Answer:
[tex]P(X=8) = 0.0194[/tex]
[tex]P(X \ge 8)= 0.9820[/tex]
[tex]P(X \ge 1)= 1[/tex]
[tex]P(X\le 1) = 0.0000049[/tex]
Step-by-step explanation:
Given
[tex]\lambda = 15[/tex]
Poisson distribution is given by:
[tex]P(X=x) = \frac{\lambda^x e^{-\lambda}}{x!}[/tex]
Solving (a): 8 bugs
This implies that:
[tex]x = 8[/tex]
So, we have:
[tex]P(X=8) = \frac{15^8 * e^{-15}}{8!}[/tex]
[tex]P(X=8) = \frac{783.99418938}{40320}[/tex]
[tex]P(X=8) = 0.0194[/tex]
Solving (b): At least 8 bugs
This is represented as: [tex]P(X \ge 8)[/tex]
Using complement rule:
[tex]P(X \ge 8)= 1 - P(X<8)[/tex]
Where
[tex]P(X<8) = P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7)[/tex]
[tex]P(X<8) = \frac{15^1 * e^{-15}}{1!} + \frac{15^2 * e^{-15}}{2!} + \frac{15^3 * e^{-15}}{3!} + \frac{15^4 * e^{-15}}{4!} + \frac{15^5 * e^{-15}}{5!} + \frac{15^6 * e^{-15}}{6!} + \frac{15^7 * e^{-15}}{7!}[/tex]
[tex]P(X<8) = (\frac{15^1}{1!} + \frac{15^2}{2!} + \frac{15^3 }{3!} + \frac{15^4}{4!} + \frac{15^5}{5!} + \frac{15^6}{6!} + \frac{15^7}{7!}) e^{-15}[/tex]
[tex]P(X<8) = (15 + 112.5 + 562.5 + 2109.375 + 6328.125 + 15820.3125 + 33900.6696429) *e^{-15}[/tex]
[tex]P(X<8) = 58848.4821429 *e^{-15}[/tex]
[tex]P(X<8) = 0.0180[/tex]
So:
[tex]P(X \ge 8)= 1 - P(X<8)[/tex]
[tex]P(X \ge 8)= 1 - 0.0180[/tex]
[tex]P(X \ge 8)= 0.9820[/tex]
Solving (c): At least 1
This is represented as: [tex]P(X \ge 1)[/tex]
Using complement rule:
[tex]P(X \ge 1)= 1 - P(X<1)[/tex]
[tex]P(X<1) = P(X = 0)[/tex]
[tex]P(X<1) = \frac{15^0 e^{-15}}{0!}[/tex]
[tex]P(X<1) = \frac{e^{-15}}{1}[/tex]
[tex]P(X<1) = e^{-15}[/tex]
So:
[tex]P(X \ge 1)= 1 - P(X<1)[/tex]
[tex]P(X \ge 1)= 1 - e^{-15[/tex]
[tex]P(X \ge 1)= 0.99999969409[/tex]
[tex]P(X \ge 1)= 1[/tex]
Solving (d): Not more than 1
This implies at most 1.
It is represented as:
[tex]P(X\le 1)[/tex]
It is calculated using:
[tex]P(X\le 1) = P(X = 0) + P(X =1)[/tex]
[tex]P(X = 0) = e^{-15}[/tex]
[tex]P(X=1) = \frac{15^1 * e^{-15}}{1!}[/tex]
[tex]P(X=1) = 15 * e^{-15}[/tex]
So:
[tex]P(X\le 1) = e^{-15} + 15 * e^{-15}[/tex]
[tex]P(X\le 1) = 0.00000489443[/tex]
[tex]P(X\le 1) = 0.0000049[/tex]
El precio de cada acción de una empresa de tecnología ha presentado a través del tiempo un comportamiento dado por la siguiente función:
Donde t es el tiempo dado en días y A es el precio de la acción inicial cuando t = 0. Un inversionista desea conocer el número de días para el cual el valor de la acción se duplica. Para conocer este resultado, el proceso que se debe realizar es reemplazar f(t) por
A.
A/2, luego, expresar la ecuación en forma de logaritmo natural y ahora despejar t.
B.
2A, luego, expresar la ecuación en forma de logaritmo natural y ahora despejar t.
C.
2A, luego, dividir ambos lados de la ecuación por e y ahora despejar t.
D.
A/2, luego, dividir ambos lados de la ecuación por e y ahora despejar t.
I will ask you to turn it in english instead of española.
NEED HELP PLEASE
We described numbers in this lesson using both powers of 10 and using standard decimal value. For example, the speed of light through ice can be written as a multiple of a power of 10, such as (2.3)⋅108 meters per second, or as a value, such as 230,000,000 meters per second. Use the number line to answer questions about points A and B.
Describe point B as:
a. A multiple of a power of 10
____ x 10 ^ ____
b. A value
_______
Describe point A as:
a. A multiple of a power of 10
_____ x 10 ^ _____
b. A value
______
Answer:
Step-by-step explanation:
B = 2×10⁸
A = 3×10⁸
The sum of two numers is 58. The smaller number is 14 less than the larger number. What are the two numbers?
what is the value of angle x?
Answer:
x=66
Step-by-step explanation:
Hello There!
∠BAC ≅ ∠CDB because in a parallelogram opposite angles are congruent
So all we have to do is solver for ∠BAC
Remember the sum of the triangles angles is 180 so to find ∠BAC
we subtract the given angles (83 and 31) from 180
180-83-31=66
so ∠BAC = 66
like stated before
∠BAC≅∠BDC so if ∠BAC = 66 then x also equals 66
Answer:
x = 66
Step-by-step explanation:
x = 66 degree
What is the mode of the data set?
A. 8
B. 9
C. 10
D. 5
Answer:
A: 8
Step-by-step explanation:
The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all. ... The mode can be the same value as the mean and/or median, but this is usually not the case
in certain mill the cost of c in thousands of dollars of producing x tons of steel is given by c(x)= 0.03x +3.4. the revenue R in thousands of dollars by selling x tons is given R(x)= 0.5x. Find x the number of tons that must be produced to break even
Answer:
well you see if u wanrt to
a
Need Help (WILL GIVE BRAINLIEST)
Answer:
A
Step-by-step explanation:
(y-5) / (7-5) = (x-1) / (2-1)
(y-5) / 2 = x-1
y-5 = 2x -2
y = 2x +3
1, 3, 5, 7, 9, 9, 11, 11, 13, 14 }
Which box plot represents the data set?
A small island country with less than 20,000 cars has decided to reissue the license plates for its cars and has decided on the following rules for assigning numbers and letters to the license plates. Each plate will have 7 character positions that each must be filled. The leftmost character position will hold a letter from the set {D, E, H, G, X}. The next three positions will hold integers from the set {0, 1, ..., 9} but none of the integers can be repeated. The rightmost three positions must be entirely from the set {I, V, X} or entirely from the set {P, Q, R}, with repetition allowed in either case. For example, a valid plate would be G 027 XXI and an invalid plate would be G 337 PQX (two rules violated). What is the maximum number of different license plates following the rules?
a. 270,000
b. 2,624,400
c. 3,645,000
d. 194,400
Answer:
The answer is "Choice d"
Step-by-step explanation:
Given data:
7 position [tex]5, 10 , 9, 8 , 2 \times 3^3[/tex]
calculating the left most filled by any of D, E, H, G, X
a possible way to fill =5
calculating the next 3 value that will be filled 0 to 10 without any repetition
possible way to fill [tex]=10 \times 9 \times 8[/tex]
calculting the last filled any if set [tex]\{I,V,X\} \ \ or \ \ \{P,Q,R\}[/tex] with repetation
possible way [tex]=2 \times 3^3[/tex]
Total different licence plates [tex]= 5 \times 10 \times 9 \times 8 \times 2 \times 3^3=194400[/tex]
Elroy enjoys roller skating and weight training. Let X represent the number of hours he spends roller skating weekly,
and let y represent the number of hours he spends weight training weekly. The mean of X is 5 hours, and the mean
of Y is 7 hours. Which answer choice correctly calculates and interprets the mean of the sum, S = X + Y?
Answer:
[tex]\mathbf{\mu_S = 12 }[/tex]; [tex]\text{Elroy can expect to roller skate and weight train, on average, 12 }[/tex][tex]\text{hours in a typical week.}[/tex]
Step-by-step explanation:
Given that:
The mean [tex]\mu_X = 5[/tex]
The mean [tex]\mu_Y = 7[/tex]
Where;
[tex]S= X+ Y[/tex]
[tex]\mu_S = \mu _X + \mu_Y \\ \\ \mu_S = 5+7 \\ \\ \mu_S = 12[/tex]
Thus;
[tex]\mathbf{\mu_S = 12 }[/tex];[tex]\text{ Elroy can expect to roller skate and weight train, on average, 12 }[/tex][tex]\text{hours in a typical week.}[/tex]
Answer:
C ♡♡
Step-by-step explanation:
jus took the quiz !!!
2x+y=5 y=x−1 system of equations please show your work
sub y = x - 1 into equation 1
2x + x - 1 = 5
3x = 6
x = 2
sub x = 2 into equation 2
y = 2 - 1
y = 1
Find AB If AC = 12 and BC = 35
Answer:
37
Step-by-step explanation:
a² =b²+ç²a²=12²+35²a=√1369a=37Given: binom(119, 0.57)
What is the Expected Value?
Answer:
The expected value, or mean, of a binomial distribution, is calculated by multiplying the number of trials by the probability of successes. For example, the expected value of the number of heads in 100 trials of head and tales is 50, or (100 * 0.5)
(PLEASE HELP)James tosses a coin 50 times. It lands on heads 23 times and on tails 27 times.
What is the relative frequency of the coin landing on heads in this experiment?
A 23%
B 46%
C 50%
D 54%
Answer:
b
Step-by-step explanation:
Please help!! No links
9514 1404 393
Answer:
10.5
Step-by-step explanation:
Corresponding sides of similar triangles are proportional, so ...
ZX/ZY = CA/CB
ZX = Zy(CA/CB) = 14(3/4)
ZX = 10.5
PLEASE HELP ITS DUE IN AN HOUR!!!!!!
Answer:
3 units to the right of -5
Step-by-step explanation:
7. Which of these expressions are equivalent to 10x + 11? Select the three that apply.
A. 5(2x + 10)+1
B. 7(x + 2) + 3x - 3
C. 3(3x + 4) + X-1
D. 2(6x + 4) + 2x + 5
E. 2(6x + 5) - 2x + 1
Answer:
B
Step-by-step explanation:
7 times 1x equals 7x. Then 7 times 2= 14. Thirdly, 7x plus 3x equals 10x. Lastly, 14 -3 equals 11. So 10-+11 altogether
8th grade math, please help.
9514 1404 393
Answer:
282.74 units³
Step-by-step explanation:
Put the given dimensions in the volume formula and do the arithmetic.
V = πr²h
V = 3.14159(3²)(10) ≈ 282.74 . . . units³
50 POINTS + BRAINLIEST
PLEASE DONT STEAL POINTS THIS IS MY 2ND TIME ASKING THIS QUESTION
Answer:
16
Step-by-step explanation:
Hope you pass good luck to you!
whats an equivalent expression for 4 + 4n
Answer:
4(1+n)
Step-by-step explanation:
4+4n
4+4n
Factor the polynomial 4+4n by it's GCF: 4
4\left(1+n\right)
4(1+n)
URGENT PLZ HELP
Solve for x. Assume that lines which appear to be diameters are actual diameters.
Answer:
Step-by-step explanation:
This is a central angel so the degree of the angle is equal to the degree of the arc which is 111.
X+114=111
add negative -114 to each side to get X alone.
-114+X+114= 111+-114
X=-3 . Answer negative 3
You have 2 spreads, 5 meats, and 2 kinds of bread. How many different sandwiches can you make using one of each type of ingredient?
A) 9
B) 12
C) 20
D) 40
Answer:
C)
Step-by-step explanation:
I need a answer ASAP
Answer:
8
Step-by-step explanation:
y = (10x^2 + 3x^4)/ 2x^2
where x is not equal to 0
(20x + 12x)/4x
32x / 4x
= 8
Axis of sym: x =
Vertex: (
,
)
Do not do the domain
Range: Pick one: A. y≥4 B. y<4 C. y≤4 D. y≤−2 E. y<−2
The Range is
Zeros:
and
Equation:
Answer:
SEE BELOWStep-by-step explanation:
to understand thisyou need to know about:quadratic functionPEMDASlet's solve:vertex:(h,k)
therefore
vertex:(-1,4)
axis of symmetry:x=h
therefore
axis of symmetry:x=-1
to find the quadratic equation we need to figure out the vertex form of quadratic equation and then simply it to standard form i.e ax²+bx+c=0vertex form of quadratic equation:
y=a(x-h)²+ktherefore
y=a(x-(-1))²+4y=a(x+1)²+4it's to notice that we don't know what a is
therefore we have to figure it out
the graph crosses y-asix at (0,3) coordinates
so,
3=a(0+1)²+4
simplify parentheses:
[tex]3 = a(1 {)}^{2} + 4[/tex]
simplify exponent:
[tex]3 = a + 4[/tex]
therefore
[tex]a = - 1[/tex]
our vertex form of quadratic equation is
y=-(x+1)²+4let's simplify it to standard form
simplify square:
[tex]y = - ( {x}^{2} + 2x + 1) + 4[/tex]
simplify parentheses:
[tex]y = - {x}^{2} - 2x - 1 + 4[/tex]
simplify addition:
[tex]y = - {x}^{2} - 2x + 3[/tex]
therefore our answer is D)y=-x²-2x+3
the domain of the function
[tex]x\in \mathbb{R}[/tex]
and the range of the function is
[tex]y\leqslant 4[/tex]
zeroes of the function:
[tex] - {x}^{2} - 2x + 3 = 0[/tex]
[tex] \sf divide \: both \: sides \: by \: - 1[/tex]
[tex] {x}^{2} + 2x - 3 = 0[/tex]
[tex] \implies \: {x}^{2} + 3x - x + 3 = 0[/tex]
factor out x and -1 respectively:
[tex] \sf \implies \: x(x + 3) - 1(x + 3 )= 0[/tex]
group:
[tex] \implies \: (x - 1)(x + 3) = 0[/tex]
therefore
[tex] \begin{cases} x_{1} = 1 \\ x_{2} = - 3\end{cases}[/tex]
A heavy rope, 50 ft long, weighs 0.6 lb/ft and hangs over the edge of a building 120 ft high. Approximate the required work by a Riemann sum, then express the work as an integral and evaluate it.
Exercise (a)
How much work W is done in pulling the rope to the top of the building?
Exercise (b)
How much work W is done in pulling half the rope to the top of the building?
Answer:
Exercise (a)
The work done in pulling the rope to the top of the building is 750 lb·ft
Exercise (b)
The work done in pulling half the rope to the top of the building is 562.5 lb·ft
Step-by-step explanation:
Exercise (a)
The given parameters of the rope are;
The length of the rope = 50 ft.
The weight of the rope = 0.6 lb/ft.
The height of the building = 120 ft.
We have;
The work done in pulling a piece of the upper portion, ΔW₁ is given as follows;
ΔW₁ = 0.6Δx·x
The work done for the second half, ΔW₂, is given as follows;
ΔW₂ = 0.6Δx·x + 25×0.6 × 25 = 0.6Δx·x + 375
The total work done, W = W₁ + W₂ = 0.6Δx·x + 0.6Δx·x + 375
∴ We have;
W = [tex]2 \times \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= 2 \times \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 750[/tex]
The work done in pulling the rope to the top of the building, W = 750 lb·ft
Exercise (b)
The work done in pulling half the rope is given by W₂ as follows;
[tex]W_2 = \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 562.5[/tex]
The work done in pulling half the rope, W₂ = 562.5 lb·ft
Eloise spent $1.65 on potato salad that costs $0.25 per pound.
How many pounds of potato salad did she buy?
Answer:
she would be able to buy 6.6
Answer:
its 6.6
Step-by-step explanation:
cause i did that already
Discount, markup, and commission word problems
You might need: Calculator
A store has a 40% off sale on headphones. With this discount, the price of one pair of headphones is $36.
What is the original price of the pair of headphones?
$
Show Calculator
Stuck? Watch a video or use a hint.
Report a problem
Answer:
90$
Step-by-step explanation:
X(40%) = 36$
X(40/100) =36
40X = 3600
X = 90$
(recheck: 90$ x 40%= 36$)
Camden is going to invest $600 and leave it in an account for 12 years.
Assuming the interest is compounded continuously, what interest rate, to the
nearest hundredth of a percent, would be required in order for Camden to
end up with $920?
Answer:
zjzjzjznnznzkznnznzidddx
Answer:
3.56
Step-by-step explanation:
just did it on delta math
can someone help me with this please
Answer:
4
This figure has 4 lines of symmetry.
Wayne charges the following for repairing washing machines:
£28 call-out charge + £16 for each half-hour he spends on the repair
If a repair costs £76, how long did it take?
