Using the binomial distribution, it is found that the probabilities are:
P(X = 4) = 0.1268.P(X = 2) = 0.2835.[tex]P(X \leq 3) = 0.9841[/tex]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.Exercise 1:
The parameters are:
n = 15, p = 0.4, x = 4.
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{15,4}.(0.4)^{4}.(0.6)^{11} = 0.1228[/tex]
Exercise 2:
The parameters are:
n = 12, p = 0.2, x = 2.
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{12,2}.(0.2)^{2}.(0.8)^{10} = 0.2835[/tex]
Exercise 3:
The parameters are:
n = 20, p = 0.05.
The probability is:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
Using the binomial formula for each value and adding them:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3585 + 0.3774 + 0.1887 + 0.0596 = 0.9841[/tex]
More can be learned about the binomial distribution at https://brainly.com/question/24863377
#SPJ1
Find the sine and the cosine of 30°.
A. sin 30° =1/2, cos 30°= √3
B. sin 30°=1/2, cos 30° = √3/2
C. sin 30° = √3/3, cos 30°= √3/4
D. sin 30° = √3/3, cos 30° = √3/2
Answer:
Option B is correct.
Step-by-step explanation:
Trigonometry is defined as the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles. There are three basic trigonometric ratios: sine, cosine, and tangent. Trigonometry and its functions have an enormous number of uses in our daily life. For instance, it is used in geography to measure the distance between landmarks, in astronomy to measure the distance of nearby stars and also in the satellite navigation system.
The trigonometric function of sine for an acute angle is the ratio between the leg opposite the angle when it is considered part of a right triangle and the hypotenuse while the cosine is the ratio of the base and the hypotenuse.
Here, [tex]sin 30[/tex]° [tex]=\frac{4}{8}[/tex]
[tex]sin 30[/tex]° [tex]=\frac{1}{2}[/tex]
[tex]cos 30[/tex]° [tex]=\frac{4\sqrt{3}}{8}[/tex]
[tex]cos30[/tex]°[tex]=\frac{\sqrt{3} }{2}[/tex]
Learn more about trigonometry-https://brainly.com/question/13729598
#SPJ10
Which of the following is a solution to the equation x[tex]x^{2}[/tex]– 6x + 5 = 0?
Answer:
[tex]\huge\boxed{\sf x =5 \ \ \ OR \ \ \ x = 1}[/tex]
Step-by-step explanation:
Given equation:[tex]x^2-6x+5=0[/tex]
Using mid-term break formulaMultiply -5 and -1 gives +5 (side term) and adding them gives -6 (mid term).So, split -6 into -5 and -1[tex]x^2-5x-x+5=0\\\\Take \ common\\\\x(x-5)-1(x-5)=0\\\\Take \ (x-5) \ common\\\\(x-5)(x-1)=0[/tex]
Either,
x - 5 = 0 OR x - 1 = 0
x = 5 OR x = 1[tex]\rule[225]{225}{2}[/tex]
A linear function contains the following points.
What are the slope and y-intercepts of this function?
The slope is -1, and the value of the y-intercept is 6 if the linear function contains the points provided.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The slope is:
[tex]\rm m =\dfrac{6-8}{0-(-2)}[/tex]
m = -1
The equation of a line:
y = mx + c
y = -x + c
Plug x = 0 and y = 6
y = 6
y-intercept is (0, 6)
Thus, the slope is -1, and the value of the y-intercept is 6 if the linear function contains the points provided.
Learn more about the slope here:
brainly.com/question/3605446
#SPJ1
Lines b and care parallel.
1/2
(7x+1)/(18x+4)
5/6
7/8
b
What is the measure of 22?
O m2 = 31°
Om42 = 50°
Om42 = 120°
Om22 130°
Answer:
Option 2angle 2 = 7x + 1 ( vertically opposite angles)
7x + 1 + 18x + 4 = 180° ( forming linear pair).
7x + 18x + 4 +1 = 180°
25x + 5 = 180°
25x = 180 - 5
25x = 175
x = 7°
angle 2 = 7(7)+ 1
= 50°
The measure of angle ∠2 of the parallel lines is ∠2 = 50°
What are angles in parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.
We can conclude three factors determining parallel lines ,
Alternate angles are equal
Corresponding angles are equal
Co-interior angles add up to 180°
Given data ,
Let the parallel lines be b and c
Now , the measure of ∠1 + ∠2 = 180° ( angles on the same line )
And , the measure of ∠2 = ( 7x + 1 )° ( alternate angles are equal )
So , ( 7x + 1 ) + ( 18x + 4 ) = 180° ( angles on the same line )
On simplifying , we get
25x + 5 = 180
25x = 175
x = 7
So , the measure of angle ∠2 = ( 7 ( 7 ) + 1 )
The measure of angle ∠2 = 50°
Hence , the angle is ∠2 = 50°
To learn more about angles in parallel lines click :
https://brainly.com/question/27400033
#SPJ5
Factor
4m^2+16m+16.
Answer:
4(m+2)²
Step-by-step explanation:
Hope this help!!
Josh made $35,000 in taxable income last year.
Suppose the income tax rate is 15% for the first $8500 plus 17% for the amount over $8500.
How much must Josh pay in income tax for last year?
Find f ° g and g ° f, if they exist. f={(-4,-5),(0,3),(1,6)} and g={(-5,0),(3,-4),(6,1)}.
The composite function of f o g are (-4,-5),(0,3),(1,6). The composite function of g o f are (-5,0),(3,-4),(6,1).
What is a function?A function is defined as a relation between the set of inputs having exactly one output each.
Given;
f = {(-4,-5),(0,3),(1,6)}
g = {(-5,0),(3,-4),(6,1)}.
In order to find f o g and g o f,
f o g = f(g)
The composite function of f o g
f(-5,0) = (-4,-5)
f(3,-4) = (0,3)
f(6,1) = (1,6)
The composite function of g o f
g(-4,-5) = (-5,0)
g(0,3) = (3,-4)
g (1,6) = (6,1)
Learn more about function sum;
https://brainly.com/question/14438192
#SPJ1
What is the slope of the following graph? (write your answer as a fraction unless divided by 1. Do not use spaces in your answer)
The slope of the graph is 4/5
How to determine the slopeUsing the formula
Slope = Δ y-axis / Δ x- axis
y2 = -4
y1 = 0
x2 = -5
x1 = 0
Slope = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
Substitute the values into the formula
Slope = [tex]\frac{-4 - 0}{- 5 - 0}[/tex]
Slope = [tex]\frac{-4}{-5}[/tex]
Slope = [tex]\frac{4}{5}[/tex]
Therefore, the slope of the graph is 4/5
Learn more about slope here:
https://brainly.com/question/3493733
#SPJ1
An entertainment company is opening a theme park in a nearby city. They are in the process of designing the theatre where a water show will take place. The following design is already under construction and will house the dolphins that perform in the show:
Main Show Tank Calculation:
The main show tank has a radius of 70 feet and forms a quarter sphere where the bottom of the pool is spherical and the top of the pool is flat. (Imagine cutting a sphere in half vertically and then cutting it in half horizontally.) What is the volume of the quarter-sphere shaped tank? Round your answer to the nearest whole number. You must explain your answer using words, and you must show all work and calculations to receive credit.
Holding Tank Calculations:
The holding tanks are congruent. Each is in the shape of a cylinder that has been cut in half vertically. The bottom of each tank is a curved surface and the top of the pool is a flat surface. What is the volume of both tanks if the radius of tank #1 is 35 feet and the height of tank #2 is 120 feet? You must explain your answer using words, and you must show all work and calculations to receive credit.
You must show all steps and provide any evidence needed in your solution to receive full credit.
The company is building a scale model of the theater’s main show tank for an investor's presentation. Each dimension will be made one sixth of the original dimension to accommodate the mock-up in the presentation room. What is the volume of the smaller mock-up tank?
Using the information from above answer the following question by filling in the blank: The volume of the original main show tank is ____% of the mock-up of the tank.
1) The volume of the quarter sphere shaped tank is; V = 20510 ft³
2) The volume of the smaller mock-up tank is; 230790 ft³
How to find the area and volume of a composite shape?1) The volume of the quarter sphere shaped tank is;
V = ⁴/₃πr²
V = ⁴/₃π * 70 * 70
V = 20510 ft³
2) We multiply dimensions by 2 not radius to make 1 whole cylinder. Thus
r = 35 feet remains the same as radius can only be half of a joined circle,
Since vertically cut, we have;
h = 125 * 2 = 250ft
Let's find the Area;
A = πr²
A = π * 35 * 35
A = Surface Area = 3846.5 ft²
Volume = Surface area * h
V = 3846.5 * 120 = 461580 combined.
For each; V = 461580/2 = 230790 ft³
3) Volume of smaller mock-up tank is;
V = (1/6) * 20510
V = 3418.33 ft³
4) 5/6 * 20510 = 17091.66 ft³
For the larger tank the increase is 17092 ft rounded up (0.165 value) of that of the smaller mock up tank. Therefore percentage is 1/6 = 16.67% and 5/6 = 83.33%
Read more about Composite shape area at; https://brainly.com/question/10254615
#SPJ1
The Function h is defined by the following rule.
h(x) = 2x-2
Complete the function table.
Answer:
[tex]\fbox {See below} \downarrow[/tex]
Step-by-step explanation:
[tex]\textsf {The function is :}[/tex]
[tex]\boxed {h(x) = 2x - 2}[/tex]
[tex]\textsf {Finding the missing values :}[/tex]
[tex]\mathsf {h(-4) = 2(-4) - 2 = -10}[/tex][tex]\mathsf {h(-2) = 2(-2) - 2 = -6}[/tex][tex]\mathsf {h(1) = 2(1) - 2 = 0}[/tex][tex]\mathsf {h(4) = 2(4) - 2 = 6}[/tex][tex]\mathsf {h(5) = 2(5) - 2 = 8}[/tex][tex]\textsf {The table :}[/tex]
[tex]\left[\begin{array}{ccc}x&f(x)\\-4&-10\\-2&-6\\1&0\\4&6\\5&8\end{array}\right][/tex]
A family originally bought a home for $654,030. Now, a few years later, the home is worth
$457,821. What was the percent of decrease in its value?
Answer:
30%
Step-by-step explanation:
First we find out the difference between them:
$654,030 - $457,821 = $196,209
Then we compare it with the original price:
196,209/654,030 = 0.3
Since 0.3 is 30%, that is 30% decrease in value.
Please answer! Will give the brainliest!
Answer: K. 3
Step-by-step explanation:
There are 30 students in total. What I did is I added everything that was in the Venn diagram and subtracted that from 30.
[tex]12+5+10=27[/tex]
[tex]30-27=3[/tex]
Therefore, there are 3 students who didn't like either English or math.
I hope this helps! Pls give brainliest!! :)
Big Oil, Inc. has a preferred stock outstanding that pays an $7 annual dividend. If
investors' required rate of return is 10 percent, what is the market value of the shares?
If the required return declines to 6 percent, what is the change in the price of the stock?
The change in the price of the stock is $46.67.
How to calculate the change in price?From the information given, the current price will be:
= Annual dividend / Required rate
= 7/0.1
= $70
The market value of the shares will be:
= 7/6%
= 7/0.06
= $116.67
Therefore, the change in the price of the stock will be:
= $116.67 - $70
= $46.67
Learn more about stock on:
brainly.com/question/18124452
#SPJ1
28.6% of city employees ride the bus to work.Last year,29.7% of city employees rode the bus to work.What is the relative change from last year to this year
The number of employees taking the bus to an office is reduced by 1.1% from the last year. The relative change will be 1.1%.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that:-
28.6% of city employees ride the bus to work. Last year,29.7% of city employees rode the bus to work.
The relative change will be calculated as follows:-
Relative change = Present year data - Last year's data
Relative change = 28.6 - 29.7
Relative change = -1.1%
Therefore the number of employees taking the bus to an office is reduced by 1.1% from the last year. The relative change will be 1.1%.
To know more about Expression follow
https://brainly.com/question/723406
#SPJ1
Mrs. jones has a body fat to body mass of 1:3.She has a body mass of 60kg.
Answer:
20 kg of body fat
Step-by-step explanation:
Multiple both sides of the ratio so that the side with body mass is 60 kg:
body fat : body mass
1 : 3
× 20 × 20
20 kg : 60 kg
Mrs. Jones has 20 kg of body fat.
how to make 27 using 1,2,3,4 only once
Answer:
1) (4 - 2 + 1)^3
2) 3^2(4 - 1)
3) 3^4/2 + 1
It can be either one of those
Answer:
(2 * 4 + 1) * 3 =Step-by-step explanation:
how to make 27 using 1,2,3,4 only once
Remember Pemdas
(2 * 4 + 1) * 3 =
(8 + 1) * 3 =
9 * 3 =
27
The blue dot is what value on the number line -6 -10
Answer:
I have no clue what I could answer that question with other than (-6,-10)
Trigonometry is crazy
Answer:
see the attachment photo!
i hope this can help you! :)
You are betting on a game with an expected value of -$0.33. What does this mean?
In a statistics class with 36 students the professor wanted to know the probability that at least two students share the same birthday. The probability would be
The probability that at least two students share the same birthday is 83.22 %.
Probability of sharing the same birthdayLet P(A) = Probability that no two students share same birthdayLet P(A') = Probability at least two students share same birthday
There are 365 days in year and there 36 students in the class.
Total sample space, n = 365³⁶
36 students will be selected as [tex]365P_{36}[/tex]
[tex]P(A) = \frac{365P_{36}}{365^{36}} = 0.1678[/tex]
Probability at least two students share same birthdayP(A') = 1 - P(A)
P(A') = 1 - 0.1678
P(A') = 0.8322
P(A') = 83.22 %
Learn more about probability here: https://brainly.com/question/24756209
#SPJ1
find the y-component of this vector
leave an explanation for brainlest
The y- component of the vector is 18.31728 m
What is Vector?A quantity that has both magnitude and direction but not position.
The y- component is
Dy = 18.6* sin80
Dy = 18.6* 0.9848
Dy= 18.31728 m
Hence, the y- component of the vector is 18.31728 m.
Learn more about this concept here:
https://brainly.com/question/20532996
#SPJ1
Jeff and Kirk can build a 75-ft retaining wall together in 4 hours. Because Jeff has more experience, he could build the wall by himself 1 hour quicker than Kirk. How long would it take Kirk (to the nearest minute) to build the wall by himself?
Answer:
8 hours 32 minutes
Step-by-step explanation:
Working together, the construction rates add. We can use the given relation to write an equation for the total time when the pair work together.
__
setupLet k represent Kirk's time (in hours) to build the wall by himself. Then (k-1) is the time it takes for Jeff to build it. Their working-together rate in "walls per hour" is ...
1/k +1/(k -1) = 1/4
__
solutionMultiplying by 4k(k-1), we have ...
4(k-1) +4k = k(k -1)
k² -9k = -4 . . . . . . . . subtract 8k and simplify
k² -9k +20.25 = 16.25 . . . . . add (9/2)² to complete the square
k -4.5 = √16.25 . . . . . . . . . take the square root
k = 4.5 +√16.25 ≈ 8.531129 . . . hours
The fractional hour is ...
0.531129 × 60 min ≈ 31.9 min ≈ 32 min
It would take Kirk about 8 hours 32 minutes to build the wall by himself.
_____
Additional comment
For most "working together" problems the rates of completing work need to be expressed in jobs per unit time. Usually, the rates are given in terms of time per job, as they are here. That is why reciprocals get involved.
It will take Kirk about 8 hours 32 minutes to build the wall by himself.
What is Quadratic Polynomial?Quadratic equations are second-degree algebraic expressions and are of the form ax² + bx + c = 0.
Here, Let k represent Kirk's time (in hours) to build the wall by himself. Then (k-1) is the time it takes for Jeff to build it. Their working-together rate in "walls per hour" is ...
1/k +1/(k -1) = 1/4
Multiplying by 4k(k-1), we have ...
4(k-1) +4k = k(k -1)
k² -9k = -4 . . . . . . . . subtract 8k and simplify
k² -9k +20.25 = 16.25 . . . . . add (9/2)² to complete the square
k -4.5 = √16.25 . . . . . . . . . take the square root
k = 4.5 +√16.25 ≈ 8.531129 . . . hours
The fractional hour is ...
0.531129 × 60 min ≈ 31.9 min ≈ 32 min
Thus, It will take Kirk about 8 hours 32 minutes to build the wall by himself.
Learn more about Quadratic Polynomial from:
https://brainly.com/question/2350120
#SPJ1
i need help can someone give me answers
Answer:
Step-by-step explanation:6 type
5/25=1/5=20%
1-1/5=4/5=80%
The types of candles are 6. And the probability of a small pink candle and NOT a small pink candle will be 0.20 and 0.80, respectively
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
The table is given below.
Small Medium Large Total
White 9 3 5 17
Pink 5 2 1 8
Total 14 5 6 25
The types of candles are given as,
⇒ 2 x 3
⇒ 6
The probability of a small pink candle is as,
P = 5/25
P = 0.20
The probability of NOT a small pink candle is as,
Q = 1 - P
Q = 1 - 0.20
Q = 0.80
More about the probability link is given below.
https://brainly.com/question/795909
#SPJ2
The first term of a sequence is 5.
The term-to-term rule is 'add 8'. What is the 10th term of the sequence?
Answer:
[tex]\fbox {77}[/tex]
Step-by-step explanation:
Given
⇒ a = 5
⇒ d = + 8
Solving :
⇒ a₁₀ = a + 9d
⇒ a₁₀ = 5 + 9(8)
⇒ a₁₀ = 5 + 72
⇒ a₁₀ = 77
An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with μ = 15.5 and σ = 3.6. What is the probability that during a given week the airline will lose less than 20 suitcases?
Answer:
[tex] \frac{?}{?} [/tex]
Solve for x: |x − 2| + 10 = 12 (1 point)
Answer:
I think that would be 1
Step-by-step explanation:
Do everything in the lines before anything else. -2 becomes a 2 and then you add that with the 12 and divide 12 on both sides to get one.
Answer:
x = 0 or 4
Step-by-step explanation:
The absolute value function can be resolved into two equations. These one- or two-step equations can be solved in the usual way.
__
negative argument-(x -2) +10 = 12
-x = 0 . . . . . . . . . simplify, subtract 12
x = 0 . . . . . . . . . multiply by -1. Check: 0 -2 is negative.
positive argumentx -2 +10 = 12
x = 4 . . . . . . . . . simplify, subtract 8. Check: 4 -2 is positive.
The two solutions are x=0 and x=4.
Which second degree polynomial function has a leading coefficient of -1 and root 4 with multiplicity 2?
f(x) = -x²-8x-16
f(x) = -x² +8x-16
f(x)=x²-8x + 16
f(x) = -x² + 8x + 16
Mark this and return
Save and Exit
Next
Subm
Answer:abc and d
Step-by-step explanation:
trust me I took the dum test
The following lots of Commodity Z were available for sale during the year. Beginning inventory 9 units at $50 First purchase 16 units at $50 Second purchase 21 units at $59 Third purchase 16 units at $62 The firm uses the periodic system, and there are 23 units of the commodity on hand at the end of the year. What is the ending inventory balance at the end of the year according to the FIFO method?
According to the FIFO method, the ending inventory balance for Commodity Z is $1,405
How much inventory is left under FIFO?FIFO means that earlier inventory is sold first and later inventory would be the last goods left.
Since there were 23 units left, all 16 units from the last purchase and 7 units from the second purchase would be available:
= (16 x 62) + (7 x 59)
= 992 + 413
= $1,405
Find out more on the FIFO method at https://brainly.com/question/11493725.
#SPJ1
In the diagram, point D divides line segment AB in the ratio of 5:3. If line segment AC is vertical and line segment CD is horizontal, what are the coordinates of point C? Diagram shows a line segment with endpoints A(2, minus 6) and B(10, 2). Point D lies on this line segment. A dashed segment extends up from point A until point C and then extends horizontally to right until point D, forming a right triangle. A. (2, -1) B. (2, -3) C. (5, -3) D. (7, -1) Reset Next
The coordinates of point C that forms the triangle is; (2, -1)
How to partition a line segment?We are told that point D divides line segment AB in the ratio of 5:3.
The line segment division formula is;
(x, y) = (m₁x₂ + m₂x₁)/(m₁ + m₂), (m₁y₂ + m₂y₁)/(m₁ + m₂)
For this question;
x₁ = 2; y₁ = -6; x₂ = 10; y₂ = 2; m₁ = 5; m₂ = 3
Thus, (x, y) gives us;
(5*10 + 3*2)/(5 + 3), (5*2 + 3*-6)/(5 + 3)
D(x, y) = (7, -1)
Now, we need to find the coordinates of C
We will use coordinate system which means the coordinate of x will be the as x coordinate of A since, AC is vertical line
And coordinate of y will be same as y in D since CD is horizontal line. Thus, coordinate of C is; C(2,-1).
Read more about Line segment partition at; https://brainly.com/question/17374569
#SPJ1
22x31
a537
b682
c492
Step-by-step explanation:
copy from there that right answer if need more then follow me Bhai or send me money
