Given that x has a Poisson distribution with
mu
μ
equals
=
13
13, what is the probability that x
equals
=
5
5?
P(
5
5)
almost equals
≈
0.9930
0.9930 (Round to four decimal places as needed.)
Answers
[tex]P(x;\mu)= \frac{e^{-\mu}\mu ^{x}}{x!} [/tex]
where
μ = mean number of successes
x = actual or expected number of successes
Given:
μ = 13
x = 5
Therefore the probability that x=5 is
P(x = 5) = (e⁻¹³*13⁵)/5!
= 0.8392/120
= 0.006994
= 0.0070 (to 4 dec. places)
Answer: 0.0070 (to 4 decimal places)
It is interesting to observe P(x) as x varies, as in the graph shown below.
Related Questions
Raphael paid 636 for camera during a 60% off sale with the cameras regular price
Answers
If the price is 60% lower than usual, Raphael is paying only (100% - 60%), or 40%, for the camera.
Thus, 0.40x = $636. Divide both sides of this eq'n by 0.40 to find the original price of the camera.
x = $636/0.40 = ?
In a circle of radius 25 inches, a central angle of 35 degrees will intersect the circle forming an arc of length ____
Answers
arc length = (central angle/360) x 2 x PI x r
= (35/360) x 2 x 3.14 x 25
=15.2638
round answer as needed, you don't say how to round it.
Peter decides to mix grades of gasoline in his truck. He puts in 11 gallons of regular and 7 gallons of premium for a total cost of $76.99. If premium gasoline costs $0.25 more per gallon than regular, what was the price of each grade of gasoline?
Answers
p = r + 0.25
11r + 7(r + 0.25) = 76.99
11r + 7r + 1.75 = 76.99
18r = 76.99 - 1.75
18r = 75.24
r = 75.24/18
r = 4.18 <=== regular : $ 4.18 per gallon
p = r + 0.25
p = 4.18 + 0.25
p = 4.43 <=== premium : $ 4.43 per gallon
Final answer:
Peter bought regular and premium gasoline at $4.18 and $4.43 per gallon respectively, after solving a system of equations based on the total gallons and cost.
Explanation:
We are given a problem where Peter mixes two grades of gasoline—regular and premium—with premium costing $0.25 more than regular. To solve this, we can set up a system of equations representing the cost of each type of gasoline and the total cost.
Let the cost per gallon of regular gasoline be r, and thus premium will be r + $0.25 as it is $0.25 more expensive. Peter buys 11 gallons of regular and 7 gallons of premium, spending a total of $76.99. So, we have two equations:
11r + 7(r + $0.25) = $76.99r = regualar gasoline price per gallonSimplifying the first equation:
11r + 7r + $1.75 = $76.99
18r + $1.75 = $76.99
18r = $76.99 - $1.75
18r = $75.24
r = $75.24 / 18
r = $4.18
So the regular gasoline price per gallon is $4.18 and the premium gasoline price per gallon is $4.18 + $0.25 = $4.43.
How do I answer this question?
Answers
2^-1 ∙ 2^-4 is what?
Answers
When the power is minus just flip the number and make it denominator and make the power positive
(a^b)(a^c)=a^(b+c)
In this case:
(2^-1)(2^-4)
2^(-1-4)
2^-5 which is equal to:
1/(2^5)
1/32
What is a ratio equivalent to 8/10 with lower terms
Answers
In this case the gcf is 2 so you divide both 8 and 10 by 2, and you get 4/5.
what is the product x 2-16/2 x+8 . x3-2x2+x/x2+3x-4
Answers
------------- * ---------------------
2x+8 x^2 + 3x -4
(x+4)(x-4) x (x - 1)(x - 1)
= ----------------- * ----------------------
2(x+4) (x + 4)(x - 1)
x(x- 4) (x - 1)
= -----------------
2 (x + 4)
Answer:
A on Edge 2021
[tex] \frac{x(x - 4)(x - 1)}{2(x + 4)} [/tex]
Write 337,060 in expanded form using exponents
Answers
Write the quadratic function in the form g(x)= a (x-h)^2 +k . Then, give the vertex of its graph. g(x)=3x^2+30x+72
Writing in the form specified: g(x)= ___
Vertex:___
Answers
is a perfect square trinomial
now, let's take a closer look at the middle guy
is just 2 * guy on the left * guy on the right
so the middle term is just the product of the two terms of the binomial, without the exponent, or square rooted, and 2
alrite... that said.... now let's do some grouping
[tex]\bf g(x)=3x^2+30x+72\implies g(x)=(3x^2+30x)+72 \\\\\\ g(x)=3(x^2+10x)+72\implies g(x)=3(x^2+10x+\boxed{?}^2)+72[/tex]
so hmm we're missing the guy on the right there... who may that be?
well, we know the middle term is 10x, wait a minute, 10x is just 2 * 5 * x
so, if the guy on the left is "x", the other guy must be "5", 2*5*x = 10x
now, what we do is, we add 5²
however, bear in mind that, all we're doing is, borrowing from our very good friend Mr Zero, 0
so, if we add 5², we also have to subtract 5², so +5² - 5²
let's do so
[tex]\bf g(x)=3(x^2+10x)+72\implies g(x)=3(x^2+10x\boxed{+5^2-5^2})+72 \\\\\\ \textit{let's take out the negative from the group} \\\\\\ g(x)=3(x^2+10x+5^2)+\boxed{3(-5^2)}+72 \\\\\\ g(x)=3(x^2+10x+5^2)-75+72\implies g(x)=3(x+5)^2-3 \\\\\\ g(x)=3[x-(-5)]^2-3[/tex]
[tex]\bf \qquad \textit{parabola vertex form}\\\\ \begin{array}{llll} y=a(x-{{ h}})^2+{{ k}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\ \begin{array}{lcclll} g(x)=3[x-&(-5)]^2&-3\\ &\uparrow &\uparrow \\ &h&k \end{array}[/tex]
A pilot can travel 540 miles with the wind in the same amount of time as 380 miles against the wind. Find the speed of the wind if the pilots speed in still air is 230 miles per hour.
Answers
540/(230+w)=380/(230-w)
540(230-w)=380(230+w)
124200-540w=87400+380w
124200-920w=87400
-920w=-36800
w=40
So the wind speed is 40 miles per hour.
What is the inverse of the function below? F(x) = x - 6
Answers
F(x)=x-6
Inverse function:
x = F(x)+6
To show that there are different mathematical objects just use e.g F(y)
F(y)=y+6
Answer:
f(x)=x+6
Step-by-step explanation:
its the exact opposite of the answer, so if it was x-6 then the inverse would be x+6
If using spss, what is the exact likelihood of obtaining a t-test value at least as extreme or as close to the one that was actually observed, assuming that the null hypothesis is true
Answers
Supposing that the null hypothesis is true, the precise possibility of obtaining a t-test value at least as extreme or as ear to the one that was actually observed was 0.1%. This value can be found in the “Independent Samples t-test” table in the SPSS output, where the exact p value is reported as 0.001. If the null hypothesis is assumed to be true, then statistically noteworthy result should be highly improbable. The rejection of the null hypothesis implies that the correct hypothesis lies in the logical complement of the null hypothesis.
To add, used for non-batched and logical batched statistical analysis, SPSS Statistics was a software package for that specific purpose.
Which if the following is the smallest value 0.79, 2.40, 3.00007, 0.424, or 100?
Answers
hope this helps
The smallest value is 0.424
-----------------------------------------------------------------------------
You might think that 0.79 is the smallest one but it also has 0 which is not written. 0.790 is bigger than 0.424
I hope that helps!
Based on the historical record what is the empirical probability that the city will be hit by a tornado
Answers
Rewrite the equation in standard form and identify a, b, and c. 2x^2 + 6x - 9 = 3x^2 - 11x - 7
Answers
Subtract 2x^2 from both sides
6x - 9 = x^2 - 11x - 7
Substract 6x from both sides
-9 = x^2 - 17x - 7
Add 9 to both sides
0 = x^2 - 17x + 2
a = 1
b = -17
c = 2
What are the spherical coordinates of the point whose rectangular coordinates are (4,1,4)?
Answers
The spherical coordinates for the given rectangular coordinates (4,1,4) can be calculated using formulas for the transformation. They approximately yield (sqrt(33), 0.505, 1.540).
Explanation:In mathematics, we can convert rectangular coordinates to spherical coordinates using given formulas. Here, we have the rectangular coordinates (4,1,4). The transformation from rectangular to spherical involves three-step calculations:
First, calculate the radial coordinate, r, which is the distance from the origin to the point. It is given by r = sqrt(x^2 + y^2 + z^2).Second, find the polar angle, theta, measured relative to the vertical z-axis. It is given by cos(theta) = z/r.Lastly, find the azimuthal angle, phi, measured relative to the x-axis. It is given by cos(phi) = x/(r*sin(theta)).
Applying the formulas, we get: r = sqrt(4^2 + 1^2 + 4^2) = sqrt(33), theta = cos^-1(4/sqrt(33)) which is approximately 0.505, and phi = cos^-1(4/sqrt(33)*sin(0.505)) which is approximately 1.540.
So, the spherical coordinates of the point whose rectangular coordinates are (4,1,4) are approximately (sqrt(33), 0.505, 1.540).
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If there are 400 cubic centimeters of a chemical in 1 liter of solution, how many cubic centimeters of water must be added to dilute it to a 25% solution?
Answers
[tex]\bf \begin{array}{lccclll} &\stackrel{cm^3}{amount}&\stackrel{\textit{\% of chemical}}{concentration}&\stackrel{total~amount}{concentration}\\ &------&------&------\\ solution&1000&0.4&400\\ water&x&0&0x\\ ------&------&------&------\\ mixture&y&0.25&0.25y \end{array}[/tex]
so.. whatever "x" and "y" are, we know that 1000 + x = y.
and that 400 + 0x = 0.25y.
thus then
[tex]\bf \begin{cases} 1000+x=\boxed{y}\\ 400+0x=0.25y\\ 400=0.25y\\ ----------\\ 400=0.25\left( \boxed{1000+x} \right) \end{cases} \\\\\\ 400=250+0.25x\implies 150=0.25x\implies \cfrac{150}{0.25}=x\implies 600=x[/tex]
Write 935.97 in expanded form
Answers
hope it helps
Can segments with lengths of 36, 48, and 60 form a triangle? If so, would the triangle be acute, right, or obtuse?
Answers
Here we have 36+48=84 > 60, so the three segments form a triangle.
Since the ratio of the sides are 36 : 48 : 60 form the ratio of 3:4:5, which is exactly the ratio of a right triangle, we conclude that the triangle is a right triangle.
Segments with lengths of 36,48 and 60 can form a triangle. By employing the Pythagorean Theorem, we find that this is a right triangle as the lengths adhere to the theorem.
Explanation:The question asks if segments with lengths of 36, 48, and 60 can form a triangle, and if so, the type of the triangle. Yes, these segments can form a triangle. To classify the triangle as obtuse, right or acute, we use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as c^2 = a^2 + b^2. Substituting our values: 60^2 equals to 36^2+48^2 (3600 = 1296+2304). Since both sides of the equation are equal, we get the conclusion that this is a right triangle.
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“the sum of eight and twice w”
Answers
Sum is +
twice w=2w
Sum of 8 and 2w
8+2w
hope this helps:)
please mark thanks and brainliest:)
Answer:
the expression is [tex]8+2w[/tex]
Step-by-step explanation:
WE need to write the expression for the given statement
“the sum of eight and twice w”
Expression represents the terms that contains variables and operations. the variable we use for the expression is 'w'
Difference represents the subtraction operation.
Sum represents the addition operation.
twice 'w' means 2 times w that is 2w
the sum of 8 and 2w
For sum we use '+'
so ,the expression becomes [tex]8+2w[/tex]
A road crew spread 1 1/3 tons of gravel evenly over 8 feet of road.how many tons of gravel did they spread on each foot of road?
Answers
this box can be packed with 48 unit cubes the edge length each unit cube is 1 meter what is the voume of the box
Answers
Answer:
48 cubic meters.
Step-by-step explanation:
48x1
unit meter is cubic meters
how do write an equation to represent a real world situation?
Answers
Can someone please solve this ASAP?
Answers
surface area = 5ab +5bh
a = 4
b=7
h=18
5*4*7 = 140
5*7*18 = 630
630+140 = 770 square meters
ΔABC has three sides with these lengths: AB = 9, BC = 40, and CA = 41. What is the value of cos C?
Answers
40*40 = 1600
9* 9 = 81
so a^2 = b^2 + c^2
1681 = 1600 + 81
1681 = 1681 ...it's right triangle
CA = 41 = Hypo.
cosC = Adj / Hypo
cosC = BC / CA = 40/41
answer
cosC = 40/41
Answer:
The correct answer is
C 40/41
Step-by-step explanation:
Which of the following is a polynomial with roots negative square root of 5, square root of 5, and −3?
x^3 − 2x^2 − 3x + 6
x^3 + 2x^2 − 3x − 6
x^3 − 3x^2 − 5x + 15
x^3 + 3x^2 − 5x − 15
Answers
What is the area of a parallelogram with a base of 20 inches and an altitude of 8 inches?
Answers
The area of a parallelogram with a base of 20inches and an altitude of 8 inches is 160 inches square.
What is a parallelogram in math?
A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles identical). A quadrilateral with equal sides is called a rhombus, and a parallelogram whose angles are all right angles is referred to as a rectangle.
Conclusion: The opposite sides are equal in length and the opposite angles are identical in degree. To find the area, multiply the base by the height. The formula is: A = B * H where B is the base, H is the height, and * means multiply.
A = base * altitude
A = 20 * 8
A = 160 inches square.
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What are the counting numbers in base 6
Answers
In the base 6 number system, we would only use numerals from 0 to 5. The idea of base 6 is just like the normal base 10 system, however instead of using the numerals from 0 to 9, we use numerals from 0 to 5. And instead of having a ones digit, a tens digit, a hundreds digit and so on, we use a ones digit, a sixes digit, a thirty-sixes digit, and so on. Therefore in base 6, the number 321 means 1 one plus 2 sixes plus 3 thirty-sixes, or 121. So to count until 15 for example, we would need:
Base 6 Base 10
1 1
2 2
3 3
4 4
5 5
10 (1 six plus 0 ones) 6
11 (1 six plus 1 one) 7
12 (1 six plus 2 ones) 8
13 9
14 10
15 11
20 (2 sixes plus 0 ones) 12
21 (2 sixes plus 1 one) 13
22 14
23 15
Final answer:
The counting numbers in base 6 are represented using the digits 0 to 5, where each digit position represents a power of six. The sequence starts at 0, followed by 1, 2, 3, 4, 5, and then continues with 10 (which is 6 in decimal), 11 (7 in decimal), etc.
Explanation:
The counting numbers in base 6, also known as base-6 or hexadecimal numbers, consist of the digits 0, 1, 2, 3, 4, and 5. Just like in the decimal system (base 10) where the digits go from 0 to 9, in base 6 we only use the digits 0 to 5 for each place value, and each place is six times greater than the place to its right. After reaching 5, the next number in the sequence would be represented as 10 (base 6), which is equal to 6 in base 10. The sequence continues with 11 (base 6 equals 7 in base 10), 12 (base 6 equals 8 in base 10), and so on.
The concept of base systems is an important aspect of number theory in mathematics. In everyday life, we use the base 10 numbering system, mainly because humans have ten fingers. However, in computing and other scientific fields, different base systems like base 2 (binary) or base 16 (hexadecimal) are often used.
a star is 3.4 light years from earth. if 1 light years is 5.87×10^12 mi, how many miles from earth is the star?
Answers
3.4 * 5.87х10^12 miles
In a case whereby a star is 3.4 light years from earth. if 1 light years is 5.87×10^12 mi, the number of miles from earth the star is can be expressed as [tex]3.4 * 5.87 * 10^12 miles[/tex]
How can the number of miles be calculated?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given that star=3.4 light years from earth
1 light years= [tex]5.87*10x^{12} miles[/tex]
The number of miles from earth is
[tex]3.4 * 5.87 *10^{12} miles\\\\=3.4 * 5.87 * 10^12 miles[/tex]
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In a glide reflection, what comes first and what comes second?
first the glide, and second another glide
first the glide, and second a reflection
first the reflection, and second another reflection
first the reflection, and second a glide
Answers
In a glide reflection, the reflection comes first and the glide comes second.
Explanation:In a glide reflection, first the reflection is applied, and second a glide is performed. The reflection is a transformation that flips the shape across a line of reflection, while the glide is a transformation that slides the shape along a vector. The combination of the reflection and glide creates a glide reflection.
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