Using the Poisson distribution, it is found that the probabilities are:
a) 0.149
b) 0.6993
c) 0.5503
We are given only the mean, hence, the Poisson distribution is used.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successes e = 2.71828 is the Euler number [tex]\mu[/tex] is the mean in the given interval.The mean is of 7 births per minute, hence [tex]\mu = 7[/tex].
Item a:
The probability is P(X = 6), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 6) = \frac{e^{-7}(7)^{6}}{(6)!} = 0.149[/tex]
Item b:
This probability is:
[tex]P(X \geq 6) = 1 - P(X < 6)[/tex]
In which:
[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]
Following the logic used in item a to find each probability, we have that [tex]P(X < 6) = 0.3007[/tex], hence:
[tex]P(X \geq 6) = 1 - P(X < 6) = 1 - 0.3007 = 0.6993[/tex]
Item c:
This probability is:
[tex]P(X > 6) = 1 - P(X \leq 6)[/tex]
[tex]P(X \leq 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)[/tex]
We have that [tex]P(X \leq 6) = 0.4497[/tex], hence:
[tex]P(X > 6) = 1 - P(X \leq 6) = 1 - 0.4497 = 0.5503[/tex]
A similar problem is given at https://brainly.com/question/16912674
True or False.
A 20° angle and a 70° angle can be
composed into a 90° angle.
Complete the table below to find solutions to the linear equation −3x−y=27.
Answer:
×=3×+y=27
Step-by-step explanation:
the variables are not the same so you cant do anything
Answer:
X Y (X,Y)
0 -27 (0,-27)
4 -39 (4,-39)
-9 0 (-9,0)
Two angles form a linear pair. The measure of one angle is twice the measure of the other angle. Find the measure of each angle.
The smaller angle measures =?
The larger angle measures =?
Answer:
The smaller angle measures = 60º
The larger angle measures = 120º
Step-by-step explanation:
The sum of angles in linear pair is 180
The measure of one angle is twice the measure of the other angle.
x + 2x = 180
Combine like terms
3x = 180
Divide both sides by 3
x = 60º
2x = 120º
Strawberries cost $3.00 per pound. For each question
a.
How many pounds of strawberries can you buy for $1.00?
b.
How many pounds of strawberries can you buy for $11.0
Answer:
A. 1/3 pound
B. 11/3 or 3.666666667
Step-by-step explanation:
:)
Find a formula for the inverse of the following function, if possible.
[tex]P(x) = 3\sqrt[3]{x} - 1[/tex]
[tex]P^{-1}(x) = \\\\[/tex]
or does not have an inverse function
to find the inverse of any expression, we start off by doing a quick variables switcheroo and then solve for "y", so let's do so
[tex]\stackrel{P(x)}{y}~~=~~3\sqrt[3]{x}-1\implies \stackrel{\textit{quick switcheroo}}{x~~ =~~3\sqrt[3]{y}-1}\implies x+1 = 3\sqrt[3]{y}\\\\\\\cfrac{x + 1}{3}=\sqrt[3]{y}\implies \left( \cfrac{x + 1}{3} \right)^3 =y\implies \cfrac{(x+1)^3}{3^3}=y\implies \cfrac{(x+1)^3}{27}=\stackrel{\stackrel{y}{\downarrow }}{P^{-1}(x)}[/tex]
{3x−5y=4 -2x+6y=18
Please help solve for x and y
Answer:
hello mam I don't know what to say to someone who makes the way to the way to the way to the way to the way to the way to work now where is my turn to the dark side I will be
If the amount of fruit increases by 40%, what percent of the original amount do you have?
Answer:
First, subtract to find the amount of change: 225 - 25 = 200. The increase is 25. Next, divide the amount of change by the original amount:.
Step-by-step explanation:
If Brianna spent $65 on necklaces and bracelets at a crafts fair.
She spent $23 on bracelets and the rest on necklaces.
If the necklaces all cost the same and Brianna bought 3, how much did each necklace cost?
1. Mark bought 5 shirts for 32.35.What was the cost of each stint in dollars and
Answer:
$6.47 for each shirt
Step-by-step explanation:
If s is the cost of a shirt, then the cost of 5 shirts is ...
5s = $32.35
s = $32.35/5 = $6.47 . . . . . divide both sides of the equation by 5
The cost of each shirt was $6.47.
_____
Additional comment
The equation formalizes the math for you, perhaps helping you see that division by 5 is required.
To find cost per shirt, divide cost by shirts. "Per" can often be thought of as meaning "divided by."
Classify the triangle by both its
sides and its angles using the
choices provided. Choose all that
apply.
H
th
130°
커
O isosceles
equilateral
scalene
acute
obtuse
right
equiangular
Answer:
obtuse isosceles
Step-by-step explanation:
the dashes on the sides show congruency. since two sides have the same number of dashes those two sides are congruent. since the third side has 3 dashes instead of 2, it isn't congruent to the other two meaning the triangle is an isosceles triangle.
since the angle is >90, the triangle is obtuse
How many equal parts are there in this image
Answer:
6
It's kind of blury, so I can't really see it.
Answer:
4
Step-by-step explanation:
The ratio of girls to boys on the school field trip is 6 to 7. There are 24 girls on the field trip. What is the total number of students on the field trip? NO LINKS!!!
A.28
B.52
C.4
D.13
Answer:
B.52 is the answer i think for the total number of kids
Use the elimination method to solve the system of equations. Choose the correct orderly pair.
2x+4y=16
2x-4y=0
A. (2,-4)
B. (4,-2)
C. (2,4)
D. (4,2)
(2x+4y=16).....1
(2x-4y=0).....2
then take equation 1 plus 2
4x=16
x=4
then take equation 2 to solve for y
2x-4y=0
(2×4)-4y=0
y=2
therefore answer is D. (4,2)
if the mean of a data is 316 and the sum of its observation is 3792 find the number of observations in the data.
Answer:
12
Step-by-step explanation:
mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
Here mean = 316 and sum = 3792 , count n is required to be found, so
[tex]\frac{3792}{n}[/tex] = 316 ( multiply both sides by n )
3792 = 316n ( divide both sides by 316 )
12 = n
There are 12 observations in the data
A jet is flying in a direction N 70° E with a speed of 600 mi/h. Find the north and east components of the velocity. Round to two decimal places.
Using vector concepts, it is found that the components of the velocity are given as follows:
North: 205.21 mi/h.East: 563.82 mi/h.How can a vector be represented in i and j notation?Given a magnitude M and angle [tex]\theta[/tex], the a vector V can be represented as follows:
[tex]V = M\sin{\theta}i + M\cos{\theta}j[/tex]
In which:
i is the horizontal(east/west) component.j is the vertical(north/south) component.In this problem, we have that the magnitude and the angle are given as follows:
[tex]M = 600, \theta = 70^{\circ}[/tex]
Hence the north component is:
[tex]600\cos{70^{\circ}} = 205.21[/tex]
And the east component is:
[tex]600\sin{70^{\circ}} = 563.82[/tex]
More can be learned about vectors at brainly.com/question/24606590
#SPJ1
How many solutions are there to the equation below?
6x + 33 = 6(x+6)
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Let's solve ~
[tex]6x + 33 = 6(x + 6)[/tex][tex]6x + 33 = 6x + 36[/tex]Here, 6x is present on both the sides of equation so they cancel out ~ therefore there is no one solution satisfying the equation ~
Answer:
there are zero solutions
\_(-_-)_/
i asked g o o g l e thats what it said
please help me with this last question
Answer:
Step-by-step explanation:
3t² - t
3(4²) - 4
3(16) - 4
48 - 4
44
Rational numbers on the number line
Answers:
A = -5/4B = -0.5C = 2=====================================
Explanation:
The fraction -5/4 converts to -1.25 after using your calculator or long division. It represents the mixed number -1 & 1/4. So we go 1 full unit to the left to arrive at -1, then we move another 1/4 unit to the left to get to point A. That's why point A is located at -5/4 = -1.25 = -1 & 1/4.
Point B is directly midway between 0 and -1, so it must be at -0.5; you can use the midpoint formula.
please need help on this question thanks. see the screenshot
Check the picture below.
F = sales for Friday
we know that the total of weekend sales for Germany was F + 317 + 405.
we also know that 405 is really 37.19% of that amount, say "x", which is the 100%, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 405&37.19\\ x&100 \end{array}\implies \cfrac{405}{x}=\cfrac{37.19}{100}\implies 40500=37.19x \\\\\\ \cfrac{40500}{37.19}=x\implies 1089~\approx ~ x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{friday}{F} + \stackrel{sat/sun}{317} + \stackrel{monday}{405} \approx 1089\implies F +722 \approx 1089\implies \boxed{F\approx 367}[/tex]
If f (x) = 2x^3 - 5x +2, then what is the remainder when f (x) is divided by x - 4?
hmm let's do that with synthetic division, Check the picture below.
A store has apples on sale for $3.00 for 2 pounds. If an apple is approximately 5 ounces, how many apples can you buy for $12.00? Complete the explanation
Answer:
you can buy 6 pounds of apples
Step-by-step explanation:
Two sides of a triangle measure 27 inches and 32 inches. Which could represent the length of the third side?
Answer:
Step-by-step explanation:
The third side could have dimension x
32 - 27 < x < 32 + 27
5 < x < 59
There are a few special triangles
Equilateral triangle could have legs
27, 32, 27
or
32, 27, 32
A right triangle could have the third side
√(27² + 32²) = √1753 which is about 41.87
or
√(32² - 27²) = √295 which is about 17.18
Notice all these fit within the original limits specified.
Answer:
The third side is greater than 5 but less than 59.
Step-by-step explanation:
Remember: Given any two sides of a triangle, the length of the third side is greater than the difference but less than the sum of the length of the two given sides.
So 27 and 32 The given two sides
32 - 27 = 5 Greater than the difference (greater than 5)
32 + 27 = 59 Less than the sum (less than 59)
1/2x - 2=3 number line
Answer:
x = 10
Step-by-step explanation:
I don't really get what you mean, so I just solved for x.
1/2x-2=3
We add 2 on both sides.
1/2x=5
Times both sides by 2 to cancel out the 1/2
x=10.
Hope this helped. :)
(sorry if I didn't do what you wanted me to.)
Which of the following statements are true? Select all that apply.
Answer:
They have 2 left one OR 2 right ones are true
Step-by-step explanation:
Complete the table for the provided graph.
The population of a large city is gradually moving to outlying metropolitan areas with the decline predicted by the functional equation, P = P,2***
If represents the present population of 1 million and Pis the predicted population in t years, what is an estimate of the city's population five
years from now? Use 2.718 for e.
1,161,816
0 223,164
0 860,721
970,448
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=21(0.97)^x
what is the % increase
Answer:
Step-by-step explanation:
As the number under the exponent is less than 1, this is a decay function.
y decreases by (1 - 0.97)100 = 3% for each unit increase in x
so the increase would be -3%
Holly ate 3 brownies from a pan with nine pieces what two equivalent fractions describe how much she ate?
How many tiles would be used to make figure five
A long distance phone company charges a flat rate of $1.01 and then $0.09 for each minute. If
a call cost $9.56, how long did it last?
Answer:
30
Step-by-step explanation:
Answer:
95 minutes
Step-by-step explanation:
Deduct the flat rate from the total to see how much was spent on minutes
9.56 - 1.01 = 8.55
to get minutes divide that by the cost per minute
8.55/0.09 = 95
95 minutes