Answer:
a) The mean number of radioactive atoms that decay per day is 81.485.
b) 0% probability that on a given day, 50 radioactive atoms decayed.
Step-by-step explanation:
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\lambda[/tex] is the mean in the given interval.
a. Find the mean number of radioactive atoms that decayed in a day.
29,742 atoms decayed during 365 days, which means that:
[tex]\lambda = \frac{29742}{365} = 81.485[/tex]
The mean number of radioactive atoms that decay per day is 81.485.
b. Find the probability that on a given day, 50 radioactive atoms decayed.
This is P(X = 50). So
[tex]P(X = 50) = \frac{e^{-81.485}*(81.485)^{50}}{(50)!} = 0[/tex]
0% probability that on a given day, 50 radioactive atoms decayed.
Terms of geometric sequence are found by the formula T n = ar n - 1. If a = 3 and r = 2, find the first 4 terms of the sequence.
9514 1404 393
Answer:
3, 6, 12, 24
Step-by-step explanation:
It helps if the formula is properly written.
Tn = a·r^(n-1)
Fill in the given values for a, r, and use n = 1 to 4.
T1 = 3·2^(1-1) = 3
T2 = 3·2^(2-1) = 6
T3 = 3·2^(3 -1) = 12
T4 = 3·2^(4 -1) = 24
__
Additional comment
The value a=3 tells you the first term is 3. The value r=2 tells you each term is 2 times the previous one. Knowing this, you can write down the sequence based on your knowledge of multiplication tables (×2). You can use the formula as we did above, but it isn't necessary.
3, 6, 12, 24, ...
ALL I NEED HELP WITH IS WITH PART D, HOW DO I GET THAT
Use the function f(x) = −16x^2 + 22x + 3 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph. (4 points)
Step-by-step explanation:
Step 1: Factor the equation
[tex]f(x) = -16x^{2} + 22x + 3\\f(x) = -(8x + 1)(2x - 3)[/tex]
Step 2: Find the x-intercepts of the graph of f(x)
[tex]-8x - 1 + 1 = 0 + 1\\-8x / -8 = 1 / -8\\x = -1/8[/tex]
[tex]2x - 3 + 3 = 0 + 3\\2x / 2 = 3 / 2\\x = 3/2[/tex]
Step 3: Describe the end behavior of the graph of f(x)
Since the function is to the power of 2, that means that it is a parabola. And since the leading coefficient is negative, means that the arrows will be pointing down therefore, the end behavior of this graph is as x goes to infinity, f(x) goes to negative infinity and as x goes to negative infinity, f(x) goes to negative infinity.
Step 4: What are the steps you would use to graph f(x)
The first step that I would do is factor the equation. Then I would find the x-intercepts of the graph and plot them on the graph. I would then plug in 0 for all of the x values to get the y intercept. After doing that I would get the vertex using the vertex formula plotting it on the graph. Finally, I would connect all of the dots together to form the graph of the equation.
Answer:
The person above me is correct!
What does labeling a problem mean?
Answer:
im sure it means labelling or using a label is describing someone or something in a word or short phrase........:>
Choose the definition for the function.
Answer:
B
Step-by-step explanation:
For x<=0, the equation is 2x+2 and hence option B is the answer.
If ABCD is dilated by a factor of 3, the
coordinate of D' would be:
4
с
3
B
2
1
-5
-4
-3
-2
-1 0
1
N
3
4
5
DAN
- 1
-2
D
-3
D' = ([?], [ ]
Enter
Pls help me
Answer:
(6,-6)
Step-by-step explanation:
First let's identify the current coordinates of D
It appears that D is located at (2 , -2)
Now let's find the coordinate of D if it were dilated by a scale factor of 3.
To find the coordinates of a point after a dilation you simply multiply the x and y values of the pre image coordinates by the scale factor
In this case the scale factor is 3 and the coordinates are (2,-2)
That being said let's apply the dilation rule
Current coordinates: (2,-2)
Scale factor:3
Multiply x and y values by scale factor
(2 * 3 , -2 * 3) --------> (6 , -6)
The coordinates of D' would be (6,-6)
Which represents the inverse of the function f(x) = 4x?
h(x) = x+ 4
H(x) =x-4
h(x) = 3/4x
h(x) = 1/4x
Answer:
h(x)=1/4x
Step-by-step explanation:
function×inverse=-1
4x=-1
Answer:
h(x) = 1/4x
Step-by-step explanation:
y = 4x
x = 4y
1/4 x = y
Point A is located at (1, 5), and point M is located at (-1, 6). If point M is the midpoint of AB, find the location of point B.
The required coordinates of point B are (-3, 7) where point M is the midpoint of AB.
What is Midpoint?A midpoint is defined as in the middle of the line connecting two points a position known as a midpoint. A location in the middle of a line connecting the two points that are equally far from both points is the midpoint.
Point A is located at (1, 5), and point M is located at (-1, 6). If point M is the midpoint of AB
We can use these coordinates to find the coordinates of point B, which is the midpoint of line segment AB.
Let the coordinates of B would be (x, y)
Substituting the coordinates of points A into the midpoint formula gives us :
-1 = (x+1)/2 ; 6 = (y+5)/2
-2 = x +1 ; 12 = y + 5
x = -3; y = 7
Therefore, the required coordinates of point B are (-3, 7).
Learn more about the midpoint here :
brainly.com/question/5127660
#SPJ5
For the following function, one zero is given. Find all other zeros.
f(x)=x3-7x2+17x-15; 2-i
Answer:
1,-3,-5
Step-by-step explanation:
Given:
f(x)=x^3+7x^2+7x-15
Finding all the possible rational zeros of f(x)
p= ±1,±3,±5,±15 (factors of coefficient of last term)
q=±1(factors of coefficient of leading term)
p/q=±1,±3,±5,±15
Now finding the rational zeros using rational root theorem
f(p/q)
f(1)=1+7+7-15
=0
f(-1)= -1 +7-7-15
= -16
f(3)=27+7(9)+21-15
=96
f(-3)= (-3)^3+7(-3)^2+7(-3)-15
= 0
f(5)=5^3+7(5)^2+7(5)-15
=320
f(-5)=(-5)^3+7(-5)^2+7(-5)-15
=0
f(15)=(15)^3+7(15)^2+7(15)-15
=5040
f(-15)=(-15)^3+7(-15)^2+7(-15)-15
=-1920
Hence the rational roots are 1,-3,-5 !
how to graph quadratic relationship for h(x)=(x-1)^2-9
Answer:
use the formula y = a(x-h)^2 + k
the a stretches or flattens the parabola,
The h shifts left to right , and the k shifts up/down
Step-by-step explanation:
If y varies directly as x, and x = 4 when y = 20, find y when x = 18.
Step-by-step explanation:
y=Kx
20=4k
k=5
when x=18
y=18 x 5
y=90
.angle bisector of any angle of a triangle bisect that angle is_____________ parts
By definition of bisector, the angle bisector of any angle of a triangle divides that angle in two equal parts.
But first you must know the definition of the bisector of a triangle. The bisector of a triangle is a segment that divides one of its interior angles into two equal parts and continues until it reaches the side opposite that angle.
In other words, the bisector of a triangle is a line that divides each interior angle of the triangle into two equal angles.
Each interior angle of the triangle corresponds to a bisector, so since each triangle has three interior angles, it has three bisectors. The three bisectors of a triangle meet at a point called the incenter and it is always an interior point of the triangle.
In summary, the bisector of any angle of a triangle is a segment that divides the angle into two equal parts.
Learn more about angle bisector of a angle of a triangle:
https://brainly.com/question/2478436?referrer=searchResultshttps://brainly.com/question/12882107?referrer=searchResultshttps://brainly.com/question/13880193?referrer=searchResults
If y = sin 3x, find y" in terms of y.
Answer:
-0.54
Step-by-step explanation:
Hope it helped.
• • •
help me out please! everyday !
Answer:
V = 904.32 ft^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
The radius is 6 and pi = 3.14
V = 4/3 ( 3.14) (6)^3
V = 904.31999 ft^3
Rounding to the hundredths place
V = 904.32 ft^3
[tex] \large\begin{gathered} {\underline{\boxed{ \rm {\red{Volume \: of \: sphere \: = \: \frac{4}{3} \: \pi \: {r}^{3} }}}}}\end{gathered}[/tex]
r = 6 ft[tex] \bf \large{\purple{ \implies}} \tt \: Volume \: of \: sphere \: = \: \frac{4}{3} \: \times \: 3.14 \: \times \: {6}^{3} \\ [/tex]
[tex]\bf \large{\purple{ \implies}} \tt \: Volume \: of \: sphere \: = \: \frac{4}{3} \: \times \: 3.14 \: \times \:216[/tex]
[tex]\bf \large{\purple{ \implies}} \tt \: Volume \: of \: sphere \: = \: \frac{4}{ \cancel3} \: \times \: 3.14 \: \times \: \cancel{216 \: {ft}^{3} } \: \: \: ^{72 \: {ft}^{3} } [/tex]
[tex]\bf \large{\purple{ \implies}} \tt \: Volume \: of \: sphere \: = \: 4 \: \times \: 3.14 \: \times \: 72 \: {ft}^{3} [/tex]
[tex]\bf \large{\purple{ \implies}} \tt \: Volume \: of \: sphere \: = \: 12.56 \: \times \: 72 \: {ft}^{3} [/tex]
[tex]\bf \large{\purple{ \implies}} \tt \: Volume \: of \: sphere \: = \: 904.32 \: {ft}^{3} [/tex]
how to work this fraction 4/11+5/22+3/44
Answer:
29/44
Step-by-step explanation:
[tex]\frac{4}{11} +\frac{5}{22} +\frac{3}{44} =\\[/tex]
-find the common denominator
[tex]\frac{4*4}{4*11} + \frac{2*5}{2*22} +\frac{3}{44} =[/tex]
[tex]\frac{16}{44} +\frac{10}{44} +\frac{3}{44} =[/tex]
-add the fractions and solve
[tex]\frac{16+10+3}{44} =[/tex]
[tex]\frac{29}{44}[/tex]
Help please 6x + 3 > a if the inequality above is true for the constant a which of the following. coupd be a vakue of z
Answer:
[tex]\frac{a+3}{6}[/tex]
Step-by-step explanation:
Treat it like any other math problem with a equals sign:
6x + 3 = a
subtract 3 from both sides: 6x = a + 3
divide both sides by 6: [tex]x = \frac{a+3}{6}[/tex]
swap the ≥ back in: [tex]x \geq \frac{a+3}{6}[/tex]
the only time the sign flips is if you divide by a negative
Which polynomial expressions are in standard form?
x2 - x - 72
(x + 3)(x - 7)
-8x + 56
05
5x(2x)
Answer:
PLATO ANSWER
Step-by-step explanation:
x2 − x − 72
-8x + 56
5
those are the correct answers
Consider the graph of the quadratic function. Which
interval on the x-axis has a negative rate of change?
3
0-2 to-1
2
O -1.5 to 0
O 0 to 1
-3
-2
21
2
3
x
О 1 to 2.5
Answer:
1 to 2.5
Step-by-step explanation:
A negative rate of change requires the instantaneous slope to be negative, and the interval from 1 to 2.5 is the only place segment where that can happen.
Algebra help needed. Overwhelmed with other papers. See attached
Answer:
Step-by-step explanation:
whitch answer how do you want us to answer
base:10 height:2.5 what is the slope of the ramp
Answer:
Slope is B. ¼
Step-by-step explanation:
Slope: is hypotenuse
[tex] = { \sf{ \frac{ \delta \: height}{ \delta \: base} }} \\ \\ { \sf{ = \frac{2.5}{10} }} \\ \\ = { \sf{ \frac{1}{4} }}[/tex]
Graph the line with the equation y = 5x – 2
9514 1404 393
Answer:
see below
Step-by-step explanation:
When doing this by hand, it can work well to start at the y-intercept (0, -2) and use the slope value to find additional points on the line. The slope of 5 indicates another point will be 5 units up for each 1 unit right from (0, -2). So, another point will be (1, 3).
Draw the line through the points you found.
__
A graphing calculator does this easily.
this is confusing ok so 1.if there r 2 boys in a class for every 3 girls what would be the ratio for it and 2.if Seth bought a 12-ounce jar of something that is $3.60 what is the unit price?
John borrowed a certain amount of money from Tebogo at a simple interest rate of 8,7% per year. After five years John owes Tebogo R10 000.Calculate how much money John initially borrowed
For the function y=f(x), find f’(a)
Answer:
-1
Step-by-step explanation:
f(x) = x²+3x+1
f(a) = a²+3a+1
f'(a) = 2a+3
putting a = -2
2×(-2)+3
= -4+3
= -1
Please help with questions 1-4.
Observe the quantities, ie. see what happens if you increase one or decrease the other.
To simplify imagination, expose one quantity. I will expose y.
1.
[tex]-\frac{y}{4}=2x\implies y=-8x[/tex]
So what is their variation or proportion? If I increase x then y is getting more and more negative. So is this direct or inverse or nothing? It is direct.
2.
[tex]14x=\frac{14}{y}\implies y=x, y\neq0[/tex] again if I increase x then y will match, will also increase. This is again direct.
3.
[tex]y=\frac{13}{x}, x\neq0[/tex] this time if I increase x, y will get smaller. When x is exactly 13, y will be 1 and when x is 10000, y will be 0.0013. This is inverse. One quantity gets really small when other quantity gets really big.
4.
[tex]y=x-2[/tex] if I increase x then y will also increase even though by slightly less (-2) it will still increase. However since there is no multiplication this is not a direct variation nor is it inverse. It is nothing/no-variation.
Hope this helps :)
Write an expression to represent: Four less than the product of one and a number xxx
Answer:
xxx-4
Step-by-step explanation:
(1×xxx)-4
yietisyksykd
Answer:
(1xxx)-4
Step-by-step explanation:
Since 1 and xxx are multiplied, they produce 1xxx and eventually 4 is subtracted so 1xxx-4 and I put the brackets just to make it clear about what is going on in the expression
The product of two consecutive even integers is 10 less than 5 times their sum. Find the two integers. Answer in
the form of paired points with the lowest of the two integers first.
or
Answer:
(0,2) and (8,10)
Step-by-step explanation:
Let the smaller integer be 2n. The larger will be 2x+2.
ATQ. 2n(2n+2)+10=5(4n+2). Solving it, we get 2n=0 or 2n=8. The pairs are (0,2) and (8,10)
[18].Simplify (TTE): x(2x+y+5) - 2(x²+xy+5) + y(x + y)
Answer:
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 5x -10 + y\²[/tex]
Step-by-step explanation:
Given
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y)[/tex]
Required
Simplify
We have:
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y)[/tex]
Open brackets
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 2x\²+xy+5x - 2x\²-2xy-10 + xy + y\²[/tex]
Collect like terms
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 2x\²- 2x\²+xy-2xy+ xy+5x -10 + y\²[/tex]
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 5x -10 + y\²[/tex]
anybody know how to do this? if so, please explain!
Answer:
The x-intercepts are at (-4, 0) and (3, 0). The y-intercept is at (0, 1.2).
The graph is increasing at (-4, 0), (2.082, -0.604), (3, 0).
The graph is decreasing at (-2.082, 3.004), (0, 1.2), (1, 0)
Step-by-step explanation:
Deidre is planting tulips in her garden, and she has 44 red bulbs and 44 purple bulbs to plant in one row. What is the probability that she randomly plants the bulbs so that all 44 red bulbs are next to each other and all 44 purple bulbs are next to each other
Answer:
[tex]P=7.62*10^{-26}[/tex]
Step-by-step explanation:
From the question we are told that:
Available plants:
44 red bulbs
44 purple bulbs
Generally the equation for Total possible arrangement is mathematically given by
[tex]n= 88!/(44!*44!)[/tex]
[tex]n=2.6*10^{25}[/tex]
Since
Its either
All 44 red bulbs and All 44 purple bulbs next to each other in one row
OR
All 44 purple bulbs and All 44 Red bulbs next to each other in one row
Therefore
Probability is
[tex]P=\frac{2}{2.6*10^{25}}[/tex]
[tex]P=7.62*10^{-26}[/tex]
An entry in the Peach Festival Poster Contest must be rectangular and have an area of 1200 square inches. Furthermore, it's length must be 20 inches longer than it's width. Find the dimensions.
Answer:
The length is 46.05551275 inches, and the width is 26.05551275 inches.
Step-by-step explanation:
We know that the area must be 1200 square inches. Using this information, we can create an equation, where x is length and y is width:
x*y=1200
We know that its length must be 20 inches longer than its width. Therefore, x=y+20. Using this new information, we can replace 'x' in 'x*y=1200' with 'y+20':
(y+20)*y=1200
[tex]y^{2} +20y=1200[/tex]
[tex]y^{2} +20y-1200=0[/tex]
I have decided to use the quadratic formula, but you could also factor this equation into the 'intercept' form to determine the roots, which ultimately provides the same answer.
[tex]y=\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex]
[tex]y=\frac{-(20)+\sqrt{(20)^{2} -4(1)(-1200)} }{2(1)}[/tex]
[tex]y=\frac{-(20)+\sqrt{400+4800} }{2}[/tex]
[tex]y=\frac{-(20)+\sqrt{5200} }{2}[/tex]
[tex]y=\frac{52.11102551 }{2}[/tex]
[tex]y=26.05551275[/tex] inches
[tex]x=y+20[/tex]
[tex]x=(26.05551275)+20[/tex]
[tex]x=46.05551275[/tex] inches
Therefore, the length is 46.05551275 inches, and the width is 26.05551275 inches.
