A committee must be formed with 3 teachers and 3 students. If there are 10 teachers to choose from, and 9 students, how many different ways could the committee be made?

Answer:

226a³b² - 824ab³ + 984b⁴

Step-by-step explanation:

We can factorize the given expression by expanding the two binomials and then combining like terms.

First, expand the two binomials:

10ab (a − 2b)³ +24ab² (3a − 6b)² = 10ab(a³ - 6a²b + 12ab² - 8b³) + 24ab²(9a² - 36ab + 36b²)

Then, combine like terms:

= 10ab(a³ - 6a²b + 12ab² - 8b³) + 24ab²(9a² - 36ab + 36b²)

= (10a³b - 60a²b² + 120ab³ - 80b⁴) + (216a³b² - 864ab³ + 864b⁴)

= (10a³b + 216a³b² - 60a²b² - 864ab³ + 120ab³ + 864b⁴ - 80b⁴)

= (10a³b + 216a³b² - 60a²b² - 864ab³ + 120ab³ + 864b⁴ - 80b⁴)

= (10a³b - 60a²b² + 120ab³ - 80b⁴) + (216a³b² - 864ab³ + 864b⁴)

= (10a³b + 216a³b² - 60a²b² - 864ab³ + 120ab³ + 864b⁴ - 80b⁴)

= (10a³b - 60a²b² + 120ab³ - 80b⁴) + (216a³b² - 864ab³ + 864b⁴)

= 226a³b² - 824ab³ + 984b⁴

Answer:

[ See the attached picture ]

The diagonals of a parallelogram bisect each other.

✧ Given : ABCD is a parallelogram. Diagonals AC and BD intersect at O.

✺ To prove : AC and BD bisect each other at O , i.e AO = OC and BO = OD.

Proof :[tex]\begin{array}{ |c| c | c | } \hline \tt{SN}& \tt{STATEMENTS} & \tt{REASONS}\\ \hline 1& \sf{In \: \triangle ^{s} \:AOB \: and \: COD } \\ \sf{(i)}& \sf{ \angle \: OAB = \angle \: OCD\: (A)}& \sf{AB \parallel \: DC \: and \: alternate \: angles} \\ \sf{(ii)} &\sf{AB = DC(S)}& \sf{Opposite \: sides \: of \: a \: parallelogram} \\ \sf{(iii)} &\sf{ \angle \: OBA= \angle \: ODC(A)} &\sf{AB \parallel \:DC \: and \: alternate \: angles} \\ \sf{(iv)}& \sf{ \triangle \:AOB\cong \triangle \: COD}& \sf{A.S.A \: axiom}\\ \hline 2.& \sf{AO = OC \: and \: BO = OD}& \sf{Corresponding \: sides \: of \: congruent \: triangle}\\ \hline 3.& \sf{AC \: and \: BD \: bisect \: each \: other \: at \: O}& \sf{From \: statement \: (2)}\\ \\ \hline\end{array}.

Proved ✔

[/tex]

♕ And we're done! Hurrayyy! ;)

# STUDY HARD! So, Tomorrow you can answer people like this , " Dude , I just bought this expensive mobile phone but it is not that expensive for me" [ - Unknown ] :P

☄ Hope I helped! ♡

☃ Let me know if you have any questions! ♪

[tex] \underbrace{ \overbrace {\mathfrak{Carry \: On \: Learning}}}[/tex] ☂

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer:

0.83333333333

Step-by-step explanation:

5 lbs. of organic red potatoes cost $6.00. The price per pound of organic red potatoes is $1.20.

To find the price per pound of organic red potatoes, we can divide the total cost by the weight in pounds.

Price refers to the monetary value or amount that is assigned or charged for a product, service, or commodity. It represents the cost or value that a buyer is required to pay in exchange for obtaining or acquiring something.

Given that 5 lbs. of organic red potatoes cost $6.00, we can set up the following equation:

Price per pound = Total cost / Weight in pounds

Price per pound = $6.00 / 5 lbs.

Dividing $6.00 by 5 pounds gives us:

Price per pound = $1.20

Therefore, the price per pound of organic red potatoes is $1.20.

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Answer:

A waiter at a restaurant earns 10 dollars per hour. How much money is earned in 4 hours?

Equation: m = 10h

m = money earned

h = hours worked

Plug in 4 for (h)

m = 10(4)

m = 40 dollars

The waiter earns 40 dollars in 4 hours.

Step-by-step explanation:

Answer:

-3/4

Step-by-step explanation:

y=mx+b is in slope-intercept form, in which m=-3/4 and b=7, describing the slope and y-intercept of a linear equation respectively.

Answer:

-10

Step-by-step explanation:

t3 = a1 + (n - 1)*d

t3 = a1 + (3 -1)*d

2 = a1 + 2d

t17 = a1 + (n - 1)*d

-40 = a1 + 16d                Put the first condition underneath and subtract

  2 = a1 + 2d

-42 = 14 d

d = - 3

2 = a1 + 2*(-3)

2 = a1 - 6                      Add 6 to both sides

2 + 6 = a1

a1 = 8

Now you want the 7th term

t7 = a1 + (n - 1)*d

t7 = 8 + (7 - 1)*d

t7 = 8 + 6*(-3)

t7 = 8 - 18

t7 = - 10

Given:

First 10 term of a geometric series are:

[tex]\dfrac{16}{25}+\dfrac{8}{5}+4+10+...+a_10[/tex]

To find:

The expression that  represents the sum of the series.

Solution:

The first term of the given geometric series is:

[tex]a_1=\dfrac{16}{25}[/tex]

The common ratio of the given geometric series is:

[tex]r=\dfrac{a_2}{a_1}[/tex]

[tex]r=\dfrac{\dfrac{8}{5}}{\dfrac{16}{25}}[/tex]

[tex]r=\dfrac{8}{5}\times \dfrac{25}{16}[/tex]

[tex]r=\dfrac{5}{2}[/tex]

The sum of first n terms of a geometric sequence is:

[tex]S_n=\dfrac{a_1(1-r^n}{1-r}[/tex]

Where r is the common ratio.

Putting [tex]a_1=\dfrac{16}{25},r=\dfrac{5}{2},n=10[/tex] in the above formula, we get

[tex]S_{10}=\dfrac{16}{25}\left(\dfrac{(1-(\dfrac{5}{2})^{10}}{1-\dfrac{5}{2}}\right)[/tex]

Therefore, the correct option is C, i.e., [tex]\dfrac{16}{25}\left(\dfrac{(1-(\dfrac{5}{2})^{10}}{1-\dfrac{5}{2}}\right)[/tex].

Answer:

the answer is option c or 16/25 ( 1 - ( 5/2 )^10 / 1 - 5/2)

Step-by-step explanation:

On solving the provided question, we can say that - the answer of the following equation is = [tex](4.2 X 10^5)(1.5 X 10^3) / 2.5 X 10^4[/tex] = 25.2

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

[tex](4.2 X 10^5)(1.5 X 10^3) / 2.5 X 10^4[/tex]

630000/25000

25.2

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Answer:

figure a must be rotated 180°

on solving the provided question we can say that - by unitary method we have 12 days.

What is unitary method ?

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

Sue ate one sweetie one day,

Sue ate 12 sweetie 12 day,

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Answer:

Step-by-step explanation:

Answer:

The slope of a line that is perpendicular to y=1/4x-3 is -4/1x

Step-by-step explanation:

To get a perpendicular line you need to have a slope that is opposite of the other line and the opposite of 1/4 is -4/1x

Answer:

9 cups

Step-by-step explanation:

1 pt = 2 c
4 1/2 x 2 = 9 c

Check the picture below.

so let's start with 34, well a centroid is the point where all "medians" meet, well a median is half of the segment, the heck does that mean?  well, it means that CG = GD, and since CD is 34, that means that GD = 17.

let's keep in mind that a centroid cuts all medians in a 2 : 1 ratio, meaning one cut-side is twice as along as the other, that said

[tex]\stackrel{\textit{keeping in mind that BG=57}}{\cfrac{BH}{HG}=\cfrac{2}{1}\implies \cfrac{BH}{HG}=\cfrac{2\cdot \frac{57}{2+1}}{1\cdot \frac{57}{2+1}}}\hspace{10em} \cfrac{BH=38}{HG=19} \\\\\\ \cfrac{HD}{EH}=\cfrac{2}{1}\implies \cfrac{HD}{15}=\cfrac{2}{1}\implies HD=30\hspace{5em}\stackrel{15~~ + ~~30}{ED=45} \\\\\\ \stackrel{\textit{keeping in mind that CF=39}}{\cfrac{CH}{HF}=\cfrac{2}{1}\implies \cfrac{CH}{HF}=\cfrac{2\cdot \frac{39}{2+1}}{1\cdot \frac{39}{2+1}}}\hspace{10em}\cfrac{CH=26}{HF=13}[/tex]

We are given:

Coordinates of center: (2,8)

Radius of circle: 3 units

Finding equation of the circle:

We know that the general form of a circle is:

(x-h)² + (y-k)² = (radius)²

where h is the x-coordinate of the center and k is the y-coordinate

replacing with the given values, we get:

(x-2)² + (y-8)² = (3)²

Answer:

it is invertible

Step-by-step explanation:

Answer:

[tex]x^{2}[/tex]+14x-32 [tex]units^{2}[/tex]

Step-by-step explanation:

a basketball court is a rectangle, therefore its area is length x width.

the length given is (x+16)

the width given is (x-2)

substitute into the rectangular area equation:

length x width = (x+16)(x-2)= [tex]x^{2}[/tex]+14x-32

specific units (e.g. centimetres, meters, feet, etc) were not given so use the term 'units', and because we are dealing with area, use [tex]units^{2}[/tex].

therefore the answer is, [tex]x^{2}[/tex]+14x-32 [tex]units^{2}[/tex].

i hope that helps :)

Answer:

therefore the answer is, [tex]x^{2} +14x-32units^{2}[/tex].

Step-by-step explanation:

keeping in mind that a function does not have any X-Repeats, that is, the 1st coordinate in every pair never repeats, Check the picture below.

Answer:

The answer is 1367.31 not sure but try it

The amount will be $1367.3 after 9 years.

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.

Given that, p = 800, r = 6%, t = 9 year, we need to find the amount if the principal is compounded quarterly,

A = P(1+r)ⁿ

Since, the principal is compounding quarterly, the formula will become,

A = P(1+r/4)⁴ⁿ

A = 800(1+0.06/4)³⁶

A = 800(1.015)³⁶

A = 1367.3

Hence, the amount will be $1367.3 after 9 years.

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Answer:

A = $258.95

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 2.6/100

r = 0.026 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 200.00(1 + 0.026/2)(2)(10)

A = 200.00(1 + 0.013)(20)

A = $258.95

Answer:

10080 ways

Step-by-step explanation:

First we find the amount of combinations of teachers who can be chosen, which is denoted by 10 choose 3 (10 nCr 3), shown below:

10! / (3! * 7!) --> 120

Next to find the amount of combinations of students, you evaluate 9 choose 3(9 nCr 3), shown below:

9! / (3! * 6!) --> 84

To find the total number of combinations, you multiply the teachers combinations by the students combinations:

120 * 84 = 10080

Answer and Step-by-step explanation:

Prime numbers are numbered that can't be divided by whole numbers other than itself and 1.

7, 11, and 37 are prime numbers that add up to 55.

7 + 11 + 37 = 55

7 + 48 = 55

55 = 55

#teamtrees #PAW (Plant And Water)

Answer:

37+17+1

Step-by-step explanation:

I think

A prime number always has 2 factors:-)

1 and itself are its factors

I hope it helps

Answer:

Neither

Step-by-step explanation:

This questions only states

[tex]y = 11.1.07\%[/tex]

This is not a fucntion because there is no variable.

This is not a valid statement, because 11.1.07% is non-sensical.

Answer:

  False

Step-by-step explanation:

You want to know if it is true that 10, 8, 6, 4, ... is a geometric sequence.

A geometric sequence has a common ratio between adjacent terms. Here the ratios are ...

  8/10 = 0.8

  6/8 = 0.75

These numbers are different, so there is no common ratio. The sequence is not a geometric sequence. (False)

Answer: 24 units.

Step-by-step explanation: To find the perimeter of a triangle, you need to add the length, width, and hypotenuse. The length and width are provided, but we need to find the hypotenuse of the triangle. To do this, we need to use the Pythagorean Theorem.

The Pythagorean Theorem is basically a^2 + b^2 = c^2 where a and b are the legs of the triangle and c is the hypotenuse (also known as the triangle's longest side). However, whatever answer you get needs to be square-rooted, which is your complete answer. Let's say that the side that's 6 units is leg a and the side that's 8 units is leg b.

6^2 + 8^2 = c^2

36 + 64 = 100

√100 = 10.

Now that we know the hypotenuse, we can add it to our other two sides.

6 + 8 + 10 = 24.

Therefore, 24 is your answer.

Let me know if this is right! :)

Answer:

v=6.6667

Step-by-step explanation:

[tex]V=L*W*H/3[/tex]

[tex]V=20/3[/tex]

[tex]V=6.6667[/tex]

Hope this helps :)