Answer:
The probability is [tex]P( X \le 4 ) = 0.0054[/tex]
Step-by-step explanation:
From the question we are told that
The percentage that are on time is p = 0.76
The sample size is n = 11
Generally the percentage that are not on time is
[tex]q = 1- p[/tex]
[tex]q = 1- 0.76[/tex]
[tex]q = 0.24[/tex]
The probability that no more than 4 of them were on time is mathematically represented as
[tex]P( X \le 4 ) = P(1 ) + P(2) + P(3) + P(4)[/tex]
=> [tex]P( X \le 4 ) = \left n } \atop {}} \right.C_1 p^{1} q^{n- 1} + \left n } \atop {}} \right.C_2p^{2} q^{n- 2} + \left n } \atop {}} \right.C_3 p^{3} q^{n- 3} + \left n } \atop {}} \right.C_4 p^{4} q^{n- 4}[/tex]
[tex]P( X \le 4 ) = \left 11 } \atop {}} \right.C_1 p^{1} q^{11- 1} + \left 11 } \atop {}} \right.C_2p^{2} q^{11- 2} + \left 11 } \atop {}} \right.C_3 p^{3} q^{11- 3} + \left 11 } \atop {}} \right.C_4 p^{4} q^{11- 4}[/tex]
[tex]P( X \le 4 ) = \left 11 } \atop {}} \right.C_1 p^{1} q^{10} + \left 11 } \atop {}} \right.C_2p^{2} q^{9} + \left 11 } \atop {}} \right.C_3 p^{3} q^{8} + \left 11 } \atop {}} \right.C_4 p^{4} q^{7}[/tex]
[tex]= \frac{11! }{ 10! 1!} (0.76)^{1} (0.24)^{10} + \frac{11!}{9! 2!} (0.76)^2 (0.24)^{9} + \frac{11!}{8! 3!} (0.76)^{3} (0.24)^{8} + \frac{11!}{7!4!} (0.76)^{4} (0.24)^{7}[/tex]
[tex]P( X \le 4 ) = 0.0054[/tex]
please help
-3(-4x+4)=15+3x
Answer:
x=3
Step-by-step explanation:
● -3 (-4x+4) = 15 + 3x
Multiply -3 by (-4x+4) first
● (-3) × (-4x) + (-3)×(4) = 15 + 3x
● 12 x - 12 = 15 +3x
Add 12 to both sides
● 12x - 12 + 12 = 15 + 3x +12
● 12 x = 27 + 3x
Substract 3x from both sides
● 12x -3x = 27 + 3x - 3x
● 9x = 27
Dividr both sides by 9
● 9x/9 = 27/9
● x = 3
write the equation of a horizontal ellipse with a major axis of 30, a minor axis of 14, and a center at (-9,-7).
Answer: [tex]\dfrac{(x+9)^2}{225}-\dfrac{(y+7)^2}{49}=1[/tex]
Step-by-step explanation:
The equation for a horizontal ellipse is: [tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex] where
(h, k) is the centera is x-radiusb is the y-radiusGiven: major axis (diameter on x) is 30 --> x-radius (a) = 15 --> a² = 225
minor axis (diameter on y) is 14 --> y-radius (b) = 7 --> b² = 49
center (h, k) is (-9, -7)
Input those values into the equation for a horizontal ellipse and simplify:
[tex]\dfrac{(x-(-9))^2}{15^2}-\dfrac{(y-(-7))^2}{7^2}=1\\\\\\\large\boxed{\dfrac{(x+9)^2}{225}-\dfrac{(y+7)^2}{49}=1}[/tex]
What is the quotient of 35,423 ÷ 15?
Answer: 2361.53
Step-by-step explanation:
Use long division and round.
(The 3 is repeated)
The domain of the following relation has how many elements?
[(1/2, 3.14/6), (1/2, 3.14/4), (1/2, 3.14/3), (1/2,3.14/2)]
a. 0
b. 1
c. 4
Answer:
b. 1
Step-by-step explanation:
All first coordinates are 1/2.
Answer: b. 1
find the h.c.f of 186,310,434
186|2
93|3
31|31
1
310|2
155|5
31|31
1
434|2
217|7
31|31
1
[tex]186=2\cdot3\cdot31\\310=2\cdot5\cdot31\\434=2\cdot7\cdot31\\\\\text{hcf}(186,310,434)=2\cdot31=62[/tex]
Solve the equation for x by graphing.-4x-1 5x=4
Answer: Undefined
Step-by-step explanation:
slope is undefined
no y intercept
This line is vertical
Use the Pythagorean theorem to find the length of the hypotenuse in the triangle shown below.4,3
Answer:
5
Step-by-step explanation:
a^2 + b^2 = c^2
4^2 + 3^2 = c^2
16 + 9 = c^2
25 = c^2
c = 5
Answer:
5Step-by-step explanation:
[tex]Hypotenuse = ?\\Opposite = 4\\Adjacent = 3\\\\Pythagoras \: Theorem ;\\\\Hypotenuse^2 =Opposite^2+Adjacent ^2\\\\Hypotenuse^2 = 4^2 +3^2\\\\Hypotenuse^2 = 16+9\\\\Hypotenuse^2 = 25\\\\\sqrt{Hypotenuse^2}=\sqrt{25} \\Hypotenuse = 5[/tex]
mortician math word problem
Answer:
wat do u want me to do
Step-by-step explanation:
AB is dilated from the origin to create A'B' at A' (0, 8) and B' (8, 12). What scale factor was AB dilated by?
Answer:
4
Step-by-step explanation:
Original coordinates:
A (0, 2)
B (2, 3)
The scale is what number the original coordinates was multiplied by to reach the new coordinates
1. Divide
(0, 8) ÷ (0, 2) = 4
(8, 12) ÷ (2, 3) = 4
AB was dilated by a scale factor of 4.
4. Solve the system of equations. (6 points) Part I: Explain the steps you would take to solve the system by eliminating the x-terms. (1 point) Part II: Explain the steps you would take to solve the system by eliminating the y-terms. (2 points) Part III: Choose either of the methods described in parts I or II to solve the system of equations. Write your answer as an ordered pair. Show your work. (3 points)
Answer:
The system of equations you want to be solved is not given. I would however give an example with which the method of elimination will be shown, and can be used in solving problems of the nature.
Step-by-step explanation:
Consider the system of equations:
x + y = 7 ................................(1)
2x - y = 8 ..............................(2)
To eliminate x:
First multiply (1) by 2 to have
2x + 2y = 14 ...........................(3)
Next, subtract (2) from (3) to have
3y = 6
y = 6/3 = 2
To eliminate y:
Add (1) and (2) to have
3x = 15
x = 15/3 = 5
Therefore, (x, y) = (5, 2).
Please help me with this ,
Answer:
(a) -2.3°/min
(b) -2.9°/min
Step-by-step explanation:
The average rate of change is the ratio of the difference in R values to the difference in the corresponding t values.
(a) m = (157.6 -226.6)/(30 -0) = -69/30 = -2.3 . . . degrees per minute
__
(b) m = (61.6 -119.6)/(70 -50) = -58/20 = -2.9 . . . degrees per minute
3 ratios that are equivalent to 6:12
Answer:
1:3
2:4
3:6
Step-by-step explanation:
we can divide both sides by 6 and get 1:2
we can divide both sides by 3 and get 2:4
we can divide both sides by 2 and get 3:6
Answer:
12:24, 3:6, 2:4
Step-by-step explanation:
What we are looking for here is a ratio that, when you divide/multiply the same constant on both parts of the ratio, you get 6:12.
6:12 is the same thing as 1:2, so we can find ratios equivalent to 1:2 (the first value will be half the second).
Hope this helped!
In how many years will
The Compounds interest
onRs. 14,000 be Rs. 4, 634 at 10%
p.a?
Answer:
3 years
Step-by-step explanation:
A = P(1 + r)^t
A = I + P
A = 14,000 + 4,634 = 18,634
18,634 = 14,000(1 + 0.1)^t
18,634/14,000 = 1.1^t
log (18,634/14,000) = log 1.1^t
log (18,634/14,000) = t * log 1.1
t = [log (18,634/14000)]/(log 1.1)
t = 3
the length of a mathematical text book the is approximately 18.34cm and its width is 11.75 calculate ?
the approximate perimeter of the front cover?
the approximate area of the front cover of the book?
Answer:
Perimeter=60.18cm
Area=215.495cm^2
Step-by-step explanation:
Given:
Length of book=18.34cm
Breadth=11.75cm
Solution:
Perimeter=2(l +b)
P=2(18.34+11.75)
P=2 x 30.09
P=60.18cm
Area=l x b
A=18.34 x 11.75
A=215.495 cm^2
Thank you!
) A random sample of size 36 is selected from a normally distributed population with a mean of 16 and a standard deviation of 3. What is the probability that the sample mean is somewhere between 15.8 and 16.2
Answer:
The probability is 0.31084
Step-by-step explanation:
We can calculate this probability using the z-score route.
Mathematically;
z = (x-mean)/SD/√n
Where the mean = 16, SD = 3 and n = 36
For 15.8, we have;
z = (15.8-16)/3/√36 = -0.2/3/6 = -0.2/0.5 = -0.4
For 16.2, we have
z = (16.2-16)/3/√36 = 0.2/3/6 = 0.2/0.5 = 0.4
So the probability we want to calculate is;
P(-0.4<z<0.4)
We can get this using the standard normal distribution table;
So we have;
P(-0.4 <z<0.4) = P(z<-0.4) - P(z<0.4)
= 0.31084
find the circle through (-4,sqrt(5) with center (0,0)
Answer:
Circle Equation : x² + y² = 21
Step-by-step explanation:
So we know that this circle goes through the point ( - 4, √5 ), with a center being the origin. Therefore, this makes the circle equation a bit simpler.
The first step in determining the circle equation is the length of the radius. Applying the distance formula, the radius would be the length between the given points. Another approach would be creating a right triangle such that the radius is the hypotenuse. Knowing the length of the legs as √5 and 4, we can calculate the radius,
( √5 )² + ( 4 )² = r²,
5 + 16 = r²,
r = √21
In general, a circle equation is represented by the formula ( x - a )² + ( y - b )² = r², with radius r centered at point ( a, b ). Therefore our circle equation will be represented by the following -
( x - 0 )² + ( y - 0 )² = (√21 )²
Circle Equation : x² + y² = 21
Find the 14th term in the sequence 1, 1/3, 1/9, … Find the sum of the first 10 terms of the sequence above.
Answer:
This is a geometric progresion that begins with 1 and each term is 1/3 the preceeding term
Let Pn represent the nth term in the sequence
Then Pn = (1/3)^n-1
From this P14 = (1/3)^13 = 1/1594323
5. The sum of the first n terms of a GP beginning a with ratio r is given by
Sn = a* (r^n+1 - 1)/(r - 1)
With n = 10, a = 1 and r = 1/3, S10 = ((1/3)^11 - 1)/(1/3 - 1) = 1.500
a vegetable garden and he's around the path of seemed like a square that together are 10 ft wide. The path is 2 feet wide. Find the total area of the vegetable garden and path
Answer:
Garden: 36 square feet
Path: 64 square feet
Step-by-step explanation:
Let's first find the total area. The total area will be 100 square feet since the side length is 10. Since the path is 2 feet wide and on all sides, that means that the inside square will have a side length of 6. That means that the vegetable garden is 36 square feet. The path will be 100 - (the garden), and the garden is 36 square feet, which means the outer path will be 64.
Find the remainder in the Taylor series centered at the point a for the following function. Then show that limn→[infinity]Rn(x)=0 for all x in the interval of convergence.
f(x)=cos x, a= π/2
Answer:
[tex]|R_n (x)| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]
Step-by-step explanation:
From the given question; the objective is to show that :
[tex]\lim_{n \to \infty} R_n (x) = 0[/tex] for all x in the interval of convergence f(x)=cos x, a= π/2
Assuming for the convergence f the taylor's series , f happens to be the derivative on an open interval I with a . Then the Taylor series for the convergence of f , for all x in I , if and only if [tex]\lim_{n \to \infty} R_n (x) = 0[/tex]
where;
[tex]\mathtt{R_n (x) = \dfrac{f^{(n+1)} (c)}{n+1!}(x-a)^{n+1}}[/tex]
is a remainder at x and c happens to be between x and a.
Given that:
a= π/2
Then; the above equation can be written as:
[tex]\mathtt{R_n (x) = \dfrac{f^{(n+1)} (c)}{n+1!}(x-\dfrac{\pi}{2})^{n+1}}[/tex]
so c now happens to be the points between π/2 and x
If we recall; we know that:
[tex]f^{(n+1)}(c) = \pm \ sin \ c \ or \ cos \ c[/tex] (as a result of the value of n)
However, it is true that for all cases that [tex]|f ^{(n+1)} \ (c) | \leq 1[/tex]
Hence, the remainder terms is :
[tex]|R_n (x)| = | \dfrac{f^{(n+1)}(c)}{(n+1!)}(x-\dfrac{\pi}{2})^{n+1}| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]
If [tex]\lim_{n \to \infty} R_n (x) = 0[/tex] for all x and x is fixed, Then
[tex]|R_n (x)| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]
Tanθ - cosecθ secθ (1-2 cos²θ) = cotθ
Answer:
I thinksomething is wrong.
I'm getting another proving it's-tan thita.
I hope this is the one you are searching for..
3. A jogger runs 4 miles on Monday, 5 miles on
Tuesday, 3 miles on Wednesday, and 5 miles on
Thursday. He doesn't run on Friday. How many
miles did he run in all?
Answer:
17 miles
Step-by-step explanation:
4+5+5+3=17
Question:
A school's band members raised money by selling magazine subscriptions and shirts. Their profit from selling shirts was per shirt minus a one-time set-up fee. Their profit from selling magazine subscriptions was per subscription. They made exactly the same profit from shirts as they did from magazines. They also sold the same number of shirts as magazine subscriptions. How many shirts did they sell?
Jamie has a jar of coins containing the same number of nickels, dimes and quarters. The total value of the coins in the jar is 13.20. How many nickels does Jamie have?
The gasoline gauge on a van initially read ⅛ full. When 15 gallons of gasoline were added to the tank, the gauge then read ¾ full. How many more gallons would be needed to fill the tank?
Answer:
Question 1: 40 shirts and 40 magizines
Question 2: $4.4
Question 3: 6 gallons
Answer:
hello
Step-by-step explanation:
Find the area of the shape shown below.
2
2
4
Hurry and answer plz!!!!
1
Answer:
7 square units
Step-by-step explanation:
We can break down this complex shape into smaller shapes.
I've broken it down into a rectangle, a square, and a triangle (See attached picture)
Let's first find the area of the triangle. To do this we use the formula [tex]\frac{bh}{2}[/tex]. The base is 1 (because the top is 2, and 1 is already used on the triangle - 2-1 = 1.) and the height is 2 (because 4 is already used on the left, and 2 was used on the right so 4-2=2).
[tex]\frac{2\cdot1}{2} = \frac{2}{2} = 1[/tex].
Now let's find the area of the top square - we can just square 2 which is 4.
To find the area of the bottom rectangle, we can multiply it's two side lengths of 2 and 1 = 2.
Adding these all together gets us 4+2+1 = 7.
Hope this helped!
Can somebody explain how trigonometric form polar equations are divided/multiplied?
Answer:
Attachment 1 : Option C
Attachment 2 : Option A
Step-by-step explanation:
( 1 ) Expressing the product of z1 and z2 would be as follows,
[tex]14\left[\cos \left(\frac{\pi \:}{5}\right)+i\sin \left(\frac{\pi \:\:}{5}\right)\right]\cdot \:2\sqrt{2}\left[\cos \left(\frac{3\pi \:}{2}\right)+i\sin \left(\frac{3\pi \:\:}{2}\right)\right][/tex]
Now to solve such problems, you will need to know what cos(π / 5) is, sin(π / 5) etc. If you don't know their exact value, I would recommend you use a calculator,
cos(π / 5) = [tex]\frac{\sqrt{5}+1}{4}[/tex],
sin(π / 5) = [tex]\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}[/tex]
cos(3π / 2) = 0,
sin(3π / 2) = - 1
Let's substitute those values in our expression,
[tex]14\left[\frac{\sqrt{5}+1}{4}+i\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}\right]\cdot \:2\sqrt{2}\left[0-i\right][/tex]
And now simplify the expression,
[tex]14\sqrt{5-\sqrt{5}}+i\left(-7\sqrt{10}-7\sqrt{2}\right)[/tex]
The exact value of [tex]14\sqrt{5-\sqrt{5}}[/tex] = [tex]23.27510\dots[/tex] and [tex](-7\sqrt{10}-7\sqrt{2}\right))[/tex] = [tex]-32.03543\dots[/tex] Therefore we have the expression [tex]23.27510 - 32.03543i[/tex], which is close to option c. As you can see they approximated the solution.
( 2 ) Here we will apply the following trivial identities,
cos(π / 3) = [tex]\frac{1}{2}[/tex],
sin(π / 3) = [tex]\frac{\sqrt{3}}{2}[/tex],
cos(- π / 6) = [tex]\frac{\sqrt{3}}{2}[/tex],
sin(- π / 6) = [tex]-\frac{1}{2}[/tex]
Substitute into the following expression, representing the quotient of the given values of z1 and z2,
[tex]15\left[cos\left(\frac{\pi \:}{3}\right)+isin\left(\frac{\pi \:\:}{3}\right)\right] \div \:3\sqrt{2}\left[cos\left(\frac{-\pi \:}{6}\right)+isin\left(\frac{-\pi \:\:}{6}\right)\right][/tex] ⇒
[tex]15\left[\frac{1}{2}+\frac{\sqrt{3}}{2}\right]\div \:3\sqrt{2}\left[\frac{\sqrt{3}}{2}+-\frac{1}{2}\right][/tex]
The simplified expression will be the following,
[tex]i\frac{5\sqrt{2}}{2}[/tex] or in other words [tex]\frac{5\sqrt{2}}{2}i[/tex] or [tex]\frac{5i\sqrt{2}}{2}[/tex]
The solution will be option a, as you can see.
I cant seem to get the second one right...
Rx=1 means to reflect the given point on the line of x= 1
The mapping for the reflection on line x is x = k
(-2,7) = (-2(1) - -2,7) = (4,7)
The missing value is 7
John painted his most famous work, in his country, in 1930 on composition board with perimeter 101.14 in. If the rectangular painting is 5.43 in. taller than it is wide, find the dimensions of the painting.
Answer:
22.57 x 28
Step-by-step explanation:
10.86 + 4x = 101.14
-10.86 -10.86
4x = 90.28
/4 /4
x = 22.57
5.43 + 22.57 = 28
22.57
What is the error in this problem?
Answer:
wrong position of tan 64
Gulnaz plans to use less than 26 eggs while baking. She uses 5 eggs for each cake that she bakes, and 3 eggs for each quiche that she bakes.
Write an inequality that represents the number of cakes (C)left parenthesis, C, right parenthesis and quiches (Q)left parenthesis, Q, right parenthesis Gulnaz can bake according to her plan.
Answer:
5(x) +3(y)<26
Step-by-step explanation:
Let x represent the number of cakes she will bake and let you know represent the nymber of quiche she will bake.
She will use less than 26 eggs while baking and 5 eggs for each cake and 3 eggs for each quiche.
The inequality representing the above statement iz given below.
5(x) +3(y)<26
If the solutions for a quadratic equation are -2 and 5 what is the equation
Answer:
f(x) = x^2 - 3x -10
Step-by-step explanation:
If the solutions are {-2, 5}, the factors of the quadratic are (x + 2) and (x - 5).
The equation is f(x) = (x + 2)(x - 5) = x^2 - 3x -10
The perpendicular bisectors of ΔKLM intersect at point A. If AK = 25 and AM = 3n - 2, then what is the value of n?
Answer:
n = 9 is the answer.
Step-by-step explanation:
Given a Triangle [tex]\triangle KLM[/tex] with its perpendicular bisectors intersecting at a point A.
AK = 25 units and
AM = 3n -2
To find:
Value of n = ?
Solution:
First of all, let us learn about perpendicular bisectors and their intersection points.
Perpendicular bisector of a line PQ is the line which divides the line PQ into two equal halves and is makes an angle of [tex]\bold{90^\circ}[/tex] with the line PQ.
And in a triangle, the perpendicular bisectors of 3 sides meet at one point and that point is called Circumcenter of the triangle.
We can draw a circle from circumcenter so that the circle passes from the three vertices of the triangle.
i.e.
Circumcenter of a triangle is equidistant from all the three vertices of the triangle.
In the given statement, we are given that A is the circumcenter of the [tex]\triangle KLM[/tex].
Please refer to the attached image for the given triangle and sides.
The distance of A from all the three vertices will be same.
i.e. AK = AM
[tex]\Rightarrow 25 = 3n-2\\\Rightarrow 3n =25+2\\\Rightarrow 3n =27\\\Rightarrow \bold{n = 9}[/tex]
Therefore, n = 9 is the answer.
