Start by doing the binomial expansion of (x+y)^6 where x represents success. This is
(x^6y^0) + 6(x^5y^1) +15(x^4y^2) +20(x^3y^3) +15(x^2y^4) +6(x^1y^5) +(x^0y^6)
We are interested in the x^3y^3 term which represents exactly 3 sucesses. Since the probalbility of sucess and failure are both .5 we should be able to figure this out just using the coefficients of the terms which is
20/64 = .3125 which is 31.25%
The probability of exactly three successes in six trials of a binomial experiment in which the the probability of is 50% is 31.25%.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
Here,
Probability =(³₆×(50%)³×(1-50%)⁶⁻³
= 20×(1/2)³×(1/2)³
= 20× 1/64
= 20/64
= 5/16
= 0.3125
= 0.3125×100
= 31.25%
Therefore, the probability of exactly three successes in six trials of a binomial experiment in which the the probability of is 50% is 31.25%.
To learn more about the probability visit:
https://brainly.com/question/11234923.
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Work out the area of the shaded shape.
Hi there!
[tex]\large\boxed{77m^2}}[/tex]
We can divide the figure into 3 rectangles.
Area of top rectangle:
5 × 5 = 25m²
Long rectangle:
14 × 3 = 42m²
Bottom rectangle:
2 × 5 = 10m²
Add up the areas:
10 + 42 + 25 = 77m²
Find the slope between the points (-3,1) and (-17,2)
(show your work pls) serious answers only
Answer:
-1/14
Step-by-step explanation:
The given points are
(-3,1) (-17,2)The slope will be the difference of ordinate divided by difference of absicca .
> m = 2-1/-17+3
> m =1/-14
> m = -1/14
2. In AABC, m < B = 22°, m < C = 52° and a = 30. Find the length of b to the nearest tenth.
Answer:
232
Step-by-step explanation:
===========================================
Explanation:
I recommend drawing out the triangle. See below.
Notice how each lowercase letter is a side length, and the uppercase letters are angles. Also, each lowercase letter is opposite their corresponding uppercase counterpart.
side a is opposite angle Aside b is opposite angle Bside c is opposite angle CWe're given that angles B and C are 22 degrees and 52 degrees in that order. Let's use the fact that the three angles of any triangle must add to 180 to solve for angle A
A+B+C = 180
A+22+52 = 180
A+74 = 180
A = 180-74
A = 106
We do this so we can then apply the law of sines
sin(A)/a = sin(B)/b
sin(106)/30 = sin(22)/b
b*sin(106) = 30*sin(22) ....... cross multiplication
b = 30*sin(22)/sin(106)
b = 11.6910908340182 ....... which is approximate
b = 11.7
Make sure your calculator is in degree mode.
PLEASE HELP!!!
Verify sin(180°- θ) = sin θ
SHOW WORK!!!
Answer:
see explanation
Step-by-step explanation:
Using the identity
sin(x - y) = sinxcosy - cosxsiny , then
sin(180 - θ)
= sin180cosθ - cos180sinθ
= (0) cosθ - (- 1)sinθ
= 0 + sinθ
= sinθ
what is the value of m in the equation 1/5m - 2/3y = 30 when y = 15
Answer:
200
Step-by-step explanation:
1/5m-2/3y=30
1/5m-2/3(15)=30
1/5m-30/3=30
1/5m-10=30
1/5m=30+10
1/5m=40
m=40/(1/5)
m=(40/1)(5/1)
m=200/1
m=200
f(x) = 3x + 2
What is (5)?
O A. 21
B. 17
C. 15
O D. 10
find the missing information
Answer:
?=83 degrees
Step-by-step explanation:
74+120=194
360-194=166
166÷2=83
You divide by two because it is an inscribed angle, so it will always be half the measure of the arc it is inscribing or enclosing.
Which of the following is a geometric sequence
Answer:
B.
Step-by-step explanation:
A geometric sequence is where a number is multiplied or divided by same number
in option be all number ar the power of 2 so the correct answer would be B
I need help with my math!!!!!!!
Answer:
B is the answer because the graph is translated 2 down. the translation cannot be included within the radical sign, so it can't be C
which equation is represented by the table
Answer:
B. b=3a+2
Step-by-step explanation:
I just substituted all of the a values in and I got the b values.
Answer:
Your answer is B, b = 3a+2
Step-by-step explanation:
for example:
3(2) + 2 = 8
Insert a number from column a into the variable and it will come out as the number in column b if it's the correct equation.
i need help trying to solve this question to the nearest tenth of a degree
Can someone help me with this math homework please!
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]h(10) \text{- the altitude of the hot air balloon after 10 minutes.}\\\\\boxed{h(10)=60}[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
As described in the question, the function [tex]h(t)[/tex] models the total altitude of a hot air balloon over time. 't' represents the number of minutes that would be given.[tex]h(10)[/tex] would be the total altitude over 10 minutes time. To solve for the value, we would replace 't' with 10 and then evaluate.⸻⸻⸻⸻
[tex]\boxed{\text{Evaluating the function...}}\\\\h(t) = 210 - 15t; \text{ } h(10)\\-------------\\\rightarrow h(10) = 210 - 15(10)\\\\\rightarrow h(10)=210 - 150\\\\\rightarrow \boxed{h(10) = 60}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
I need help, I can’t figure out the answer
Answer:
Step-by-step explanation:
in negative exponents you should switch both numerator and denominator so for 2 raised to -1 you should switch the numerator and denominator and it will become 1/2 in which 2 is raised to power 1
you can do the same for the remining sums
so a is 1/2 in which 2 is raised to 6 so answer is 1/64
the angle of elevation of the top of a tower from a point 42 metres away from it's base on level ground is 26 degrees. find the height of the tower.
Answer:
20.485 Meters
Step-by-step explanation:
So first you wanna draw a diagram. Start with the tower, then on the ground to the left (or right) draw a point. The point will be labeled as 42 m away from the tower. Now draw a line from that point to the top of the tower. This makes your triangle, and that angle you just drew that touches the point is 26 degrees.
Now, since you have a right triangle you can use trig. You know an angle and a side. Specifically, relative to the 26 degree angle you know the adjacent angle and want the opposite, which is the tower. So opposite and adjacent is tangent. So you set up tan(26) = o/42 where o is the opposite side.
So solving you get o = 20.485 meters
Use the distributive property to write the next step in simplifying the numerical expression. Use the asterisk symbol (*) to represent multiplication. Do not multiply factors fully and do not use spaces. 4(x + 9)
Answer:
This is the expression:
4*x+4*9
What is the value of y in the equation y = 3x - 2. whenx = 2? *
Answer:
4
Step-by-step explanation:
y=3x-2
y=3(2)-2
y=6-2
y=4
Whats the mean, modian, mode, and range, of these five?
6) 35, 74, 76, 93, 84, 22
Mean=
Median=
Mode=
Range=
7) 72, 55, 11, 55, 42, 25, 79, 69
Mean=
Median=
Mode=
Range=
8) 93, 15, 11, 58, 94, 87, 73, 16, 21
Mean=
Median=
Mode=
Range=
9) 17, 45, 12, 74, 89, 57
Mean=
Median=
Mode=
Range=
10) 52, 35, 55, 23, 30
Mean=
Median=
Mode=
Range=
Answer:
Step-by-step explanation:
mean:64
median: (74+76)/2=75
mode: no mode
Range: 71
#2
mean:51
median:(55+55)/2=55
mode:55
Range; 68
Answer:
6)
Mean = 35+ 74+ 76+ 93+ 84+ 22 = 384
mean = total amount/total numbers
384/6 = 64
Median = 76 + 93/2 = 169/2 = 84.5
Mode = there is no mode (there are no numbers repeated)
Range = (biggest - smallest) = 93 - 22 = 71.
7)
Mean = total amount/total numbers
72+ 55 +11+ 55 + 42 + 25 + 79 + 69 = 408/8 = 51
Median = 55 + 42/2 = 97/2 = 48.5
Mode = 55
Range = 79 - 25 = 54
8) Mean = 93 + 15 + 11+ 58+ 94+ 87 + 73+ 16+ 21 = 468/9 = 52
Median = 94
Mode = nothing
Range = 93 - 11 = 82
9)
Mean = 17+45+ 12+ 74+ 89 + 57 = 294/6 = 49
Median = 12 + 74/2 = 43
Mode = nothing
Range = 89 - 12 = 77
10)
Mean = 52+ 35+ 55+ 23+ 30 = 195/5 = 39
Median = 55
Mode = nothing
Range = 55 - 23 = 32
Step-by-step explanation:
I rlly hope this helped i took soooo long(sry for that btw)
The combined mass of two children is 75lbs. The first child is four times the mass of the second child. What are the masses of the two children?
Which ordered pair is the best estimate for the solution of the
system of equations?
y= -1/2x +4 and y=1/2x - 3
Answer:
Where are the ordered pairs?
Step-by-step explanation:
lines b and c are parallel. no links.
Answer:
Value of x:
[tex]{ \tt{(13x + 9) + (5x + 9) = 180 \degree}} \\ { \tt{18x + 18 = 180 }} \\ { \tt{18x = 162}} \\ { \tt{x = 9}} \\ [/tex]
Angle m‹6:
[tex]{ \boxed{ \tt{m \angle6 = (5x + 9) \degree}}} \\ { \tt{m \angle6 = (5 \times 9) + 9}} \\ { \tt{m \angle6 = 54 \degree}}[/tex]
Answer:
B. 54 degrees
Step-by-step explanation:
Set up an equation that equals 180 degrees because a line is 180 degrees:
(13x+9)+(5x+9)=180
Solve for x:
x=9
Substitute 9 in 5x+9:
5(9)+9
Solve.
54
Since angle 6 is complementary, it is the same as the 7th angle.
So the answer is B, 54 degrees.
Hope this helps!
∠1 and ∠2 are supplementary angles. m∠1 = x − 39, and m∠2 = x + 61. Find the measure of each angle.
∠1 = 79, ∠2 = 101
∠1 = 40, ∠2 = 150
∠1 = 40, ∠2 = 140
∠1 = 79, ∠2 = 111
Johnny asks you to guess the specific coins he has in his pocket if he has $3.70 in change. You say you need a little
more information, to guess. So he tells you all he has is quarters and dimes and that he has 22 colns in all.
Answer:
10 quarters and 12 dimes :)
Step-by-step explanation:
3 questions only pls help gota finish tofday
5a) 3x3x13
b) 3x7x7
c)11x5x2x2
d)3x3x3x5x2
6a)2x2x2x131
7a)5x5x2x2
b) 3x2x17
c)5x2x2x2x2x2x2
d)5x5x5x3
e) 2x2x103
f)5x3x137
g) 2x2x2x2x2x2x2x2x2
h)5x5x7x7x3
The three straight paths, , , and , meet each other at three points, A, B, and C. How do these points of intersection differ from each other? Explain the differences in terms of the angles that you see. Also look at the length of the side opposite each angle. What pattern do you see regarding the measurements? In what situation would all the points of intersection resemble one another? Modify the triangle in GeoGebra to help you with your answers
Answer:
Step-by-step explanation:
I am sort. I have no idea
Answer:
The three straight paths intersect at different angles. In other words, the amountrequired to turn one path onto the other is different about each vertex. Thelargest angle is opposite the longest side, and the smallest angle is opposite theshortest side. If all three points of intersection look the same, the result is atriangle with three equal angles and three equal sides.
Step-by-step explanation:
Quadrilateral ABCD is a rectangle. FindBD ifAO = 6x - 22 and OC = 2x + 6.
40 units
20 units
7 units
10 units
Which is a simplified form of the expression -5(y – 2) – 7y?
A. -12y + 10
B. 2y - 10
C. -2y + 10
D. 12y - 10
Answer:
the answer is B
Step-by-step explanation:
-5(y-2)-7y
-5y-10-7y
+7y +7y
answer: 2y-10
Answer:
A. (-12y+10)
Step-by-step explanation:
-5(y-2) - 7y can be simplified to:
-5y + 10 - 7y when you factor the parenthesis.
If you add the y's together, the answer should be:
-12y + 10.
.
please answer asap and dont get it wrong T0T
Step-by-step explanation:
answer what ?
all we can see is a grid of coordinates with a functional graph drawn into it.
and we know this function is called y=h(x).
that is it.
what answer is needed ? there is no question visible.
a. 12.4
b. 12.9
c. 8.5
d. 8.1
-5(x+4) + -3x + -9x+-7
Answer:
x - 27
Step-by-step explanation:
Our goal here is to solve for x.
Start by performing the indicated multiplication:
-5(x+4) + -3x + -9x+-7 => -5x - 20 - 3x + 9x - 7
Combine like terms: x - 27
Answer:
[tex]-5(x+4) + -3x + -9x+-7[/tex]
[tex]\longmapsto -5\left(x+4\right)+\left(-3\right)x+\left(-9\right)x+\left(-7\right)[/tex]
[tex]\longmapsto -5\left(x+4\right)-3x-9x-7[/tex]
[tex]\longmapsto -5(x+4)=-5x-20[/tex]
[tex]\longmapsto -5x-20-3x-9x-7[/tex]
[tex]\longmapsto =-17x-27[/tex]
[tex]ANSWER:=-17x-27[/tex]
-------------------------------
hope it helps....
have a great day!!
Directions: Graph each equation by using the y-intercept and slope( make sure too show your work)
FIRST QUESTION: y= -2/3x-1
y-intercept=____
Slope:____
Given:
The equation of a linear function is:
[tex]y=-\dfrac{2}{3}x-1[/tex]
To find:
The y-intercept and slope of the given equation, then draw the graph of the equation.
Solution:
Slope intercept form of a line is:
[tex]y=mx+b[/tex] ...(i)
Where, m is the slope and b is the y-intercept
We have,
[tex]y=-\dfrac{2}{3}x-1[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]m=-\dfrac{2}{3}[/tex]
[tex]b=-1[/tex]
Therefore, the y-intercept is -1 and the slope of the line is [tex]-\dfrac{2}{3}[/tex].
It means the graph intersect the y-axis at point (0,-1) and having slope [tex]-\dfrac{2}{3}[/tex]. So, the graph of the equation is shown below.
