Find the 5th term of the expansion of (x + y)9.

Answers

Answer 1
(r + 1)th term of (x + y)^n  = nCr x^(n-r)y^r

so here we have  9C4 x^(9-4)y^4

=  126x^5y^4  Answer

Related Questions

What is the measure of angle 1

Answers

The horizontal lines are parallel. Draw the figure on a piece of paper. Now, extend the segment that forms the 36-deg angle with the upper horizontal line until it intersects the lower horizontal line. Now you have a triangle. One angle of the triangle is 31 degrees at the bottom right. At the bottom left, you have an angle that is an alternate interior angle to the 36-deg angle at the top right, so the angle at the bottom left of the triangle also measures 36 deg. Angle 1 is an exterior angle of this triangle. The measure of an exterior angle of a triangle is the sum of the measures of the remote interior angles. The 31-deg angle and the 36-deg angle are the remote interior angles to angle 1, so m<1 = 31 + 36 = 67.

Evaluate the expression for x = 3 and y = 6.

5(x2 + y) + y2

Answers

5 (3*2+6) +6*2

Do parenthesis first

5 ( 12 ) + 6 * 2

multiply from left to right

60 + 12

add

72
5(3x2 + 6) + 6x2
5(6 + 6) + 6x2
5 x 12 + 6x2
60 + 12
72

HELP!! WHAT IS THE VALUE OF X ?

Answers

You are right!!!!!!!!!!!!!!!

what is the slope-intercept equation of a line that has a slope of -2 and a y-intercept of (0,3)

Answers

Your equation would be y = -2x + 3

-2 represents the constant, or slope, and +3 represents what y equals when x is zero

Hope this helps!

Round 103.468 to the nearest liter

Answers

You can not round to a litre it is a measurement of something. Or your asking for 103 litres

What steps would you do to solve n/7 + 3 ≥ -4? Multiply by seven, then subtract three. Add three, then multiply by seven. Subtract three, then multiply by seven. Subtract three, then divide by seven.

Answers

Step 1: Simplify both sides of the inequality.17n+3≥−4

Step 2: Subtract 3 from both sides.17n+3−3≥−4−317n≥−7

Step 3: Multiply both sides by 7.7*(17n)≥(7)*(−7)n≥−49

Answer:n≥−49

△EFG≅△JKL. What is m∠K?

Answers

Download the app Photomath that will help you

Answer:

62

Step-by-step explanation:

A square has an area of 121 yd^2 what is the length of each side

Answers

A=s^2 = 121 sq in. 
a= 11 inches

The side of the square having an area of 121 yards² is 11 yards

What is the area of a square?

A square is a 4 sided polygon where all the sides are of equal length.

The area of the square is the square of any one of its side

Let a be the side of the square

Area of the square = a²

Given data ,

Let the area of the square be Y = 121 yards²

Now , let the side of the square be = a

And the equation for the area of the square is

Area of the square = a²

where a is the side of the square

So , substituting the values in the equation , we get

a² = 121 yards²

Taking square root on both sides , we get

a = 11 yards

Therefore , the value of a is 11 yards

Hence , The side of the square having an area of 121 yards² is 11 yards

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Find the missing angle.

Answers

check the picture below.

make sure your calculator is in Degree mode.

but will run you about 36.8698976458°  and  53.13010235415598°.

What property of equality is used to transform equation 1 to equation 2?

Equation 1: 35 = 5x
Equation 2: 7 = x


addition Property of Equality

subtraction Property of Equality

multiplication Property of Equality

division Property of Equality

Answers

Multiplication property of equality

Final answer:

The division Property of Equality is used to transform Equation 1 (35 = 5x) into Equation 2 (7 = x) by dividing both sides of the equation by 5.

Explanation:

The property of equality used to transform Equation 1 (35 = 5x) to Equation 2 (7 = x) is the division Property of Equality.

This property states that if you divide both sides of an equation by the same non-zero number, the two sides remain equal. To get from Equation 1 to Equation 2, both sides of Equation 1 are divided by 5.

Division is similar to multiplication in that it follows the same rules for signs and equality. When dividing both sides by the same number, the numerator and denominator cancel out if they are the same, leaving a value of 1.

For instance, dividing 5x by 5 will lead to x, and dividing 35 by 5 will give 7, hence 7 = x, which is Equation 2.

Point m is the midpoint between A (-4,4) and B(-1,-6) find the location of M

Answers

Point M is the middle point, or also referred to as midpoint. It is the point on a line segment that divides the segment in two congruent segments. Between A(-4,4) and B(-1,-6) the point M would be:
((x1+x2)/2,(y1+y2)/2), where x1=-4, x2=-1, y1=4 and y2=-6
So, we have
M=(-4-1/2,4-(-6)/2)
M=(-5/2, 5)



If she steals 100 buys 70 worth of stuff owner gives u 30 back how much did owner lose

Answers

Owner would lose out on $100

A squirrel climbs 15 feet up a tree. He then runs 8.26 feet down the tree. How much further does the squirrel need to go before reaching the ground?

A)7.36 feet
B)7.26 feet
C)6.74 feet
D)8.11 feet

Answers

the answer is c 6.74 feet

Answer:

C

Step-by-step explanation:

solve the following equation by completing the square

Answers

answer is (x-1)and (x-2).First make the equation 3x^2- 9x+6=0. then divide both sides by 3 and then the two factors are (x-1)(x-2)

foil (ab - 9)(ab + 8)

Answers

Step 1: (ab-9)(ab+8)

Step 2: ab x ab +8 x ab -9 x ab -9 x 8

Step 3:  ab2  +8ab-9ab-72=

Step 4: ab2 -ab-72

solved!!! that how you would solve it everything will continue as normal

(ab)² + 8ab - 9ab - 72
a²b² - ab - 72

How many solutions does the equation have?y+7=y–3many solutions1 solutionno solutions?

Answers

No solution
Subtract y on both sides, giving you...
7= -3
Which is false

True or false: there are infinitely many bisectors, but only one perpendicular bisector for any segment.

Answers

The answer is to your question is : (TRUE)

I thought this was much more easier for you! :)

Answers

Problem 1)

The base of the exponential is 12 which is also the base of the log as well. The only answer choice that has this is choice B.

======================================================================
Problem 2)

log(x) + log(y) - 2log(z)
log(x) + log(y) - log(z^2)
log(x*y) - log(z^2)
log[(x*y)/(z^2)]

Answer is choice D

======================================================================
Problem 3)

log[21/(x^2)]
log(21) - log(x^2)
log(21) - 2*log(x)

This matches with choice B

======================================================================
Problem 4)

Ln(63) = Ln(z) + Ln(7)
Ln(63)-Ln(7) = Ln(z)
Ln(63/7) = Ln(z)
Ln(9) = Ln(z)
z = 9

======================================================================
Problem 5)

Ln(5x-3) = 2
5x-3 = e^2
5x = e^2+3
x = (e^2+3)/5

This means choice A is the answer

4747​% of men consider themselves professional baseball fans. you randomly select 10 men and ask each if he considers himself a professional baseball fan. find the probability that the number who consider themselves baseball fans is​ (a) exactly​ five, (b) at least​ six, and​ (c) less than four.

Answers

Given:
p = 47% = 0.47, the probability that a man considers himself a professional baseball fan.
q = 1 - p = 0.53, the probability that a man does not consider himself a professional baseball fan.
n = 10, the number of men surveyed.

(a) Calculate the probability that exactly 5 of 10 men surveyed consider themselves as professional baseball fans.
P(5 of 10) = ₁₀C₅ p⁵q⁵ = 252*0.47⁵*0.53⁵ = 0.242

Answer: 0.242 or 24.2%

(b) Calculate the probability of at least 6 out of 10.
P(at least 6 of 10)
= ₁₀C₆ p⁶q⁴ + ₁₀C₇ p⁷q³ + ₁₀C₈ p⁸q² + ₁₀C₉ p⁹q + ₁₀C₁₀ p¹⁰ q⁰
= 0.1786 + 0.0905 + 0.0301 + 0.0059 + 0.0
= 0.3057

Answer: 0.3057 or 30.6%
 
(c) Calculate the probability of less than 4 of 10.
P(less than 4 of 10)
= ₁₀C₁ pq⁹ + ₁₀C₂ p²q⁸ + ₁₀C₃ p³q⁷
= 0.0155 + 0.0619 + 0.1464
= 0.2238

Answer: 0.2238 or 22.4%

The situation represents a binomial probabilty with the probability of success (p) = 47% or 0.47 and the number of trials (n) = 10.

The probability of a binomial distribution is given by:

[tex]P(X)=\left(^n_x)p^x(1-p)^{n-x}[/tex]


Part A:

The probability that the number who consider themselves baseball fans is​ exactly​ five is given by:

[tex]P(5)=\left(^{10}_{\,5}\right)(0.47)^5(1-0.47)^{10-5} \\ \\ =252(0.022935)(0.041820)=\bold{0.2417}[/tex]



Part B:

The probability that the number who consider themselves baseball fans is​ at least​ six is given by:

[tex]P(X\geq6)=P(6)+P(7)+P(8)+P(9)+p(10) \\ \\ =\left(^{10}_{\,6}\right)(0.47)^6(1-0.47)^{10-6}+\left(^{10}_{\,7}\right)(0.47)^7(1-0.47)^{10-7} \\ +\left(^{10}_{\,8}\right)(0.47)^8(1-0.47)^{10-8}+\left(^{10}_{\,9}\right)(0.47)^9(1-0.47)^{10-9} \\ +\left(^{10}_{10}\right)(0.47)^{10}(1-0.47)^{10-10} \\ \\ =210(0.010779)(0.078905)+120(0.005066)(0.148877) \\ +45(0.002381)(0.2809)+10(0.001119)(0.53)+1(0.000526)(1) \\ \\ =0.1786+0.0905+0.0301+0.0059+0.0005=\bold{0.3056}[/tex]

This can be approximated using normal distribution as I will illustrate in part c.



Part C:

The probability that the number who consider themselves baseball fans is​ less than four is given by:

[tex]P(X\ \textless \ 4)=P(0)+P(1)+P(2)+P(3)[/tex]

We can approximate this using normal distribution by subtracting 0.5 from the least value and adding 0.5 to the greatest value.

This gives [tex]P(0-0.5\ \textless \ X\ \textless \ 3+0.5)=P(-0.5\ \textless \ X\ \textless \ 3.5)[/tex]

The mean of a binomial distribution is given by [tex]\mu=np[/tex], while the standard deviation is given by [tex]\sigma= \sqrt{np(1-p)} [/tex].

Thus,

[tex]\mu=10(0.47)=4.7 \ and \ \sigma=\sqrt{10(0.47)(0.53)}=1.578[/tex]

The probability of a nomal distribution between two values (a, b) is given by:

[tex]P(a\ \textless \ X\ \textless \ b)=P\left( \frac{b-\mu}{\sigma} \right)-P\left( \frac{a-\mu}{\sigma} \right)[/tex]

Thus,

[tex]P(-0.5\ \textless \ X\ \textless \ 3.5)=P\left( \frac{3.5-4.7}{1.578} \right)-P\left( \frac{-0.5-4.7}{1.578} \right) \\ \\ =P(-0.7605)-P(-3.295)=0.2235-0.0005=\bold{0.223}[/tex]

What is the number to the right of the decimal point called?

Answers

Tenths. Hope this helped.


What is the multiple zero and multiplicity of f(x) = x3 − 8x2 + 16x?



multiple zero = −4; multiplicity = 2


multiple zero = 2; multiplicity = 4


multiple zero = 4; multiplicity = 2


multiple zero = 2; multiplicity = −4









Answers

Answer:

B

Step-by-step explanation:

If you divide x so only x and a number remains, you will get B.

[tex]f(x) = x^{3} - 8x^{2} + 16x[/tex] has multiple zero = 4; multiplicity = 2.

What is multiple zero and multiplicity?

" A multiple zero has the multiplicity which represents the number of times linear factor of multiple zero occur in the polynomial .Zero of the polynomial is associated with multiple zero."

According to the question,

Given,

[tex]f(x) = x^{3} - 8x^{2} + 16x[/tex]

       

Simplify the given polynomial to get the multiple zero and multiplicity,

[tex]f(x) = x^{3} - 4x^{2}- 4x^{2} + 16x[/tex]

       [tex]\implies x^{2} (x-4) -4x(x-4)=0\\\\\implies (x^{2} -4x)(x-4) =0\\\\\\\implies (x) (x-4)(x-4)=0\\\\\implies x(x-4)^{2} =0[/tex]

Zero is associated with x =4.

(x-4) occur twice.

Hence, multiple zero = 4 and multiplicity = 2 of the given function.

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53 plz help me with this

Answers

3 large beads cost 2.50 * 3 = 7.50

30-7.50 = 22.50

20-7.50 = 12.50

 so they can spend between 12.50 and 22.50 on small beads

12.50 / 1.25 = 10

22.50/1.25 = 18

can buy between 10 and 18 small beads

1.25x >=12.50 and 1.25x<=22.50

A segment with endpoint a(3,1) and b(-1,1) is rotated 90° about the origin.what are the coordinates of a' and b' ? (geometry 10 a lesson 3 unit 5,if you know the answers to this whole practice pls give them to me pls and tysm)

Answers

You know that the segment is rotated at a 90 degree angle. 
As seen, the segment is in quadrant one and two. 

For a': 
a(3, 1) --> (-3, -1) 

For b': 
b(-1, 1) --> (1, -1) 

As you can see, the coordinate's signs are reversed for each case.

Hope I helped :) 

0.5(7d+4)=7−1.5d

solve for d

Answers

I can help!
Let's solve your equation step-by-step.0.5(7d+4)=7−1.5dStep 1: Simplify both sides of the equation.0.5(7d+4)=7−1.5d(0.5)(7d)+(0.5)(4)=7+−1.5d(Distribute)3.5d+2=7+−1.5d3.5d+2=−1.5d+7Step 2: Add 1.5d to both sides.3.5d+2+1.5d=−1.5d+7+1.5d5d+2=7Step 3: Subtract 2 from both sides.5d+2−2=7−25d=5Step 4: Divide both sides by 5.5d5=55d=1Answer:d=1

The number of random samples (without replacement) of size 3 that can be drawn from a population of size 5 is ___

Answers

5 size 3's are needed because there is a population of five size 3's.

A box with a square base and no top is to be made from a square piece of carboard by cutting 3 in. squares from each corner and folding up the sides. the box is to hold 9075 in3. how big a piece of cardboard is needed?

Answers

Final answer:

To create a box with a volume of 9075 in3, a 61 in. by 61 in. piece of cardboard is needed after cutting out 3 in. squares from each corner and folding up the sides.

Explanation:

To determine the size of the cardboard needed to construct a box with a volume of 9075 in3 when 3 in. squares are cut from each corner and the sides are folded up, we first need to express the volume of the box in terms of the dimensions of the cardboard. Let x represent the length of one side of the original square piece of cardboard. After cutting out 3 in. squares from each corner, the length and width of the base of the box will be x - 6 inches (since 3 inches are removed from each side), and the height will be 3 inches (the size of the squares cut from the corners).

The volume V of the box can be expressed as V = (x - 6)(x - 6)(3). Given that V = 9075 in3, we can set up the equation 9075 = (x - 6)2 × 3. Solving for x will give us the size of the original cardboard piece.

To solve the equation, divide both sides by 3 to isolate (x - 6)2, which gives 3025 = (x - 6)2. Taking the square root of both sides gives x - 6 = 55, so x = 61. Therefore, a 61 in. by 61 in. piece of cardboard is needed to construct the box.

What is the term for the point where angle bisectors of a triangle meet?

Answers

The three perpendicular bisectors of the sides of a triangle meet in a single point,called the circumcenter . A point where three or more lines intersect is called a pointof concurrency. So, the circumcenter is the point of concurrency of perpendicular bisectors of a triangle.
I think the answer is circumcentre

Helppppp plzz quickkk

Answers

Im sure the answer would be D

he hiked 4 km east in 45 minutes

45 minutes = 3/4 of an hour

4 /.75 = 5.33

 so the answer would be D. 5.3 km per hour east

If you horizontally stretch the quadratic parent function, f(x) = x2, by a factor of 5, what is the equation of the new function?

A. g(x) = (5x)2
B. g(x) = x2
C. g(x) = 5x2
D. g(x) = (x)2

Answers

Answer:

g(x)= (1/5x) ^2

Step-by-step explanation:

Just did the test got a 100.

The function f(x) = x² after stretching horizontally by a factor of 5 will be g(x) = [(1/5)x]² so none of the given option are correct.

What is a function?

A certain kind of relationship called a function binds inputs to essentially one output.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

If we streatch a function f(x) horizontally by factor of c then the value of new function g(x) become f(x/c)

By stretching f(x) by 5 it will  be

g(x) = f(x/5)

So replace x → x/5

Since,f(x) = x²

So,

g(x) = (x/5)²

Hence "The function f(x) = x² after stretching horizontally by a factor of 5 will be g(x) = [(1/5)x]²".

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The cost for parking at a parking garage is $2.25 plus an additional $1.50 for each hour. What is the total cost to park for 5 hours?

Answers

P=$2.25+5*$1.50=$9.75
The total cost to park for 5 hours is $9.75
1.5h+2.25    h=hours=5   1.5•5=7.5     7.5+2.25=9.75
the answer is $9.75
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