.25; b = $0.25
(B) a= $0.25; b = $0.50
C a= $0.50; b = $0.25
=
D a= $0.50; b = $0.50
10. Which statement is false?
Answer:
C is true
Step-by-step explanation:
The only true answer is C.
If a is 2 times greater than b, then:
A. is not possible because both sides are equal
B. is not possible because b is 2 times greater
D. is not possible because both sides are equal
Simplify the expression 4(2f−5g) + 6g.
Answer:
8f-14g is the answer
Step-by-step explanation:
Convert the exponential to a logarithmic form: 10^4 = 10,000
Question 1 options:
A)
log 10 = 4
B)
log 4 = 10
C)
log 10,000 = 4
D)
log 4 = 10,000
Answer:
C
Step-by-step explanation:
Exponential form is y = b^x, with b as the base, and logarithmic form is x = log_b(y).
In this case, 10 is the base, 4 is x, and 10,000 is y. In logarithmic form, this can be changed into 4 = log_10(10,000). Logarithms with base 10 can also be written as 4 = log(10,000). Therefore C is the correct answer.
What is the constant of proportionality shown in the
table?
Answer:
0.5
Step-by-step explanation:
An equation is written as :
y = kxk is the constant of proportionalityTaking the first row data (x = 2, y = 1),
y = kx1 = 2kk = 1/2k = 0.5Answer:
Option A, 0.5
Step-by-step explanation:
Step 1: Determine the slope/proportionality
[tex]Slope = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]Slope = \frac{1.5-1}{3-2}[/tex]
[tex]Slope = \frac{0.5}{1}[/tex]
[tex]Slope =0.5[/tex]
Answer: Option A, 0.5
I need help pls I need to get to 80%
Answer:
False (no)
Step-by-step explanation:
A polygon needs at least three straight sides and angles
3/5 = 24/40 =?/60. what comes at the question mark?
Answer:
? = 36
Step-by-step explanation:
Knowing that 3/5 and 24/40 is equal
Therefore we can either use:
3/5 = ?/60 or 24/40 = ?/60
I will use 3/5 = ?/60
Let ? = x
Hence we have
3/5 = x/60
Multiply both sides by 10
6 = x/6
Multiply both sides by 6
x = 36
Therefore, the question mark = 36
Let's check the answer by Simplifying the fraction:
3/5 = 36/60
3/5 is in already simplify
36/60 simplify = 3/5
3/5 = 3/5
Thus, the question mark = 36
[RevyBreeze]
Step-by-step Solution:
Let the "?" be known as "x".
Given equation:
3/5 = 24/40 = x/60
Therefore, we obtain the following equations:
Equation 1: 3/5 = 24/40Equation 2: 3/5 = x/60Equation 3: 24/40 = x/60Clearly, the second and the third equation have the "x" variable included. Therefore, we will only focus on the second and third equations.
3/5 = x/6024/40 = x/60Note: We can choose any equation to solve for x. The value of x in both equations will be the same as 3/5 = 24/40.
Determining the "x" variable in Equation 2:
⇒ 3/5 = x/60⇒ 5x = 60 × 3 [Cross multiplication]⇒ 5x = 180 [Simplifying]⇒ 5x/5 = 180/5 [Dividing]⇒ x = 36 [Simplifying]Determining the "x" variable in Equation 3:
⇒ 24/40 = x/60⇒ 40x = 24 × 60 [Cross multiplication]⇒ 40x = 1440 [Simplifying]⇒ 40x/40 = 1440/40 [Dividing]⇒ x = 36 [Simplifying]Therefore, the value of "?" is 36.