The probability that more than 12 particles occur in the area of a disk under the study is 0.20844.
The number of particles follows a Poisson Distribution.
A Poisson Distribution over a variable X, having a mean λ, has a probability for a random variable x as [tex]P(X = x) = e^{-\lambda} \frac{\lambda^{x}}{x!}[/tex] .
In the question, x = 12.
λ = 100*0.1 = 10.
To find : P(X > 12)
P(X > 12) = 1 - P(X ≤ 12) = 1 - poissoncdf(10,12)
As to find the probability of a Poisson Distribution P(X ≤ x), for a mean = λ, we use the calculator function poissoncdf(λ,x).
Therefore, P(X > 12) = 1 - 0.79156 = 0.20844.
Therefore, the probability that more than 12 particles occur in the area of a disk under the study is 0.20844.
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Solve the equation.
7h-5(3h-8)= -72
7h-15h+40=-72
40+72=15h-7h
112=8h
h=14
Find the remainder when f(X)=2x^3+2x^2-3x-3 is divided by X-2
The remainder when f(x) = 2x³ + 2x² - 3x - 3 is divided by x - 2 is 15.
We know that the remainder theorem states that if a polynomial p(x) is divided by a linear polynomial q(x) whose zero is x = a, then the remainder is given by r = p(a).
Here p(x) = f(x) = 2x³ + 2x² - 3x - 3 and q(x) = x - 2. First, we have to find the zero of q(x).
Now, q(x) = 0
i.e. x - 2 = 0
i.e. x = 2.
So, the zero of q(x) is 2, i.e. a = 2.
Then by the remainder theorem,
r = p(a) = f(2) = 2(2)³ + 2(2)² - 3(2) - 3 = 2 × 8 + 2 × 4 - 6 - 3 = 16 + 8 - 9 = 16 - 1 = 15
We can conclude that the remainder when f(x) = 2x³ + 2x² - 3x - 3 is divided by x - 2 is 15.
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On a piece of paper, graph y-5>2x-10. Then determine which answer
choice matches the graph you drew.
A
B
C
D
(21)
(0.5)
OA. Graph A
B. Graph B
C. Graph C
D. Graph D
(0.5)
((3.1)
(0.5)
(3.1).
(0.5)
Answer:
Graph B
Step-by-step explanation:
When graphing inequalities:
< or > : draw a dashed line≤ or ≥ : draw a solid line< or ≤ : shade under the line> or ≥ : shade above the lineGiven inequality:
[tex]y-5 > 2x-10[/tex]
Rearrange the given inequality to make y the subject:
[tex]\implies y-5+5 > 2x-10+5[/tex]
[tex]\implies y > 2x-5[/tex]
Therefore, we need to draw a dashed line and shade above it.
To draw the line:
Replace the > with = to find two points on the line:
[tex]\implies y=2x-5[/tex]
[tex]x=0 \implies y=2(0)-5=-5 \implies (0,-5)[/tex]
[tex]x=3 \implies y=2(3)-5=1 \implies (3,1)[/tex]
Plot the two found points: (0, -5) and (3, 1)
As the inequality is y > 2x - 5
Draw a dashed straight line through the two points.Shade above the line.The inequality equation is solved and the solution is plotted on the graph
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
y - 5 > 2x - 10
On simplifying , we get
Adding 5 on both sides , we get
y > 2x - 5
where 2 is the slope and 5 is the the intercept
Now , let the first point be P ( 0 , -5 )
when x = 0 and y = -5
-5 > -5
And , the graph of the inequality is plotted
Hence , the inequality is solved
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A cube has side length x. one side of the cube is increased by 4 inches, and another side is doubled. the volume of the new rectangular prism is 450 cubic inches. the equation 2 x cubed 8 x squared = 450 can be used to find x. what was the side length of the original cube? use a graphing calculator and a system of equations to find the answer.
The side length of the original cube is 1.95 inch.
Let each side length of each cube be 'x' inch.
Given : New side = (x+4 ) inch
Another new side = 2x inch
Since the sides are not equal, so it forms a cuboid in the case of new sides as given.
Also, according to question,
The volume of new rectangular prism is 450 cubic inches
= (x+4)*2x*x = 450
⇒ 2x cubed 8x squared =450
=16x5=450= 1.95 inch ( by taking out the cubic root of x3=7.5)
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The function f(x)= 4x + 3 represents the length of a rectangle. The function g(x)=2x-5 represents the width of the rectangle. Use ( g(4) to determine the area of the rectangle.
57
19
16
3
Answer:
57 square units
Step-by-step explanation:
Area is = Length x Width
Given:
f(x)= 4x + 3 Length
g(x)=2x-5 Width
x = 4
============
Width
g(x)=2x-5
g(4)=2(4)-5
g(4)= 3
Length
f(x)= 4x + 3
f(4) = (4)(4) + 3
f(4) = 19
Area = (length)*(width)
Area = f(x)*g(x) for x = 4
Area = (f(4))*(g(4))
Area = (19)*(3)
Area = 57 square units
Find the range of the function f(x) = 3x² - 2x for the domain (1, 2, 3).
Answer:
Step-by-step explanation:
bag has 2 blue marbles, 3 red marbles, and 5 white marbles. Which events have a probability greater than One-fifth? Select three options.
choosing 1 blue marble
choosing 1 red marble
choosing 1 red marble, not replacing it, and then choosing a blue marble
choosing 1 white marble, replacing it, and choosing another white marble
choosing 1 white marble
Answer:
choosing 1 red marble
choosing 1 white marble, replacing it, and choosing another white marble
choosing 1 white marble
Step-by-step explanation:
red marble has a 30 percent chance
1 white marble and then replacing and another white marble is 25% chance
1 white marble is 50% chance
Find the value of x, given that the two triangles are similar.
Answer:
10.5 is the correct answer.
Step-by-step explanation:
Due to the fact Triangle CAB has "6" as its length, and Triangle FDE has "2" as its length, you multiply 3.5 and 3.
3.5 x 3=10.5
2 x 3=6
3.5/2=10.5/6, so the answer is 10.5.
Answer:
x = 10.5 cmStep-by-step explanation:
Find the value of x, given that the two triangles are similar.
Given that the two triangles are similar we can solve with a proportion
6 : 2 = x : 3.5
x = 6 * 3.5 : 2
x = 21 : 2
x = 10.5
NEED HELP ASAP 1 HOUR LEFT
The number of units that will maximize revenue will be 672 units.
How to calculate the revenue?From the given information, p = 336 - 0.5x. The revenue function will be:
= (336 - 0.5x)x
= 336x - 0.5x²
This will be equated to 0. This will be:
336x - 0.5x² = 0
0.5x² = 336x
0.5x = 336
x = 336/0.5
x = 672
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Which of the following best describes how the y values are changing over each interval?
X
y
1
4
2
8
3
12
4
16
5
20
They are increasing by 4 each time.
O They are increasing by 6 each time.
O They are being multiplied by 2 each time.
O They are being multiplied by 4 each time
Answer:
y=ax+b
a=-0.6020457867
b=-2.256697516 <------- There is your value for b, which is the answer to the problem.
You can use these values for a and b to generate an equation in slope-intercept form, which you can then enter under Y= and view the graph.
Step-by-step explanation:
The value of y is multiplied by 2 each time when the value of x increases by 1 and this can be determined by using the arithmetic operations.
What is an mathematical expression?Using operations like addition, subtraction, multiplication, and division, a mathematical expression is defined as a group of numerical variables and functions.
Given that,
Table -- x y
1 20
2 40
3 80
4 160
5 320
The following steps can be used in order to describe how the y values are changed over each interval:
Step 1 - When value of (x = 1) and the value of (y = 20).
Step 2 - When value of (x = 2) and the value of (y = 40).
Step 3 - When value of (x = 3) and the value of (y = 80).
Step 4 - When value of (x = 4) and the value of (y = 160).
Step 5 - From the above steps, it can be concluded that the value of y is multiplied by 2 each time when the value of x increases by 1.
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Write the quadratic equation whose roots are 3 and -3, and whose leading coefficient is 3.
(Use the letter x to represent the variable.)
The quadratic equation is 3x² - 27.
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 .
Given:
The roots are 3 and -3
We have
α= 3 and β=-3
So,
α+β = -b/a and αβ = c/a
α+β = 0 =-b/a and αβ= -9 = c/a
Comparing from above
a=1, b= 0 and c=-9
Also, the leading coefficient is 3.
Then the quadratic equation is,
= 3(ax² + bx + c)
= 3( x² +0x- 9)
Hence, the quadratic equation is 3x² - 27.
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If u get 2 points every 5 minutes, how long will it take to get 3,600 points?
Answer:
9,000 minutes (150 hours)
Step-by-step explanation:
You have 3,600 points total; you need to divide it by 2 points.
3,600 ÷ 2 = 1,800
So, now you need to multiply the 1,800 points by 5 minutes.
1,800 × 5 = 9,000
Another way:
You can figure out how long it takes to get 1 point. If 2 points takes 5 minutes, divide 5 by 2.
5 ÷ 2 = 2.5
Now you need to figure out how long it would take to get 3,600 points. If each point takes 2.5 minutes, just multiply.
3,600 × 2.5 = 9,000
It would take 9,000 minutes (which is equivalent to 150 hours) to get to 3,600 points.
The table shows the outputs, y, for different inputs, x: Input (x) 2 5 9 12 Output (y) 20 15 12 8 Part A: Do the data in this table represent a function? Justify your answer. (3 points) Part B: Compare the data in the table with the relation f(x) = 5x + 14. Which relation has a greater value when x = 9? (2 points) Part C: Using the relation in Part B, what is the value of x if f(x) = 64? (5 points) (10 points)
The table is a function and the relation f(x) = 5x + 14 has a greater value when x = 9
Is the table a function?The table of values is given as:
Input (x) 2 5 9 12
Output (y) 20 15 12 8
In the above table of values, each x value have a unique y value.
This means that the table is a one-to-one relation
A one-to-one relation is a function
Hence, the table is a function.
The greater relation at x = 9The function is given as:
f(x) = 5x + 14
This gives
f(9) = 5 * 9 + 14
Evaluate
f(9) = 59
From the table, we have:
y = 12 when x = 9
Hence, the relation f(x) = 5x + 14 has a greater value when x = 9
The value of x if f(x) = 64We have
f(x) = 5x + 14
This gives
5x + 14 = 64
Subtract 14 from both sides
5x = 50
Divide by 5
x = 10
Hence, the value of x when f(x) = 64 is 10
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For the data set 7, 5, 10, 11, 12, the mean, x, is 9. What is the standard
deviation?
Answer:
Standard Deviation is s = 2.9
Step-by-step explanation:
Count = [tex]N[/tex] = 5
Mean = [tex]x^-[/tex] = 9
Variance = [tex]s^2[/tex] = 8.5
SD Formula = [tex]s = \sqrt \frac{1}{N - 1} (x_{i} - x^-)^2[/tex]
Variance Formula[tex]s^2 = \frac{(x_{i} - x^-)^2}{N- 1}[/tex]
Step 1: Calculate the variance
[tex]= \frac{(7-9)^2 + (5-9)^2 + (10-9)^2 + (11-9)^2 + (12 -9)^2 }{5-1}[/tex]
[tex]=\frac{34}{4} = 8.5[/tex]
Step 2: Apply square root/SD formula
[tex]=\sqrt{8.5} = 2.9[/tex]
Enter the correct answer in the box.
Consider this expression.
x² + x - 72
Replace the values of a and b to rewrite the given expression.
(x+ a)(x+b)
The correct values of a and b to rewrite the expression as (x + a)(x + b) are:
a = 9
b = -8
So, (x + 9)(x - 8) is the correct form of the given expression.
Here, we have to rewrite the expression x² + x - 72 in the form (x + a)(x + b), we need to find two numbers a and b such that when multiplied,
it give us the constant term -72 and when added, it give us the coefficient of the x term, which is 1.
The expression x² + x - 72 can be factored as follows:
x² + x - 72
= x² + 9x - 8x - 72
=x(x+9) -8(x+9)
= (x + 9)(x - 8)
Therefore, the correct values of a and b to rewrite the expression as (x + a)(x + b) are:
a = 9
b = -8
So, (x + 9)(x - 8) is the correct form of the given expression.
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f(x)=23x−1 and g(x)=−4x+6.
What transformation occurs from function f to function g?
a horizontal stretch by a factor of −6
a horizontal translation 6 units left
a vertical translation 6 units down
a horizontal compression by a factor of −6
The transformation occurs from function g is a vertical translation 6 units down.
What is Transformation?A function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f : X → X.
Given:
g(x) = 4x + 6
g(x) = 0
4x + 6=0
x= -6/4
Now,
f(-6/4) = 2 - 1
=-1
By seeing g(x), we can say that function g is a vertical translation 6 units down.
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What is the mean of the data
Answer:
hey diddle the medians the middle
you add and then divide for the mean
the mode is the one you see the most and the range is the difference between.
Hope this helps you with your question
Step-by-step explanation:
For Rs 10,000 at 10% per annum. What will be the interest after 4 years?
Step-by-step explanation:
please mark me as brainlest
What are the zeros of the function f(x) = x4 − x2 − 2?
±3, ±i
±2, ±i
positive or negative square root of 2 comma ±i
positive or negative square root 3, ±i
Answer:
x = ± [tex]\sqrt{2}[/tex] , x = ± i
Step-by-step explanation:
f(x) = [tex]x^{4}[/tex] - x² - 2
to find the zeros , equate f(x) to zero , that is
[tex]x^{4}[/tex] - x² - 2 = 0
using the substitution u = x² , then
u² - u - 2 = 0 ← in standard form
(u - 2)(u + 1) = 0 ← in factored form
equate each factor to zero and solve for u
u - 2 = 0 ⇒ u = 2
u + 1 = 0 ⇒ u = - 1
convert u back into terms of x
x² = 2 ( take square root of both sides )
x = ± [tex]\sqrt{2}[/tex]
x² = - 1 ( take square root of both sides )
x = ± [tex]\sqrt{-1}[/tex] = ± i
Answer: Positive or negative square root of 2, ±i
Proof o fvalidity is shown below.
What is the equation if the blue line?
Answer:15
Step-by-step explanation:
Start off using Java. As u progress you cant move over to C and the then transfer to python.
Quick I need an answer to this Queston:
The functions f(x)= −3/4x + 2 1/4 and g(x)= (1/2)x + 1 are shown in the graph.
What are the solutions to −3/4x + 2 1/4 = (1/2)x + 1?
Select each correct answer.
−1
0
1
2
3
Step-by-step explanation:
[tex] - \frac{3}{4} x + 2 \frac{1}{4 } = \frac{1}{2} x + 1[/tex]
[tex] - \frac{3}{4} x + \frac{9}{4} = \frac{1}{2} x + \frac{2}{2} [/tex]
[tex] \frac{ - 3x + 9}{4} = \frac{2x + 4}{4} [/tex]
[tex] - 3x + 9 = 2x + 4[/tex]
[tex] - 3x - 2x = 4 - 9[/tex]
[tex] - 5x = - 5[/tex]
[tex]x = \frac{ - 5}{ - 5} [/tex]
[tex]x = 1[/tex]
The answer is C.
What is the closest benchmark for 99%?
The closest benchmark for 99% is 100%.
We know that benchmarks in mathematics are the norm or point of comparison that something can be measured, compared, or evaluated against. Benchmark values are values that can be used to estimate and contrast other values or quantities. Typically, benchmark figures are multiples of 10 or 100. 0 percent, 10 percent, 25 percent, 50 percent, 75 percent, and 100 percent are the most popular benchmark percentages.
Here we have to find the closest benchmark for 99%. Clearly, from the definition 100% is the required answer.
We can conclude that the closest benchmark for 99% is 100%.
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Someone help me as fast as possible!!
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: length = 11 \: \: in[/tex]
[tex]\qquad \tt \rightarrow \: width = 4 \: \: in[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Let the measures be :
width = xlength = x + 7[tex] \textsf{\large Area of rectangle :} [/tex]
[tex]\qquad \tt \rightarrow \: Area = length \sdot width [/tex]
[tex]\qquad \tt \rightarrow \: 44 = x \sdot(x + 7)[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 7x = 44[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 7x - 44 = 0[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 11x - 4x - 44 = 0[/tex]
[tex]\qquad \tt \rightarrow \: x(x + 11) - 4(x + 11) = 0[/tex]
[tex]\qquad \tt \rightarrow \: (x + 11)(x - 4) = 0[/tex]
possible values of x = -11 and 4
[tex] \textsf{But the acceptable value of x = 4} [/tex]
[ length or width of rectangle can't be negative ]
[tex]\qquad \tt \rightarrow \: length = x + 7 = 4 + 7 = 11 \: \: in[/tex]
[tex]\qquad \tt \rightarrow \: width = x = 4 \: \: in[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
L
E
N
4
8
1
O
k
M
What is the value of k?
k=
Answer: 2
Step-by-step explanation:
By the geometric mean theorem,
[tex]\sqrt{8k}=4\\\\8k=16\\\\k=\boxed{2}[/tex]
in exponential growth functions. the base of the exponent must be greater than 1? how would the function change if the base of the exponent were between 0 and 1?
The function would become an exponential decay function.
Brian is drawing a scale diagram of a building. for every 10 m of the building he draws a line 5 cm long. Bryn thinks he is using a ratio of 2:1. Alun thinks Bryn is using a ratio of 200:1, is either of them correct? explain your answer
Answer:
200:1, Bryn is correct.
Step-by-step explanation:
Each 10 m is represented by a 5cm length on the diagram. We first note that 100 cm = 1 meter. 5 cm is (0.5 cm)*(1 meter/100 cm) =0.05 meters.
The 0.05 meters on the diagram represents 10 meters on the actual building. The ratio is (10 meters/0.05 meters) or 200:1. This is what Bryn believes is the ratio.
What number is the opposite of -2?
O A. ¹/2
O B. -¹/2
5
O C. - 13/
OD. /
12
Answer: 2
Step-by-step explanation:
The opposite of a negative number is the corresponding positive number.
These box plots show the basketball scores for two teams.
Wolverines
35
55
80 85
96
Panthers
33
50
70
90
107
Compare the shapes of the box plots.
O A . Both distributions are negatively skewed.
O B. The Wolverines' distribution is negatively skewed, but the
Panthers' distribution is symmetric.
O C. Both distributions are symmetric.
OD. The Wolverines' distribution is positively skewed, but the Panthers'
distribution is symmetric.
The correct option is B. The Wolverines' distribution is negatively skewed, but the Panthers' distribution is symmetric.
When is data symmetric for a given box plot?Data is symmetric if the median is in the mid of the box plot and the box is mid to the line connecting both whiskers.
The box plot showing scores for the Panthers basketball team has the median shown by a vertical line dividing the box into 2 equal halves.
Also, both whiskers on either side are relatively equal which shows that the data set for bulldogs is symmetric.
On the other side, the box plot for wolverine shows the median closer to the upper quartile.
That shows that the data set for team Wolverines' distribution is negatively skewed.
The correct option is B. The Wolverines' distribution is negatively skewed, but the Panthers' distribution is symmetric.
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Please help!!!!!
The equation of a circle is x² + y² – 8x + 10y + 37 = 0. What is the center and the radius of the circle? Show all your work.
Let's take this problem step-by-step:
Let's convert the equation back into the standard form:
⇒ standard form: (x-h)² +(y-k)² = r²
(h, k): center's coordinater: radius[tex]x^2+y^2-8x+10y + 37 = 0\\\rm \hookrightarrow x^2 - 8x + y^2+10y = -37\\\rm \hookrightarrow (x^2 - 8x) + (y^2 + 10y) = -37\\\rm \hookrightarrow (x^2-8x+16) + (y^2+10y+25) = -37 + 16 +25\\\rm \hookrightarrow (x-4)^2 + (y+5)^2 = 4\\\rm \hookrightarrow (x-4)^2 + (y+5)^2 = 2^2[/tex]
Based on the equation found
⇒ center: (4, -5)
⇒ radius: 2
Answer:
center: (4, -5)radius: 2Hope that helps!
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Answer:
Hey there : y= 3x - 3
Answer:
y = [tex]\frac{3}{2}[/tex] x + 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line
m = [tex]\frac{3-0}{0-(-2)}[/tex] = [tex]\frac{3}{0+2}[/tex] = [tex]\frac{3}{2}[/tex]
the line crosses the y- axis at (0, 3 ) ⇒ c = 3
y = [tex]\frac{3}{2}[/tex] x + 3 ← equation of line
