Using the binomial distribution, it is found that:
3.1 There is a 0.5033 = 50.33% probability that he makes at most one sale.
3.2 There is a 0.8322 = 83.22% probability that he makes at least one sale.
3.3. There is a 0.4404 = 44.04% probability that he makes two or three sales.
3.4. There is a 0.0011 = 0.11% probability that he makes six sales.
What is the binomial distribution formula?
The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
1 out of 5 of consultations result is a sale, hence p = 1/5 = 0.2.8 consultations are considered, hence n = 8.Item 1:
The probability that he makes at most one sale is:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{8,0}.(0.2)^{0}.(0.8)^{8} = 0.1678[/tex]
[tex]P(X = 1) = C_{8,1}.(0.2)^{1}.(0.8)^{7} = 0.3355[/tex]
Then:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.1678 + 0.3355 = 0.5033[/tex]
There is a 0.5033 = 50.33% probability that he makes at most one sale.
Item 2:
The probability that he makes at least one sale is:
P(X > 1) = 1 - P(X = 0) = 1 - 0.1678 = 0.8322.
There is a 0.8322 = 83.22% probability that he makes at least one sale.
Item 3:
The probability that he makes two or three sales is given by:
[tex]P(2 \leq X \leq 3) = P(X = 2) + P(X = 3)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{8,2}.(0.2)^{2}.(0.8)^{6} = 0.2936[/tex]
[tex]P(X = 3) = C_{8,1}.(0.2)^{3}.(0.8)^{5} = 0.1468[/tex]
Then:
[tex]P(2 \leq X \leq 3) = P(X = 2) + P(X = 3) = 0.2936 + 0.1468 = 0.4404[/tex]
There is a 0.4404 = 44.04% probability that he makes two or three sales.
Item 4:
The probability that he makes six sales is P(X = 6), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 6) = C_{8,6}.(0.2)^{6}.(0.8)^{2} = 0.0011[/tex]
There is a 0.0011 = 0.11% probability that he makes six sales.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
Evaluate arithmetic series:-
Step-by-step answer, please!
Let's see
[tex]\\ \rm\Rrightarrow {\displaystyle{\sum^{275}_{k=1}}}(-5k+12)[/tex]
[tex]\\ \rm\Rrightarrow (-5(1)+12)+(-5(2)+12)\dots (-5(275)+12)[/tex]
[tex]\\ \rm\Rrightarrow 7+5+3+2+1+\dots -1363[/tex]
So
a=7l=-1363n=275Sum:-
[tex]\\ \rm\Rrightarrow S_n=\dfrac{n}{2}[a+l][/tex]
[tex]\\ \rm\Rrightarrow \dfrac{275}{2}(7-1363)[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{275}{2}(-1356)[/tex]
[tex]\\ \rm\Rrightarrow 275(-678)[/tex]
[tex]\\ \rm\Rrightarrow -186450[/tex]
Answer:
-186,450
Step-by-step explanation:
Sum of arithmetic series formula
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
where:
a is the first termd is the common difference between the termsn is the total number of terms in the sequence[tex]\displaystyle \sum\limits_{k=1}^{275} (-5k+12)[/tex]
To find the first term, substitute [tex]k = 1[/tex] into [tex](-5k+12)[/tex]
[tex]a_1=-5(1)+12=7[/tex]
To find the common difference, find [tex]a_2[/tex] then subtract [tex]a_1[/tex] from [tex]a_2[/tex]:
[tex]a_2=-5(2)+12=2[/tex]
[tex]\begin{aligned}d & =a_2-a_1\\ & =2-7\\ & =-5\end{aligned}[/tex]
Given:
[tex]a=7[/tex][tex]d=-5[/tex][tex]n=275[/tex][tex]\begin{aligned}S_{275} & = \dfrac{275}{2}[2(7)+(275-1)(-5)]\\& = \dfrac{275}{2}[14-1370]\\& = \dfrac{275}{2}[-1356]\\& = -186450\end{aligned}[/tex]
Latoya used 4 gallons of ginger ale, 1 gallon of orange juice, and 1 gallon of pineapple juice to make punch for her brother's birthday party.
How many cups of punch will Latoya have for her brother's birthday party?
Answer: 96 cups
Step-by-step explanation: A gallon holds 128 ounces there were 6 gallons used to make the punch. 128x6= 768 ounces
A cup holds 8 ounces so you would do 768/8 and that would give you 96 cups
Write a recursive formula for a n a n , the n th n th term of the sequence 6 , − 12 , 24 , . . .
Answer:
See below ↓↓
Step-by-step explanation:
a₁ refers to the first term of the sequence.
That is clearly : a₁ = 6
The formula for the nth term is :
aₙ = a₁rⁿ⁻¹Common ratio (r) = quotient of consecutive termsr = -12/6 = -2Therefore, the nth term is :
aₙ = 6(-2)ⁿ⁻¹There are letter tiles in a bag. Four A’s, five B’s, six C’s and five D’s. You select one tile, replace it, and then draw another.
P( A and A)=______
A. 2/5
B. 1/25
C. 4/20
D. 1/20
Answer:
[B] 1/25
Step-by-step explanation:
From the given:
There are letter tiles in a bag. Four A’s, five B’s, six C’s and five D’s. You select one tile, replace it, and then draw another.
To Find:
P( A and A)=______
Solution:
Since it given that:
Four A’s, five B’s, six C’s and five D’s.
Thus we have:
A,A,A,A,B,B,B,B,B,C,C,C,C,C,C,D,D,D,D,D
Total number of letters tiles = 20
Probability of selecting A = 4/20 = 1/5
Probability of selecting A = 4/20 = 1/5
P( A and A)= 1/5 × 1/5 = 1/25
Thus, the answer is [B] 1/25
Kavinsky
The surface area of a cylinder is 432 pi yd2. The height of the cylinder is five times the radius. What is the diameter of the cylinder?
Since the surface area of this cylinder is [tex]432\pi \;yd^2[/tex], its diameter is equal to 12 yards.
How to calculate surface area.Mathematically, the surface area (SA) of a cylinder is given by this formula:
[tex]S.A = 2\pi rh + 2\pi r^2[/tex]
Where:
h is the height.r is the radius.Given the following data:
Surface area of cylinder = [tex]432\pi \;yd^2[/tex]Height = 5r.Substituting the given parameters into the formula, we have;
[tex]432\pi = 2\pi r(5r) + 2\pi r^2\\\\432\pi = 2\pi 5r^2 + 2\pi r^2\\\\216=5r^2+r^2\\\\216=6r^2\\\\r^2=36\\\\r=\sqrt{36}[/tex]
r = 6 yards.
For the diameter:
Diamter = 2 x radius
Diamter = 2 x 6
Diameter = 12 yards.
Read more on surface area here: brainly.com/question/21367171
What is the exact value of tan 150
Answer:
-0.5774
Step-by-step explanation:
Tan 150 degrees is the value of tangent trigonometric function for an angle equal to 150 degrees. The value of tan 150° is -1/√3 or -0.5774 (approx).
Find the surface area of this figure.
Step-by-step explanation:
6x3 (3 is because it's half of 6) =18 to find the area of I triangle, I now divide it by 2. 18÷2=9. there are 8 separate triangles so 9x8=72. now the square. 6x6=36. now add 72 + 36=108 in.
The points scored by a basketball team in its last 6 games
are shown. Use these data for 7 and 8.
Which measure better describes the typical number of points scored?
Explain.
(Points scored= 73,77,85,84,37,115)
Answer:
73+78+85+84+37+115 because you will add all point scored by the last 6games =471
Which function is graphed below?
Answer:
The function y =f (x) is graphed below. Plot a line segment connecting the points on f where x = -9 and x = -3. Use the line segment to determine the average rate of change of the function f (x) on the interval -9 <x <-3?
Step-by-step explanation:
I am not sure where or what you are talking about?
add then round???????????????????
Answer:
400,000
Numbers given:
479,369113,572After rounding them to nearest hundredth thousand:
500,000100,000Difference:
500,000 - 100,000400,000Find the surface area of a cylinder with radius 2 yards and height 6 yards.
Give me the answer
Find the value of x.
I’m desperate for help
Answer:
the answer is 24 since 24 x 5 = 120
Step-by-step explanation:
Hope this helps you!
help me with this question also
[tex]\text{Given that,}\\\\[/tex]
[tex]~~~~~~~\cos \theta = \dfrac 89\\\\\\\implies 2\cos^2 \left(\dfrac{\theta}2 \right) -1 = \dfrac 89~~~~~~;\left[1+ \cos 2\theta = 2\cos^2 \theta \right]\\\\\\\implies 2 \cos^2 \left(\dfrac{\theta}2 \right)= \dfrac 89 +1\\\\\\\implies 2 \cos^2 \left(\dfrac{\theta}2 \right)=\dfrac{17}9\\\\\\\implies \cos^2 \left(\dfrac{\theta}2 \right) = \dfrac{17}{18}\\\\\\\implies \cos \left(\dfrac{\theta}2 \right)=\sqrt{\dfrac{17}{18}}~~~~~~~~~~~;\left[\text{Positive value of} ~\cos \left(\dfrac{\theta}2\right) \right][/tex]
[tex]\implies \cos \left(\dfrac{\theta} 2 \right) =\dfrac{\sqrt{17}}{\sqrt{9 \times 2}}\\\\\\\implies \cos \left(\dfrac{\theta} 2 \right)=\dfrac{\sqrt{17}}{3\sqrt 2}\\\\\\\implies \cos \left(\dfrac{\theta} 2 \right)=\dfrac{\sqrt{17} \cdot \sqrt 2}{3\cdot 2}\\\\\\\implies \cos \left(\dfrac{\theta} 2 \right)=\dfrac{\sqrt{34}}{6 }[/tex]
NEED HELP ASAP!! 5TH GRADE MATH, WILL GIVE BRAINLIEST!!!
Answer:
14,880: So yes, it will be greater than 12400.
Step-by-step explanation:
Because you can simplify the fraction from 1 1/5 to 6/5, and 6/5 is equal to 1.2, simply multiply 12400 by 1.2, which would get you 14800. In other words, if it was multiplying by a number less than 1.2, then it would be less than 12400.
Hope this helps!
What is the location of point G, which partitions the directed line segment from F to D into an 8:5 ratio?
A number line goes from negative 5 to 10. Point D is at negative 4 and point F is at 9. A line is drawn from point D to point F.
1
2
3
4
Answer:
A) 1
Step-by-step explanation:
We want to find G such that ...
(G-F)/(D-G) = 8/5
5(G-F) = 8(D-G)
5G -5F = 8D-8G . . . . eliminate parentheses
13G = 8D +5F . . . . . . add 5F +8G to both sides
G = (8D +5F)/13 . . . . divide by the coefficient of G
G = (8(-4) +5(9))/13 = (-32 +45)/13 = 13/13
G = 1 . . . . . . matches choice A
Answer:
A
Step-by-step explanation:
EDGE 22
Tim drew a triangle with one angle of measure 40 degrees and the other 70 degrees. Which triangle did Tim draw?
Answer:
Isocoles (I can't spell)
Step-by-step explanation:
180-70=110. 110-40=70.
Two angles are 70
Time drew the isosceles triangle because the two angles are equal.
Given that,
Tim drew a triangle with one angle of measure 40 degrees and the other 70 degrees. which triangle Tim drew is to be determined.
A triangle with two sides and two congruent angles is called an isosceles triangle.
Here,
Let one of the angles be x
Sum of angles = 180
40 + 70 + x = 180
x = 70
As two of the angle become equal the triangle becomes an isosceles triangle.
Thus, Time drew the isosceles triangle because the two angles are equal.
Learn more about the isosceles triangle here: https://brainly.com/question/2456591
#SPJ2
what is the mode of the data set 29,22,19,20,29,23,29,19,31
Answer:
Mean (Average): 21.44444
Median (Middle): 22
Mode (Most Common): 29
Step-by-step explanation:
the area of a square is 32 cm. find the length of the diagonal
Answer:
8 cm
Step-by-step explanation:
Squares have equal side lengths so if we call each side x, then x × x gives us the area (32 cm²). This means that x² = 32 and therefore, one side is √32 cm.
Next, to work out the diagonal we can use Pythagoras' theory, since we can form a right-angled triangle. a² + b² = c² (c is the diagonal or the hypotenuse)
(√32)² + (√32)² = c²
(note: the square and the square root cancel out)
32 + 32 = 64
c² = 64 ∴ c = √64 which is 8
Hope this helps!
Answer:
The length of the diagonal is 8 cm.
Step-by-step explanation:
The side length of the square is √32 cms.
The diagonal divide the square into 2 congruent right triangles.
We use Pythagoras Theorem here:
d^2 = (√32)^2 + (√32)^2
d^2 = 32 + 32 = 64
d = √64 = 8.
Question 3 options: lily is building a picture frame. the larger rectangle represents the frame. the smaller rectangle represents the picture. the shaded area represents the 2-inch border around the picture. what is the area of the border, or the shaded region, of this figure in square inches?
The area of the shaded region of this figure which can be calculated by the difference of the larger region from the smaller region would be 104 in.²
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
Area of a larger rectangle
= Length × Width
= 18 × 12
= 216 in.²
Area of the smaller rectangle
Length = 12 - 2 - 2 = 8 in.
Width = 18 - 2 - 2 = 14 in.
= Length × Width
= 8 × 14
= 112 in.²
Area of the shaded region = Area of a larger rectangle - Area of the smaller rectangle
= 216 - 112
= 104 in.²
Hence, the area of the shaded region of this figure is 104 in.²
Learn more about the area;
https://brainly.com/question/2289492
1. Find the lateral area and surface area of the given prism. Round your
answer to the nearest whole number
Answer:
LA = 720 , SA = 780
Step-by-step explanation:
find the missing length of the triangle using Pythagoras then use this value (8) to find the surface area of the sides and the triangle.Add up the values.
Answer:
Step-by-step explanation:
To find the lateral surface area of triangular prism, first we need to know the three sides of the triangle. Here, one side is missing and we have to find that using Pythagorean theorem. Let the unknow side of the triangle be 'c'
Pythagorean theorem,
15² + c² = 17²
225 + c² = 289
c² = 289 - 225
c² = 64 = 8*8
c = 8 in
a = 17 in & b = 15 in & h = 18 in
[tex]\boxed { \text{Lateral surface area = (a + b + c)*h }}[/tex]
= ( 17 + 15 + 8 ) * 18
= 40 * 18
= 720 in²
[tex]\boxed { \text{total surface area = LSA + 2* area of base triangles}}[/tex]
[tex]\text{ area of base triangles = 2* $ \dfrac{1}{2}*base*height $}[/tex]
= base * height
= 8 * 15
= 120 in²
Total surface area = 720 + 120
= 840 in²
Solve for x. Leave your answer in simplest radical form.
SOMEONE PLEASE HELP ME ILL GIVE YOU BRAINLIST ANSWER
Step-by-step explanation:
REFER TO THE ATTACHMENT!!
can we friends
An archer shoots an arrow up towards a target located on a hill, which is shown by the graph.
A graph of a line and a parabola intersecting at (46.5, 9.3).
Which set of equations best models the point of intersection of the arrow and the target?
y = 0.006x2 + 0.35x + 6 and y = x
y = –0.006x2 + 0.35x + 6 and y = –x
y = 0.006x2 + 0.35x + 6 and y = 0.2x
y = –0.006x2 + 0.35x + 6 and y = 0.2x
As no graph is shown some basic information of parabola can be helpful
As it's. a hill hence the parabola facing downwardsa is negativeAnd a coordinate is given check it whether it is equal to second part of options
(46.5,9.3)We get
y≠xy≠-xy=0.2xLast two are radar now
As a must be negative option D has such similarities.
Option D is correct (Assumption)Answer:
[tex]\sf y = -0.006x^2 + 0.35x + 6\quad and\quad y = 0.2x[/tex]
Step-by-step explanation:
As the archer shoots the arrow up, the trajectory of the arrow can be modeled as a parabola that opens downwards. Therefore, this is a quadratic equation with a negative leading coefficient.
From inspection of the answer options, the path of the arrow is :
[tex]y=-0.006x^2+0.35x+6[/tex]
This means the options for the line equation are [tex]y=-x[/tex] and [tex]y=0.2x[/tex]
We are told that the point of intersection of the line and the parabola is at (46.5, 9.3). As both the x-value and y-value are positive, the equation of the line must be [tex]y=0.2x[/tex]
To confirm, substitute [tex]x=46.5[/tex] into the equation:
[tex]\implies y=0.2(46.5)=9.3[/tex]
I need help rn.................
Answer:
Alex has £44
Pierre has £66
Step-by-step explanation:
P = A + 20
P+ 22 = 2A
solve for A
plug in p
(A + 20) + 22 = 2A
A + 44 = 2A
subtract A from both sides
44 = A
solve for P
plug A in
P = 44 +22
P = 66
Pls give brainlyist
what is an equation of the line that passes through the points (3,0) and (-6,-3)
Step-by-step explanation:
given ponts,
(3,0)=(x1,y1)
(-6,-3)=(x2,y2)
we know,
Eqn of any line joining two points be,
(y-y1)={(y2-y1)/(x2-x1)}*(x-x1)
y-0={(-3-0)/(-6-3)}*(x-3)
y=(1/3)*(x-3)
y=(x-3)/3
3y=x-3
0=x-3y-3
x-3y-3=0
Therefore it is required eqn
Can someone help???????
Answer:
8x-3y-24
Step-by-step explanation:
[tex] \frac{3}{4} y = 2x - 6 \\ \\ \\ 3y = 4(2x - 6) \\ \\ 3y = 8x - 24 \\ \\ 8x - 3y - 24 = 0 \\ \\ \\ is \: the \: required \: equation[/tex]
anyone know the awnser to this?
Answer:
61
Step-by-step explanation:
straight line = 180 degree
to find the measure of angle QPR,
subtract 119 from 180
=> 180-119
=> 61
angle QPR = 61 degree
Answer:
Hope the picture will help you!!
NEED HELP ASAPPP !!!
Answer:
I believe D is the correct answer
I'LL GIVE BRAINLIEST AND 100 POINTS| Which answer choice correctly completes the sentence? When solving a story problem, the first step is to
A. guess the correct answer and then check to see if you are correct.
B. write the facts, organize your thoughts and then define your strategy.
C. identify what you need to do to solve the problem.
D. read the problem carefully and find the question.
Answer:
D read the problem carefully and find the question. :)
Have an amazing day!!
Please rate and mark brainliest!!
option C and D (C is actually)
So steps are
First read the story problem completelyThen find out what do you need to solve and what else you have givenThen solve that outThe sum of consecutive positive integers is 93.find number
Answer:
46 and 47.
Step-by-step explanation:
Let the 1st number be x,
Now,
or, x + x = 92
or, 2x = 92
or, x = 46
Again,
Let the 2nd number be x + 1
And,
x + 1 = 46 + 1 = 47.
Please help me and please no links or bot me cuz i really need help
Answer:
hope this helps
Step-by-step explanation:
1) x =3 - S
2) x = 1 - O
3) x = 5 - L
4) x =. I don't understand this one. its 1/2 * 21? = V?
5) x = 10 - E