WILL MARK AS BRAINLIEST 4. Suppose there is a card game where you are dealt a hand of three cards. You have already learned that the total number of three-card hands that can be dealt from a deck of 52 cards is: 52C3=52!/49!3! 52C3=22100 Calculate the probability of getting a hand that has exactly two aces in it (A A X). Do this by finding out the number of possible hands that have exactly two aces, and then dividing by the total possible number of three-card hands that is stated above. Part A: Use the multiplication principle to tell the total number of three-card hands (permutations) that can be made with two aces. (2 points) Part B: In the answer from Part I, each two-ace hand got counted twice. For example, A A X got counted as a separate hand from A A X. Since order should not matter in a card hand, these are really the same hand. What is the actual number of two-ace hands (combinations) you can get from a deck of 52 cards?(2 points) Part C: Find the probability of drawing a three-card hand that includes two aces from a deck of 52 cards. Write your answer as a fraction. (2 points)

Answer:

The number stays the same

Step-by-step explanation:

The power of 1 equals the number itself

Answer:

O (1,-1)  is collinear with (2, 1) and (3, 3).

Step-by-step explanation:

equation of line in point slope form is

y-y1/x-x1 = m

where m is the slope of line

slope of line is given by

m = (y2-y1)/(x2-x1)

where(x1,x2) and (y1,y2) are points on the given line

_______________________________________

Given point

(2, 1) and (3, 3)?

m = 3-1/3-2 = 2

Equation of line

y-1/x-2 = 2

=> y-1 = 2(x-2)

=> y-1 = 2x-4

=> y= 2x-4+1

=> y = 2x-3

col-linear points are one which lie on the same line

To solve the problem we will check which  of the given points satisfy the equation of line derived above.

y = 2x-3

(0,0)

if we put value of x = 0 the above equation we should get y =0

y = 2*0 -3 = -3

since -3 is not equal to 0, hence (0,0) is not collinear with  (2, 1) and (3, 3).

1,-1

y = 2*1 -3 = -1

since -1 is  equal to -1, hence (1,-1) is collinear with  (2, 1) and (3, 3).

(4,4)

y = 2*4-3 = 5

since 5 is not equal to 4 , hence (4,4) is not collinear with  (2, 1) and (3, 3).

(-1,2)

y = 2*-1 -3 = -5

since -5 is not equal to 2, hence (-1,2) is not collinear with  (2, 1) and (3, 3).

Hence answer is O (1,-1)  s collinear with (2, 1) and (3, 3).

Answer:

The mean is more useful in this case because it would give an average value of the accidents for example 3 accidents per year but the median would give the middle value which may be 5  or greater or much lesser than the average. It would not give an approximate value of occurrences.

Step-by-step explanation:

Mean is the averaage of all the values.

Median is the value of the data which gives an estimate of the middle value. Middle values can be different than the average values.

The mean is

1) rigorously defined by a mathematical formula.

2) based on all the observations of the data

3) affected by extreme values

The meadian is

1) computed for open end classes like income etc.

2) not rigorously defined

3) is located when the values are not capable of quantitative measurment.

4) is not affected by extreme values.

The mean is more useful in this case because it would give an average value of the accidents for example 3 accidents per year but the median would give the middle value which may be 5  or greater or much lesser than the average. It would not give an approximate value of occurrences.

Answer:

4.647 to the nearest thousandth.

Step-by-step explanation:

The formula for the length of an arc between  x = a and x = b is

  a

    ∫  √( 1 + (f'(x))^2) dx

  b

Here f(x) = √x so

we have  ∫  (√( 1 + (1/2 x^-1/2))^2 )   between x = 0 and x = 4.

=   ∫ ( √( 1 + 1/(4x)) dx   between  x = 0 and x = 4.

This is not easy to integrate  but some software I have gives me the following

length =  √17 + 1/8 log(33 + 1/8 √17)

= 4.647.

Answer: B) -2/3

Step-by-step explanation:

First turn this equation into slope-intercept form(y = mx + b), where m is the slope.

2x+3y=4

3y=-2x+4

y=-2/3x+4/3

Thus, the slope is -2/3

Hope it helps <3

Answer:

Step-by-step explanation:

[tex]2x + 3y = 4?\\\mathrm{Slope}\:\mathbf{m}\:\mathrm{of\:a\:line\:of\:the\:form}\:\mathbf{Ax+By=C}\:\mathrm{equals}\:\mathbf{-\frac{A}{B}}\\\mathbf{A}=2,\:\mathbf{B}=3\\m=-\frac{2}{3}[/tex]

Answer: The answer is two

Step-by-step explanation: If you look for opposites of a number its either negative or positive. So when the answer is negative, the opposite is positive and if the answer is positive, the opposite is negative.

Answer:

[tex]\boxed{2}[/tex]

Step-by-step explanation:

The opposite of a number is the number that is the same distance from 0 on the number line.

-2 opposite is 2.

Answer:

Answer D

Step-by-step explanation:

The formula is [tex]A = pi r(r+\sqrt{h^2+r^2})[/tex]. We have our r (radius) and h (height), so plugging it all in would give us A = (3.14)(5 + sqrt(12^2)+(5^2). After computing this, you would get answer D, 282.6.

Answer:

396

Step-by-step explanation:

Answer:

(0,8.5)

Step-by-step explanation:

Change 2x+y=17 to 4x+2y=34

Cancel it out with -4x=2y - 34

It would be 4y=0

Transfer it to the first or second equation 2x+0=17

x=17/2 or 8.5

Answer:  6 feet from the pivot point

Step-by-step explanation:

Girl's weight x distance from center = Boy's weight x distance from center

65 (7) = 75x

[tex]\dfrac{65(7)}{75}=x[/tex]

6.066 = x

The boy needs to be placed 6 feet from the center (aka pivot point) which is the same as saying 1 foot from the end of the seesaw.

Answer:

x = 9.9 in.

2 of the same type of triangle = 1 square

To find x, you have to remember that a square is made from two right triangles combined. In this photo, we can see that the length and width of the triangle have the same value (the two sides that point up and to the right), so that means if we multiply the area by two, then we get the area of a square or two of the same triangle's area.

Step 1:

To find the area of the square/two triangles, multiply the area by two.

[tex]49*2=98[/tex]

98 is the area of the square.

Step 2:

Now we have to find the square of 98 (find two numbers that are the same that multiply to 98).

[tex]\sqrt{98}[/tex]

When we solve this square, we find out that it is not a perfect number. So:

[tex]\sqrt{98} =\\9.89949[/tex]

That is just an estimate of x, so when we round to the nearest tenth, we get 9.9.

To check our answer, multiply 9.9 by 9.9 and we get 98.01, but since we rounded our answer, 98.01 is correct. If we round that to 98 and divide by 2, we get our original area of one triangle, 49.

x = 9.9

Answer:

9.9

Step-by-step explanation:

Well let's work backwards.

If the area is 49 then we do 49*2 because after doing b*h you divide by 2.

So 49*2 = 98.

If the b and h is the same then we find the square root of 98,

which is 9.899494937.

Thus,

the answer is 9.9 rounded to the nearest tenth.

Hope this helps :)

Answer:

x = -7/5

Step-by-step explanation:

If we square both sides of the equation, we get:

[tex]\sqrt{x^2-3x-6}=x-1\\ (\sqrt{x^2-3x-6})^2=(x-1)^2\\x^2-3x-6=x^2-2x+1\\[/tex]

Then, solving for x, we get:

[tex]x^2-3x-6=x^2-2x+1\\-3x-6=2x+1\\-6-1=2x+3x\\-7=5x\\\frac{-7}{5}=x[/tex]

So, x is equal to -7/5

Answer:

its -7

Step-by-step explanation:

gots it right!

Answer:

( 4, 9 ) is our solution in an ordered pair, as you could also say x = 4, and y = 9

Step-by-step explanation:

So we have the following system of equations at hand ( given directly below ), and want to make it such that each equation is multiplied by a value that makes a common variable, say x, have opposite values of coefficients such that they cancel each other out when the two equations are added, enabling you to solve for the value of the other variable, in this case variable y.

[tex]\begin{bmatrix}x-3y=-23\\ 5x+6y=74\end{bmatrix}[/tex] - Multiply this top equation by -5, so the coefficient of variable x becomes - 5, opposite to the respective x coefficient in the second equation.

[tex]\begin{bmatrix}-5x+15y=115\\ 5x+6y=74\end{bmatrix}[/tex] - Adding the two equations we receive the simplified equation 21y = 189. y = 189 / 21 = 9. If y = 9, x should = - 23 + 3y = - 23 + 3 [tex]*[/tex] 9 = 4. To get this value of x simply isolate the value of x in the first equation given to us, and substitute the known value of y. We have our solution in the form ( 4, 9 ), where x = 4 and y = 9.

Answer:

4,9

Step-by-step explanation:

Answer:

[tex]\boxed{t=\frac{A-p}{pr}}[/tex]

Step-by-step explanation:

[tex]A=p+prt[/tex]

Subtract p on both sides.

[tex]A-p=p+prt-p[/tex]

[tex]A-p=prt[/tex]

Divide both sides by pr.

[tex]\displaystyle \frac{A-p}{pr} =\frac{prt}{pr}[/tex]

[tex]\displaystyle{\frac{A-p}{pr} =t}[/tex]

Answer:

A=p+prt

=>A/R=2pt

=>A/RT=2p

=>A/RTP=2

=>A/2RP=T

Answer:

[tex] Area = 316.6 mi^2 [/tex]

Step-by-step explanation:

Given:

Angle of arc = 300°

Radius of circle = 11 miles

Take π as 3.14

Required:

Area of the major sector

Solution:

Area of sector is given as: angle of arc/360*πr²

Thus,

[tex] Area = \frac{300}{360}*3.14*11^2 [/tex]

[tex] Area = 316.616667 [/tex]

[tex] Area = 316.6 mi^2 [/tex] (rounded to the nearest tenth)

Answer:

15

Step-by-step explanation:

Answer:

12 people heard the joke?

Step-by-step explanation:

Answer:

21.7

Step-by-step explanation:

When anything is 5 or above in a decimal place you round up to the next number for example

2.35 this would round up to be 2.4

21.65

Place value of 1 = ones place

Face value of 1 = 1

Note : The face value of a number will not change at all

Hope it helps you..If it's wrong plz say and I'll try to recorrect it :)

Answer:

38.68 cm

Step-by-step explanation:

Perimeter of an equilateral triangle : P = 3a

Area of an equilateral triangle : A = [tex]\frac{\sqrt{3} }{4}a^2[/tex]

a = side length

The area is given, solve for a.

[tex]72= \frac{\sqrt{3} }{4}a^2[/tex]

[tex]a = 12.894839[/tex]

The side length is 12.894839 centimeters.

Find the perimeter.

P = 3a

P = 3(12.894839)

P = 38.684517 ≈ 38.68

The perimeter is 38.68 centimeters.

Answer:

The statement

the product of 60 and the number of seconds is written as

60 * s

Hope this helps you

Answer:

52 minutes

Step-by-step explanation:

This should be a proportional statement, because if each individual person painted there own wall it should still take 52 minutes.

Answer:

Hey! The answer will be below!! :)

Step-by-step explanation:

In least to greatest the answer will be....

0.652, 6.52, 65.2

0.652 comes first because since the decimal point is between the 0 and 6

It’s also because 0 is less than 6 and 65.

Here is a easy way to do this, when you have this kind of question.

First look where the decimal is.

Pretend it’s a whole number like, 0.652 becomes 0

And 6.52 becomes 6, also 65.2 becomes 65

You have to use the decimal to find out least to greatest, also you will have to round the number.

So remember, when ever you have this kind of question...after the decimal point like 65.2 you take away the .2 and just have 65....this will help you do least to greatest faster! :)

Hope this helps!

Answer:

0.652, 6.52, 65.2

Step-by-step explanation:

You have to round to find the answer in a easy way.

Least to greatest would be 0.652, 6.52, 65.2

Hop it will help u

Answer:

fmax = xy =  26 × 13 = 338

(x,y) = (26,13)

Step-by-step explanation:

Given that:

f(x, y) = xy

subject to x + 2y = 52

So;

x = 52 - 2y

and;

f(x, y) = xy

f(x, y) = (52- 2y) y

f(x, y) =  52y - 2y²

In order to maximize this function;

52y - 2y² = 0

26 y - y² = 0

26 - 2y = 0

-2y = -26

y = -26/-2

y = 13

Again:

x = 52 - 2y

x = 52 - 2(13)

x = 52 - 26

x = 26

fmax = xy =  26 × 13 = 338

(x,y) = (26,13)

Answer:

A. True

Step-by-step explanation:

Since it is lesser, it will also bring in lesser profit :)

Answer:

The total amount is $2250.

Step-by-step explanation:

Given that each person pays $5 and there is 450 people so you have to multiply :

$5 × 450 = $2250

Answer:

Step-by-step explanation:

If [tex]\sum a_n[/tex] is a series, for the series to converge/diverge according to ratio test, the following conditions must be met.

[tex]\lim_{n \to \infty} |\frac{a_n_+_1}{a_n}| = \rho[/tex]

If [tex]\rho[/tex] < 1, the series converges absolutely

If [tex]\rho > 1[/tex], the series diverges

If [tex]\rho = 1[/tex], the test fails.

Given the series [tex]\sum\left\ {\infty} \atop {1} \right \frac{n^2}{5^n}[/tex]

To test for convergence or divergence using ratio test, we will use the condition above.

[tex]a_n = \frac{n^2}{5^n} \\a_n_+_1 = \frac{(n+1)^2}{5^{n+1}}[/tex]

[tex]\frac{a_n_+_1}{a_n} = \frac{{\frac{(n+1)^2}{5^{n+1}}}}{\frac{n^2}{5^n} }\\\\ \frac{a_n_+_1}{a_n} = {{\frac{(n+1)^2}{5^{n+1}} * \frac{5^n}{n^2}\[/tex]

[tex]\frac{a_n_+_1}{a_n} = {{\frac{(n^2+2n+1)}{5^n*5^1}} * \frac{5^n}{n^2}\\[/tex]

aₙ₊₁/aₙ =

[tex]\lim_{n \to \infty} |\frac{ n^2+2n+1}{5n^2}| \\\\Dividing\ through\ by \ n^2\\\\\lim_{n \to \infty} |\frac{ n^2/n^2+2n/n^2+1/n^2}{5n^2/n^2}|\\\\\lim_{n \to \infty} |\frac{1+2/n+1/n^2}{5}|\\\\[/tex]

note that any constant dividing infinity is equal to zero

[tex]|\frac{1+2/\infty+1/\infty^2}{5}|\\\\[/tex]

[tex]\frac{1+0+0}{5}\\ = 1/5[/tex]

[tex]\rho = 1/5[/tex]

Since The limit of the sequence given is less than 1, hence the series converges.

Answer:

Hello There. ☆~---_●₩●__---☆~ The students in each grade, that way it wont focus just on one group like the club, the teachers, or the boys.

Hope It Helps!~ ♡

ItsNobody~ ☆

Answer:

(2x - y)³ = 8x³ - 12x²y + 6xy² - y³

Step-by-step explanation:

Pascal's Theorem uses a set of already known and easily obtainable numbers in the expansion of expressions. The numbers serve as the coefficients of the terms in the expanded expression.

For the expansion of

(a + b)ⁿ

As long as n is positive real integer, we can obtain the coefficients of the terms of the expansion using the Pascal's triangle.

The coefficient of terms are obtained starting from 1 for n = 0.

- For the next coefficients of terms are 1, 1 for n = 1.

- For n = 2, it is 1, 2, 1

- For n = 3, it is 1, 3, 3, 1

The next terms are obtained from the previous one by writing 1 and summing the terms one by one and ending with 1.

So, for n = 4, we have 1, 1+3, 3+3, 3+1, 1 = 1, 4, 6, 4, 1.

The Pascal's triangle is

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1

1 9 36 84 126 126 84 36 9 1

The terms can also be obtained from using the binomial theorem and writing the terms from ⁿC₀ all through to ⁿCₙ

So, for n = 3, the coefficients are 1, 3, 3, 1

Then the terms are written such that the sum of the powers of the terms is 3 with one of the terms having the powers reducing from n all through to 0, and the other having its powers go from 0 all through to n

So,

(2x - y)³ = [(1)(2x)³(-y)⁰] + [(3)(2x)²(-y)¹] + [(3)(2x)¹(-y)²] + [(1)(2x)⁰(-y)³]

= (1×8x³×1) + (3×4x²×-y) + (3×2x×y²) + (1×1×-y³)

= 8x³ - 12x²y + 6xy² - y³

Hope this Helps!!!

Answer:

6 units

Step-by-step explanation:

Distance between 2 points

[tex] = \sqrt{(x1 - x2)^{2} + (y1 - y2)^{2} } [/tex]

Thus, distance between (-3, 5) and (-9, 5)

[tex] = \sqrt{( - 3 - ( - 9))^{2} + (5 - 5)^{2} } \\ = \sqrt{( - 3 + 9)^{2} } \\ = \sqrt{6 ^{2} } \\ = 6[/tex]

Alternatively, notice that this line is a horizontal line as both points have the same y-coordinate of 5.

Thus, distance between the 2 points

= -3 -(-9)

= -3 +9

= 6 units

Answer:

h = 109.9 in

Step-by-step explanation:

The above question can be solved using trigonometric ratio formula,

tan θ = opposite/adjacent

tan θ = tan 70° ≈ 2.7475

opposite = height of lamppost = h in

Adjacent = 40 in

Thus,

[tex] tan 70 = \frac{h}{40} [/tex]

[tex] 2.7475 = \frac{h}{40} [/tex]

Multiply both sides by 40 to solve for h

[tex] 40*2.7475 = h [/tex]

h = 109.9 inches

The height of the lamppost = h = 109.9 inches (to nearest tenth)