Answer:
a) Probability of getting exactly 7 hits = 0.001075
b) Probability of getting fewer than seven = 0.999
c) Probability of getting at least seven hits = 0.001
Step-by-step explanation:
The process is a Poisson process.
Rate, [tex]\lambda = 0.4[/tex]
The probability is to be calculated between 8:27 PM and 8:31 PM
t = 4
[tex]\lambda t = 0.4 * 4 = 1.6[/tex]
If the number of hits is represented by X
[tex]P(X = x) = \frac{e^{- \lambda t} (\lambda t)^x}{x!}[/tex]
a) Probability of getting exactly 7 hits
[tex]P(X = x) = \frac{e^{- 1.6} (1.6)^7}{7!}\\P(X= 7) = 0.001075[/tex]
b) Probability of getting fewer than seven
[tex]P(X < 7) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6)\\P(X < 7) = e^{- 1.6} [ \frac{1.6^0}{0!} + \frac{1.6^1}{1!} + \frac{1.6^2}{2!} + \frac{1.6^3}{3!} + \frac{1.6^4}{4!} + \frac{1.6^5}{5!} + \frac{1.6^6}{6!} ][/tex]
P(X < 7) = 0.999
c) Probability of getting at least seven hits
[tex]P(X \geq 7) = 1 - P(x < 7)\\P(X \geq 7) = 1 - 0.999\\P(X \geq 7) = 0.001[/tex]
Using the Poisson distribution, it is found that:
a) 0.0011 = 0.11% probability of exactly 7 hits in a 4 minute interval, which means that over many 4 minute intervals between 7 and 10 PM, 0.11% of them will have exactly 7 hits.
b) 0.9985 = 99.85% probability of fewer than seven hits in a 4 minute interval, which means that over many 4 minute intervals between 7 and 10 PM, 99.95% of them will have fewer than 7 hits.
c) 0.0015 = 0.15% probability of at least seven hits in a 4 minute interval, which means that over many 4 minute intervals between 7 and 10 PM, 0.15% of them will have at least 7 hits.
In a Poisson distribution, the probability is:
[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.In this problem, we have a mean of 0.4 hits per minute, interval of 4 minutes, thus:
[tex]\mu = 0.4(4) = 1.6[/tex]
The probabilities we are going to use are:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-1.6}1.6^{0}}{(0)!} = 0.2019[/tex]
[tex]P(X = 1) = \frac{e^{-1.6}1.6^{1}}{(1)!} = 0.3230[/tex]
[tex]P(X = 2) = \frac{e^{-1.6}1.6^{2}}{(2)!} = 0.2584[/tex]
[tex]P(X = 3) = \frac{e^{-1.6}1.6^{3}}{(3)!} = 0.1378[/tex]
[tex]P(X = 4) = \frac{e^{-1.6}1.6^{4}}{(4)!} = 0.0551[/tex]
[tex]P(X = 5) = \frac{e^{-1.6}1.6^{5}}{(5)!} = 0.0176[/tex]
[tex]P(X = 6) = \frac{e^{-1.6}1.6^{6}}{(6)!} = 0.0047[/tex]
[tex]P(X = 7) = \frac{e^{-1.6}1.6^{7}}{(7)!} = 0.0011[/tex]
Item a:
P(X = 7) = 0.0011, thus:
0.0011 = 0.11% probability of exactly 7 hits in a 4 minute interval, which means that over many 4 minute intervals between 7 and 10 PM, 0.11% of them will have exactly 7 hits.
Item b:
This probability is:
[tex]P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)[/tex]
Then, with the values we found:
[tex]P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.2019 + 0.3230 + 0.2584 + 0.1378 + 0.0551 + 0.0176 + 0.0047 = 0.9985[/tex]
0.9985 = 99.85% probability of fewer than seven hits in a 4 minute interval, which means that over many 4 minute intervals between 7 and 10 PM, 99.95% of them will have fewer than 7 hits.
Item c:
This probability is:
[tex]P(X \geq 7) = 1 - P(X < 7) = 1 - 0.9985 = 0.0015[/tex]
0.0015 = 0.15% probability of at least seven hits in a 4 minute interval, which means that over many 4 minute intervals between 7 and 10 PM, 0.15% of them will have at least 7 hits.
A similar problem is given at https://brainly.com/question/24098004
Find the inverse of g(x) = 3x^2 - 5
Answer:
[tex]\boxed{\sf \ \ \ g^{-1}(x)=\sqrt{\dfrac{x+5}{3}} \ \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex]x=(gog^{-1})(x)=g(g^{-1}(x))=3(g^{-1}(x))^2-5\\\\<=>3(g^{-1}(x))^2 = x+5\\\\\\<=> (g^{-1}(x))^2=\dfrac{x+5}{3}\\<=>g^{-1}(x)=\sqrt{\dfrac{x+5}{3}}[/tex]
hope this helps
The inverse of function is x= √1/3( y+5 )
what is Inverse of function?A function that reverses the effects of another function is called an inverse function. When y=f(x) and x=g(y), a function g is the inverse of a function f. . Applying f and then g is equivalent to doing nothing, in other words. This can be expressed as g(f(x))=x in terms of the relationship between f and g.
Given:
g(x) = 3x² - 5
To find the inverse of the function take g(x) = y
Then, solve for x
y= 3x² - 5
y + 5= 3x²
x² = 1/3( y+5 )
x= √1/3( y+5 )
Hence, the inverse of function is x= √1/3( y+5 ).
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Solve for r: C = 2 pi r. (1
Answer:
C/2pi = r
Step-by-step explanation:
C = 2 pi r
divide with 2 pi on both sides to solve for r
C/2pi = r
please help will give brainliest
Answer:
√24Option C is the correct option.
Please see the attached picture for full solution.
Hope it helps ...
Good luck on your assignment...
A bank offers a 1% annual interest rate for a savings account. Aaron puts $3,100
into an account to save for college. How much will be in the account after a year?
Answer:
$3,131
Step-by-step explanation:
1% of 3,100 is 31. 3,100 + 31 = 3,131.
Can someone help please 3x-y=13 A. (6,5) B.(3,-4) C. (6,5) and (3,-4) D. neither
Answer:
C. (6, 5) and (3, -4)
Step-by-step explanation:
Given the equation 3x - y = 13, we need to figure out which points satisfy it. In order for an ordered pair to satisfy an equation, when we plug the x-coordinate in for x and the y-coordinate in for y, the equation should hold true.
Let's try with (6, 5):
3x - y = 13
3 * 6 - 5 =? 13
18 - 5 =? 13
13 = 13
Since this is true, we know that (6, 5) is indeed a solution.
Now let's try with (3, -4):
3x - y = 13
3 * (3) - (-4) =? 13
9 + 4 =?13
13 = 13
Again, since this is true, then (3, -4) must be a solution.
Thus, the answer is C.
~ an aesthetics lover
Answer: c
Step-by-step explanation:
lol
Round to the nearest tenth
10x^2+5x-15=-12+8x^2
Answer:
x = - 3, x = 0.5
Step-by-step explanation:
Given
10x² + 5x - 15 = - 12 + 8x² ( subtract 8x² from both sides )
2x² + 5x - 15 = - 12 ( add 12 to both sides )
2x² + 5x - 3 = 0 ← in standard form
(x + 3)(2x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
2x - 1 = 0 ⇒ 2x = 1 ⇒ x = 0.5
Study the following figure, where two concentric circles share center C.
Segment AB is a diameter of the larger circle.
Segment AB intersects a chord of the smaller circle, PQ, at a right angle at point Z.
Segment AB intersects a chord of the larger circle, MN, at a right angle at point 0.
If MO=7x-4, and NO=6x, what is the length of MN
Answer:
Length of MN = 48 units
Step-by-step explanation:
AB is the diameter of the larger circle which is perpendicular to both the chords PQ (chord of the smaller circle) and MN(chord of the larger circle).
Theorem says,
"Radius or a diameter of a circle which is perpendicular to the chord divides the chord in two equal parts."
Therefore, MO ≅ ON
m(MO) = m(ON)
7x - 4 = 6x
7x - 6x = 4
x = 4
m(MN) = m(MO) + m(ON)
= (7x - 4) + (6x)
= 13x - 4
= (13 × 4) - 4
= 52 - 4
= 48
Length of chord MN will be 48 units.
Answer the question in the pic...
Answer:
L''(3,2), M''(0,2), N''(0,-2), O''(3,-2)
Step-by-step explanation:
The points that you start off with are L(-4,6), M(-1,6), N(-1,2), and O(-4,2), and when you reflect the rectangle across the y-axis, you will have (4,6), (1,6), (1,2), and (4,2). Now you can translate your rectangle down four and once to the left, which will give you L''(3,2), M''(0,2), N''(0,-2), O''(3,-2).
Which of the following statements could be used in the proof?
Answer:
Option (3)
Step-by-step explanation:
To prove ΔULV ≅ ΔKLY,
Statements Reasons
1). VL ≅ LY 1). Radii of a circle are equal
2). UL ≅ KL 2). Radii of a circle are equal
3). ∠ULV ≅ ∠KLY 3). Vertical angles are equal
4). ΔULV ≅ ΔKLY 4). SAS property of congruence
Therefore, property (3) given in the options will be used to prove the triangles congruent.
Can u plz help me with this question
Answer:
300 - 5t means that Ann pays $300 - 5 times the number of guests she brings to the gym.
when t = 5, it equals $275
when t = 10, it equals $250
when t = 15, it equals $225
when t = 20, it equals $200
Step-by-step explanation:
I WILL MARK BRAINLIEST IF YOU ARE RIGHT please help me ive been stuck on this ever since monday haha im not sure how to do it thanks!
I'll remember some concepts:
[tex]\log_{a}{b} = \log_{a}{c} \implies b=c\\\\\log_{a}{b}+ \log_{a}{c} = \log_{a}{b\cdot c}[/tex]
Question:
[tex]\log_{6}{(x^2-5x)}=\log_{6}{(2x-9)}+\log_{6}({x+3)}\\\\\\\log_{6}{(x^2-5x)}=\log_{6}{(2x-9)\cdot(x+3)}\\\\\\(x^2-5x) = (2x-9)\cdot(x+3)\\\\\\x^2-5x=2x^2+6x-9x-27\\\\\\0 = x^2+2x-27\\\\\\\Delta = 4+108 = 112\\\\\\\\\sqrt{\Delta} = \sqrt{112} = 4\sqrt{7}\\\\\\\\x = \dfrac{-2\pm 4\sqrt{7}}{2}\\\\\\\\x = -1 \pm 2\sqrt{7} \\\\\\\\x_1 = 2\sqrt{7} -1\\\\\\x_2 = -1-2\sqrt{7}[/tex]
The negative solution cant exist since we are talking about logarithms.
HELP ASAP Angle FGH is a central angle, what is the measure of FH A. 54° B. 108° C. 145° D. 216°
Answer:
A
Step-by-step explanation:
We can calculate this using circle theorems
The correct circle theorem to use here is that angle at center is 2 times angle at circumference
The angle we want to calculate here is the angle at circumference but we were given the angle at the center
So the value of the angle at the circumference would be 108/2 = 54
If a point is inside ZAVB, then m AVC + ___- MZAVB.
Answer:
BV
Step-by-step explanation:
i think is the missing gap
1 point
5) Malia earns $3,567 each month. She spends $2,895 each month and
saves the rest of her money. Select the equation that represents how much
is left over that she is able to save each month.
$3,567 - $2,895 = $6,462
$3,567 + $2,895 = $6,462
0 $3,567 - $2,895 = $672
O $3,567 + $2,895 = $672
1 point
roconts equivalent fractions? *
Answer:
C
Step-by-step explanation:
She earns $3,567 and spends $2,895. That means that $2,895 is taken away from how much she earns each month. Subtraction is the correct operation, cancelling out choices B and D
$3,567 - $2,895
Now, you need to figure out the answer to the above problem. Choice C is your answer.
$3,567 - $2,895 = $672
Marla is making 2 liters of cherry lemonade, 5 deciliter dog limeade and 2,500 milliliters strawberry lemonade for a party after the party was over she still a total of 1.3 liters of lemonade left. How many liters of lemonade were consumed during the party?
→Answer:
3.2 liters of lemonade were consumed during the party.
→Step-by-step explanation:
What we know
_____________________________________
Well there is 2,500 mL of strawberry lemonade
There are 2 liters of cherry
There are 5 deciliters of dog limeade
_____________________________________
So the 5 deciliters of dog limeade doesn't count because it is limeade, not lemonade.
The question is asking for the number of liters so we need to convert the 2,500 milliliters of lemonade to liters.
Which will be 2.5 liters of lemonade.
There are also 2 liters of cherry lemonade so 2.5 + 2 is 4.5.
So if 1.3 liters were left over doing 4.5 - 1.3 we get 3.2, meaning 3.2 liters of lemonade were consumed during the party.
An intelligent trader travels from 1 place to another carrying 3 sacks having
30 coconuts each. No sack can hold more than 30 coconuts. On the way
he passes through 30 checkpoints and on each checkpoint he has to give 1
coconut for each sack he is carrying. How many coconuts are left in the
end? *
Answer:
none
Step-by-step explanation:
the man is carrying 3 sacks
each has 30 coconuts
so at total he has 90 coconuts: 30*3= 90
he passe through 30 checkpoints
ha has to give 1 coconut for each sack
so he gives 3 coconuts each time: 3*1=3
there are 30 ckeckpoints so : 3*30= 90
he has spent all the coconuts unless he has a trick
He starts with 3 sacks with 30 in each sack.
He has to give 1 coconut per sack away. So at first he gives 3 coconuts away.
The first 10 checkpoints he gives away 30 coconuts, so he is left with 2 sacks.
Now he has to give 2 coconuts away. 30/2 = 15, so the next 15 checkpoints he ends up giving away another full sack, so he is left with 1 full sack of 30 coconuts and he has 5 checkpoints left.
Giving away 1 coconut at those checkpoints, he would have 25 left
Provide Two Column proof
Given: ABCD is a quadrilateral, Segment AB is congruent to Segment CD, <1 is congruent to <2
Prove: ABCD is a parallelogram
Answer and Step-by-step explanation:
When angle 1 is contrary to angle 2 the adjacent sides are parallel or identical instead. The diagonal from 1 is completely consistent with the other 2nd angle by different outward.
ASA produces two strong or contrugent triangles on the diagonal if both angle 1 and 2 are opposing one another.
Therefore ABCD is a parallelogram
if a savings account is opened with an initial deposit of $250, and interest is compounded monthly at 6.25% for 50 years, how much will the account be worth at the end of the 50-year period?
Answer:
$-9125
Step-by-step explanation:
6.25÷100 = 0.0625 50×12=600
0.0625×250= $15.625
6.25%=$15.625
15.625×600= $9375
$250-$9375= -9125
The account be worth at the end of the 50-year period will be 9125 dollar.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that savings account is opened with an initial deposit of $250, and interest is compounded monthly at 6.25% for 50 years.
The rate is 6.25÷100 = 0.0625
Therefore, 50×12=600
0.0625×250= $15.625
Since we know that 6.25%=$15.625
15.625×600= $9375
Thus we get;
$250-$9375 = -9125
Hence, the account be worth at the end of the 50-year period will be 9125 dollar.
Learn more about the unitary method, please visit the link given below;
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the original price P of a shirt less $5 discount
Answer:
P - 5
Step-by-step explanation:
hello
original price is P
$5 discount means that the final price is P - 5
hope this helps
Answer:
p-5
Step-by-step explanation:
the mass of the earth is 1/95 of the mass of the planet Saturn. the mass of the earth is 5.97×10^24 kilograms. calculate the mass of the planet Saturn, giving your answer in standard form, correct to 2 significant figures
Answer:
5.8 * 10^26 kg
Step-by-step explanation:
If the mass of the earth is 1/95 of that if saturn, this means that the mass of saturn is 95 times that of earth
From the question we were given the mass of the earth as 5.97 * 10^24
The mass of saturn is thus 95 * 5.97 * 10^24 =
576.15 * 10^24
This is 5.8 * 10^26 kg
If the denominator of 5/7 is increased by a number and the numerator is doubled, the result is 1. Find the number.
Answer:
3
Step-by-step explanation:
let n be the number, then
[tex]\frac{10}{7+n}[/tex] = 1 ← multiply both sides by 7 + n
10 = 7 + n ( subtract 7 from both sides )
3 = n
Simplify the expression -4.6+( -1.4) .on the test , when maureen simplified the expression she got 3.2 .
Answer:
Step-by-step explanation:
-4.6+( -1.4)=
-4.6-1.4=-6 maureen is wrong, because both have the minus , so she should add with the minus symbol.
5/8 of the cats perferred drinking with there tongue but 3/16 wanted a straw if there was 39 cats that gave one of these 2 answers how many were surveyed in total GIVING BRAINLIST IF CORRECT AND THANKS. AND 5 STARS PLEASE HELP
Answer:
208cats
Step-by-step explanation:
⅝=tongue
³/16=straw=39cats
⅝+³/16=13/16
meaning total number of cats is 16/16
If ³/16=39cats
16/16=?
39×16/3
=208cats
An experiment to determine the most effective way to teach safety principles applied four different teaching methods. Some employees were given programmed instruction booklets and worked through the course at their own pace. Other employees attended lectures. A third group watched a television presentation, and a fourth group was divided into small discussion groups. A high of 10 was possible. A sample of five tests was selected from each group. The test grade results were: At the 0.01 level, what is the critical value?5.291.003.241.96
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
An experiment to determine the most effective way to teach safety principles applied four different teaching methods. Some employees were given programmed instruction booklets and worked through the course at their own pace. Other employees attended lectures. A third group watched a television presentation, and a fourth group was divided into small discussion groups. A high of 10 was possible. A sample of five tests was selected from each group. The test grade results were:
Sample Programmed Instructions Lecture TV Group Discussions
1 6 8 7 8
2 7 5 9 5
3 6 8 6 6
4 5 6 8 6
5 6 8 5 5
At the 0.01 level, what is the critical value?
a. 5.29
b. 1.00
c. 3.24
d. 1.96
Answer:
The correct option is (a)
The critical value is 5.29
Step-by-step explanation:
To obtain the critical value, we need to perform a satistical test on the given data.
Since we are given data for four independent teaching methods to determine the most most effective way to teach safety principles, therefore, a one-way analysis of variance (ANOVA) may be used to get the critical value.
ANOVA:
The one-way analysis of variance (ANOVA) may be used to find out whether there is any significant difference between the means of two or more independent categories of data.
ANOVA in Excel:
Step 1:
In the data tab, select data analysis
Step 2:
Select "Anova single factor" from the analysis tools
Step 3:
Select the destination of input data in the "input range"
Step 4:
Select "columns" for the option "Group By"
Step 5:
Tick the option "labels in first row"
Step 6:
Set alpha = 0.01
Step 7:
Select the destination of output data in the "output options"
Output results:
Please refer to the attached results
As you can see in the output results, the critical value is 5.2922
Therefore, the correct option is (a)
Find the value of k for x^2 - 2kx+7k -12=0 so that they have two equal roots
Step-by-step explanation:
x^2 -2kx +7k -12 = 0
two equal roots -->Δ = b^2 -4ac = 4k^2 - 4(7k-12)=0 = 4(k^2 - 7k +12)=4(k-4)(k-3)=0
so k =3 and k =4
HELP ME PLEASE AND THANKS :) <3
Answer:
D. Cost
It is cost because the y axis is the dependent variable because the cost depends on the weight and the dependent is the y axis.
Step-by-step explanation:
Please mark brainliest I hope this helps.
Answer:
D the cost
Step-by-step explanation:
cause the costs always go on the y axis
What is the volume of the pyramid? A rectangular pyramid with a base of 8 centimeters by 6 centimeters and a height of 5 centimeters. 10 centimeters cubed 80 meters cubed 120 centimeters cubed 240 centimeters cubed
Answer:
Step-by-step explanation:
8•6= 48•5=240 divided by 3= 80
The volume of the rectangular pyramid is 80 cubic centimeter.
What is volume?
Volume is the measure of the capacity that an object holds.
Formula for the volume of a rectangular pyramid[tex]v = \frac{lwh}{3}[/tex]
Where,
V is the volume of the rectangular pyramid
l is the base length
w is the base width
h is the Pyramid height
According to the given question
We have
Base length of the rectangular pyramid = 8cm
Base width of the rectangular pyramid = 6cm
And the height of the rectangular pyramid = 5cm
Therefore,
The volume of the rectangular pyramid is given by
V = [tex]\frac{(8)(6)(5)}{3}[/tex]
⇒ V = 8 × 2 × 5
⇒ V = 30 cubic centimeter
Hence, the volume of the rectangular pyramid is 80 cubic centimeter.
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Is Lmn=OPQ? If so, name the congruence postulate that applies.
Answer:
Answer D
Step-by-step explanation:
Since 3 sides are congruent to 3 other sides, the two triangles are congruent due to the SSS postulate.
SSS stands for "side side side". It means that if you have three pairs of congruent corresponding sides, then the triangles are congruent. It's like saying every corresponding piece of two houses are the same, so the two houses overall must be identical.
A rectangular plot measures 20 ft. By 30ft. A 3ft wide side walk surrounds it. Find the area of the side walk
Answer:
336 feet²
Step-by-step explanation:
If we have a rectangle that is 30 by 20 feet, that means the area of that rectangle would be 20 × 30 feet squared, which is 600 ft².
If there is a 3 feet sidewalk surrounding it, that means that the end of the sidewalk will extend 3 feet extra around each side of plot. Since there are two ends to one side, that means an extra six feet is added on to each dimension. Therefore, 36 × 26 are the dimensions of the sidewalk+plot. 36 × 26 = 936 ft².
To find the area of the sidewalk itself, we subtract 600 ft² from 936 ft². This gets us with 336 ft².
Hope this helped!
Factorize 3x to second power minus 6x
Answer:
3x( 3x -2)
Step-by-step explanation:
(3x) ^2 - 6x
9x^2 -6x
The greatest common factor is 3x
3x( 3x -2)