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.
#SPJ5
Diego runs for 32 seconds at -8. meters per second .what is his finish point?
Answer:
The finishing point 4
Step-by-step explanation:
32/8=4
the set of all possible factors of 18, 30 and 36 then make a set of their common factors and find the H.C.F . please explain briefly
Answer:
HCF = 6
Step-by-step explanation:
Listing the factors of each number
18 is 1, 2, 3, 6, 9, 18
30 is 1, 2, 3, 5, 6, 10, 15, 30
36 is 1, 2, 3, 4, 6, 9, 12, 18, 36
common factors are 1, 2, 3, 6
the HCF is 6
Find the measure of the indicated angle
Answer:
73 degrees
Step-by-step explanation:
The line on the two sides of the triangle indicates that the triangles is isosceles. This means that the base angles are congruent.
PLEASE HELP!!! What is the volume of the solid? Let π=3.14.
A. 5,425.92 m3
B. 2,1714.7 m3
C. 8,131.09 m3
D. 3,214.54 m3
Answer:
A. 5,425.92 m3
Step-by-step explanation:
Radius = 24m
Length = 12m
Volume = Area * Length
Area = π * (radius ^2)
Radius = Diameter / 2
Radius = 24m / 2 = 12m
Area = π * (12m^2)
Area = 3.14 * 144 = 452.16m
Volume = 452.16m * 12m
Volume = 5425.92m3
Quais são os zeros(ou raízes) da função quadrática f(x) = x² + 3x - 4? Assinale a alternativa correta. *
a) 2 e 3
b) 1 e - 4
c) 3 e 4
d) 4 e -1
Given:
The quadratic function is:
[tex]f(x)=x^2+3x-4[/tex]
To find:
The zeros of the given quadratic function.
Solution:
We have,
[tex]f(x)=x^2+3x-4[/tex]
Splitting the middle term, we get
[tex]f(x)=x^2+4x-x-4[/tex]
[tex]f(x)=x(x+4)-1(x+4)[/tex]
[tex]f(x)=(x+4)(x-1)[/tex]
For zeros, [tex]f(x)=0[/tex].
[tex](x+4)(x-1)=0[/tex]
[tex]x=-4,1[/tex]
Therefore, the correct option is (b).
What is the smallest 6 digit palindrome that is divisible by 99
I've been trying for 3 hours and I still cant figure it out PLEASE help.
Answer:
108801Step-by-step explanation:
6-digit palindrome is the number n the form of:
xyzzyxThis is divisible by 11 by default as the sum of the digits in odd placed is same as sum of the number in even places (remember the divisibility rule by 11):
x + z + y = y + z + xNow, in order to be divisible by 99, the number must be divisible by 11 and 9.
According to divisibility rule by 9 the sum of all digits must be divisible by 9. You can see In our case we need to have (the minimum):
x + y + z = 9The smallest number we could get is when x is minimum, y is minimum, so:
x = 1, y = 0, then y = 8The number we get is:
108801Proof:
108801/99 = 1099Hello,
Let's assume n the palindrome
[tex]n=\overline{abccba}\\\\Since\ 99=9*11:\\\\the \ smallest\ \Longrightarrow \ a=1\\\\a+b+c+c+b+a=9*k\ ,\ k\in \mathbb{N}\\2*(a+b+c)=9*k\ \Longrightarrow \ k\in 2\mathbb{N} , \ : k=2\\\\1+b+c=9 \Longrightarrow \ b=0\ and\ c=8\\\\n=108801\\\\Proof:\\108801=9*12089 =11*9891\\Nota\ bene:(a+c+b)-(b+c+a)=11*p \Longrightarrow \ 0=11*p \Longrightarrow \ p=0[/tex]
What is the measure of x in the figure below?
Answer:
115 degree
Step-by-step explanation:
x + 65 = 180 (Sum of angles in a straight line = 180 [Also known as Linear pair])
x = 180 - 65
x = 115 degree
What is the slope of the line? What is the y-intercept of the line? y = 1
Answer:
m = 0
y intercept = 1
Step-by-step explanation:
The given equation of the line is ,
[tex]\implies y = 1[/tex]
We know that the Standard equation of Slope Intercept Form of the line is,
[tex]\implies y = mx + c[/tex]
Where ,
m is slope c is y interceptOn comparing to the Standard form of the line we get ,
[tex]\implies Slope = 0 [/tex]
[tex]\implies y - intercept= 1[/tex]
Slope of the line is 0, since y=mx+c, if m = 0, then y = c, where the constant (c)=1
y intercept of the line is y = 1.
Answered by GAUTHMATH
help me por favor?!?!?!
Answer:
both lines have the same slope, hence they are parallel to each other
Step-by-step explanation:
The equation of a straight line is given by:
y = mx + b;
where y, x are variables, m is the slope of the line and b is the y intercept.
Two lines are said to be parallel to each other if they have the same slope, whereas two lines are perpendicular to each other if the product of their slopes is -1.
Given a line with an equation:
y = (2/3)x - 17
From the equation of the line with can see that the slope of the line is 2/3 and the y intercept is -17.
Also the other line has an equation of 4x - 6y = -6
6y = 4x + 6
y = (2/3)x + 1
Hence this line has a slope of 2/3 and a slope of 1.
Since both lines have the same slope, hence they are parallel to each other
find the area of the kite. please help thank you
Answer:
1/2×d1×d2
=1/2× (4+4)(6+3)
=36
Rewrite the following expression.
A.
B.
C.
D.
Answer:
da
Step-by-step explanation:
Find the measure of ∠AED for m∠BEC = 118
Answer: 118°
Step-by-step explanation:
Need help on this!! 10 points!!!
Answer:
The answer is B
Pes
Refer to the figure below to answer the following questions.
2 ft
4 ft
Find the surface area. Round to the nearest tenth.
75.4 ft2
50.3ft2
62.8 ft2
0 25.1 ft2
Answer:
75.4
Step-by-step explanation:
75.4area of cylinder is 2pie r h plus 2 pie * 2^2
which table represents a linear function graph 1. pleasee help also giving brainliest
Answer:
2 i think it is
Step-by-step explanation:
Determine the simplest expression for the area of shaded region below
Answer:
5x^2+3x^2+(3x+1)^2+(2x-4)^2
If €1 is £0.72
What is £1 in €
Answer:
€1.39
Step-by-step explanation:
£0.72 ÷ 0.72 = 1÷0.72
£1= €1.39
Help with math question
Answer:
z=4x
=14y10
Step-by-step explanation:
this is the answer
Weiling took part in a Mathematics quiz which consist of 60 questions. For every correct answer, 3 marks would be awarded. For every wrong answer, 2 marks would be deducted. Weiling answered all the questions and scored a totał of 140 marks for the quiz. How many questions did she answer correctiy?
Answer:
Right answer = 52
Wrong answers = 8
Step-by-step explanation:
Every correct answer = + 3
Every wrong answer = - 2
Number of correct answers = x
Number of wrong answers = y
x + y = 60 - - - (1)
3x - 2y = 140 - - - (2)
From (1) :
x = 60 - y
Put x = 60 - y into (2)
3(60 - y) - 2y = 140
180 - 3y - 2y = 140
180 - 5y = 140
-5y = 140 - 180
-5y = - 40
y = 8
x = 60 - y
x = 60 - 8
x = 52
Right answer = 52
Wrong answers = 8
A furnace operates at 2,300°F. Before it
can be used to extract metal from an ore,
the temperature must be raised to
3,600°F. This takes place at a rate of
250°F per quarter hour. Which equation
gives the furnace temperature T after q
quarter hours?
A T= 2509 + 2300
B T = 250q + 3600
C T = 2300q + 250
DT= 3600q + 250
Multiply the rate per quarter hour by quarter hours: 250g. This then gets added to the starting temperature of 2300
The answer would be : A. T = 250g + 2300
Convert the following 4.5 hours Into Second- ( Soin 24
Answer: 16,200 Seconds
Step-by-step explanation:
Data: 4.5 hours(h)=x seconds(s)
Step One, Convert Hours Into Minutes
4.5h=4h and 30 minutes(m)
1h=60mx4=240m+30=270m
Reason: Since to convert to seconds, minutes are needed, you have to convert everything to minutes. And with 60 minutes in an hour you have to multiply 60 by 4 to get 240 and add 30 minutes to it(since it's 4.5 hours) to find ourselves at 270 minutes.
Step two, Convert Minutes Into Seconds
1m=60s
270mx60=16,200s
Reason: Since we are ultimately trying to get 4.5 hours into seconds, we have to convert the minutes we have into seconds by multiplying 270 minutes by 60(since 60 seconds are in a minute) to get our final answer of 16,200 seconds.
I hope this helps!
CAN SB HELP ME !! Use the image and your knowledge of the isosceles triangle to find the value of x
Answer:
x = 41 degrees
Step-by-step explanation:
Since two of the sides are shown as being congruent, the base angles are the same. We are given the top angle, which is 98 degrees. All the angles of a triangle add up to 180. We can subtract 98 from 180, giving us 82, and divide that by two (since the base angles are congruent), giving us a measure of 41 degrees for each of the bottom angles of the isosceles triangle.
A drawer is filled with 2 black shirts, 7 white shirts, and 11 gray shirts.
One shirt is chosen at random from the drawer. Find the probability that it is not a black shirt.
Write your answer as a fraction in simplest form.
Answer:
Probability of the chosen T-shirt not being black will be equal to 9/10
Step-by-step explanation:
In order to solve this we need to understand that probaility is equal to the number of those outcomes that we want divided by the total number of outcomes. In our case the total number of outcomes is 20 (2 + 7 + 11) which is the total number of T-shirts, and the number of outcomes that are favorable to us is equal to 18 (outcomes without a black T-shirt). Therefor probability of the chosen T-shirt not being black will be equal to...
18/20 = 9/10
Find the volume of the cone shown as a decimal rounded to the nearest tenth.
Answer:
1866.10604
Step-by-step explanation:
V=3.14(r sqaured)1/3h
100 x 54 + 77 ÷ 2 = ? (RIGHT ANSWER GETS BRAINLIEST)
Answer:
5438.5
Step-by-step explanation:
To complete this equation, we must use the order of operations also known as PEMDAS.
For the case of this problem, we start by multiplying or dividing numbers before adding or subtracting numbers.
First let's start on the left:
100 x 54 + 77 ÷ 2
5,400 + 77 ÷ 2
5,400 + 38.5
5438.5
I hope this helps! Just remember to always add or subtract number last and start on the left, so that you don't get confused.
Answer:
So 2,738.5
Step-by-step explanation:
100×54 equals
— 5,400
5,400+77 equals
—5,477
5,477÷2 equals
—2,738.5
The answer is 2,738,5
Simplify:
-4a + 2(a + 9)
A. -2a + 9
B. -2a + 18
C. 2a + 9
D. 2a + 18
Answer:
B. - 2a + 18
Step-by-step explanation:
- 4a + 2( a + 9 )
= - 4a + 2a + 18
= - 2a + 18
Answer:
B
Step-by-step explanation:
got it right on edge :))
(a) Determine a cubic polynomial with integer coefficients which has $\sqrt[3]{2} + \sqrt[3]{4}$ as a root.
(b) Prove that $\sqrt[3]{2} + \sqrt[3]{4}$ is irrational.
Answer:
(a) [tex]x\³ - 6x - 6[/tex]
(b) Proved
Step-by-step explanation:
Given
[tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex] --- the root
Solving (a): The polynomial
A cubic function is represented as:
[tex]f = (a + b)^3[/tex]
Expand
[tex]f = a^3 + 3a^2b + 3ab^2 + b^3[/tex]
Rewrite as:
[tex]f = a^3 + 3ab(a + b) + b^3[/tex]
The root is represented as:
[tex]r=a+b[/tex]
By comparison:
[tex]a = $\sqrt[3]{2}[/tex]
[tex]b = \sqrt[3]{4}$[/tex]
So, we have:
[tex]f = ($\sqrt[3]{2})^3 + 3*$\sqrt[3]{2}*\sqrt[3]{4}$*($\sqrt[3]{2} + \sqrt[3]{4}$) + (\sqrt[3]{4}$)^3[/tex]
Expand
[tex]f = 2 + 3*$\sqrt[3]{2*4}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
[tex]f = 2 + 3*$\sqrt[3]{8}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
[tex]f = 2 + 3*2*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
[tex]f = 2 + 6($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
Evaluate like terms
[tex]f = 6 + 6($\sqrt[3]{2} + \sqrt[3]{4}$)[/tex]
Recall that: [tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex]
So, we have:
[tex]f = 6 + 6r[/tex]
Equate to 0
[tex]f - 6 - 6r = 0[/tex]
Rewrite as:
[tex]f - 6r - 6 = 0[/tex]
Express as a cubic function
[tex]x^3 - 6x - 6 = 0[/tex]
Hence, the cubic polynomial is:
[tex]f(x) = x^3 - 6x - 6[/tex]
Solving (b): Prove that r is irrational
The constant term of [tex]x^3 - 6x - 6 = 0[/tex] is -6
The divisors of -6 are: -6,-3,-2,-1,1,2,3,6
Calculate f(x) for each of the above values to calculate the remainder when f(x) is divided by any of the above values
[tex]f(-6) = (-6)^3 - 6*-6 - 6 = -186[/tex]
[tex]f(-3) = (-3)^3 - 6*-3 - 6 = -15[/tex]
[tex]f(-2) = (-2)^3 - 6*-2 - 6 = -2[/tex]
[tex]f(-1) = (-1)^3 - 6*-1 - 6 = -1[/tex]
[tex]f(1) = (1)^3 - 6*1 - 6 = -11[/tex]
[tex]f(2) = (2)^3 - 6*2 - 6 = -10[/tex]
[tex]f(3) = (3)^3 - 6*3 - 6 = 3[/tex]
[tex]f(6) = (6)^3 - 6*6 - 6 = 174[/tex]
For r to be rational;
The divisors of -6 must divide f(x) without remainder
i.e. Any of the above values must equal 0
Since none equals 0, then r is irrational
Describe the error Sadie made, and explain how to find the correct answer.
Answer:
She could've factored further
Step-by-step explanation:
a^5 can be written as a^4*a
so the answer should've been 3a^3b*sqrt(6ab)
BRAINLIEST PLEASEEEEEEEEEEE
Answer:
She should have factored a^7 as a^6 * a. Then sqrt(a^6 * a) = a^3 * sqrt(a).
[tex] 3a^3b\sqrt{6ab} [/tex]
Step-by-step explanation:
She should have factored a^7 as a^6 * a. Then sqrt(a^6 * a) = a^3 * sqrt(a).
Correct answer:
[tex] 3a^3b\sqrt{6ab} [/tex]
William used 15 cm of tape to wrap 3 presents. Find the length of tape to wrap for 1 present?
Answer:
The length of tape to wrap = 5 cm
Step-by-step explanation:
Let the length of tape used to wrap 1 present be = x
Tape length Number of presents
15 cm 3
x 1
[tex]\frac{15}{x} = \frac{3}{1} \\\\x \times 3 = 1 \times 15\\\\x = \frac{15}{3} = 5 \ cm[/tex]
Neeedddd answweerrrr plaeeessee
9514 1404 393
Answer:
B. log_b(a) - log_b(d)
Step-by-step explanation:
The applicable rule of logarithms is ...
log(a/b) = log(a) -log(b)
All the logs need to have the same base.
__
Here, the base is 'b', but the rule still applies:
[tex]\log_b{\dfrac{a}{d}}=\log_b{(a)}-\log_b{(d)}[/tex]
