What is the length of the hypotenuse in the right triangle shown below?

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Explanation:

We have 12*11*10 = 1320 permutations possible. This is where order matters. However, order does not matter with swim teams as there are no positions or ranks. All that matters is the group overall (rather than any individual in the group).

Consider the set {A,B,C}. We have 3*2*1 = 6 ways to arrange this set of letters. When considering a permutation, there are 6 permutations but only 1 combination since order doesnt matter and ABC is the same as BAC. Therefore, we divide 1320 over 6 to get the final answer of 1320/6 = 220.

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You can use the combination formula with n = 12 and r = 3. Doing so will give the following:

[tex]_n C _r = \frac{n!}{r!*(n-r)!}\\\\_{12} C _3 = \frac{12!}{3!*(12-3)!}\\\\_{12} C _3 = \frac{12!}{3!*9!}\\\\_{12} C _3 = \frac{12*11*10*9!}{3!*9!}\\\\_{12} C _3 = \frac{12*11*10}{3!}\\\\_{12} C _3 = \frac{12*11*10}{3*2*1}\\\\_{12} C _3 = \frac{1320}{6}\\\\_{12} C _3 = 220\\\\[/tex]

As you can see, we get the same result and note how 1320/6 is also present as well.

The greatest number of different 3-person teams that can be chosen is 220.

We can use combinations for this case,

The Total number of distinguishable things is m.

Out of those m things, k things are to be chosen such that their order doesn't matter.

This can be done in total of

[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!} ways.[/tex]

So, total number of choices in that case would be:

[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]

This is called permutation of k items chosen out of m items (all distinct).

Consider the set {A,B,C}.

3*2*1 = 6 ways to arrange this set of letters.

When considering a permutation, there are 6 permutations but only 1 combination since order doesnt matter and ABC is the same as BAC.

We can use the combination formula with n = 12 and r = 3.

[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!} ways.\\\\^{12}C_3= \dfrac{12!}{3! \times (12-3)!} ways.\\\\\\^{12}C_3= \dfrac{12!}{3! \times (9)!} ways.\\\\^{12}C_3= \dfrac{12 \times 11 \times 10 \times 9}{3! \times (9)!} ways.[/tex]

1320/6 = 220

Thus, the greatest number of different 3-person teams that can be chosen is 220.

Learn more about combinations and permutations here:

https://brainly.com/question/16107928

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Answer:

A. (-2,-4)

Step-by-step explanation:

If CR:RB is 2:3, and C is (-4,-7), then R is (-2,-7)

You can stop here because only A has the x value as -2.

If you want to look at the y value also, -4 is 2/5 of the way between -2 and -7, which has the same 2:3 proportion.

Answer:

M=-1, N=7

Step-by-step explanation:

Something went wrong on the 4th line.

From the third line, it should read

2x^2-x+6Mx-3M+4

=x(2x-1+6M) - 3M+4

Equating with the RHS,

2x-1+6M = 2x-7

6M = -7+1 = -6

M = -1

Therefore

N = -3M+4 = -3(-1)+4 = 7

or

M=-1, N=7

Step-by-step explanation:

1.) first simplify or combine like terms.[tex]\frac{3a}{5} -p-\frac{p}{9}+\frac{7p}{3} -\frac{q}{10}+\frac{1}{9}[/tex]

2.) then condense. [tex]\frac{3a}{5} +\frac{11p}{9}-\frac{q}{10}+\frac{1}{9}[/tex].

Answer:

None of the above

Step-by-step explanation:

In my opinion, I believe the answer is none of the above because

answer A says it has a peak from 10 to 15 km but the graph goes higher than 15 km

answer B says it has a gap from 25 to 30 km but the graph doesn't go that high.

Hope did helps:)

Answer:

how many feet of fencing does he have?

\

Step-by-step explanation:

Answer:

24 kg

Step-by-step explanation:

40/5 = 8 and 3x8 = 24

Answer:

24 kg

Step-by-step explanation:

[tex]\frac{5}{40} =\frac{3}{w} \\5w=120\\w=\frac{120}{5}=24[/tex]

Answer:

- 7x

Step-by-step explanation:

Given

(x - 4)(x - 3)

Each term in the second factor is multiplied by each term in the first factor, that is

x(x - 3) - 4(x - 3) ← distribute both parenthesis

= x² - 3x - 4x +  12 ← collect like terms

= x² - 7x + 12

with middle term = - 7x

Answer:

Step-by-step explanation:

= x(x-3) - 4(x-3)

= x²-3x - 4x + 12

= x² -7x +12

So -7x is the middle term

Answer:

8110

Step-by-step explanation:

80+80+50+50=260

3.14(50)²=7810

7810+260=8110

You posted a lot of questions. I'll do the first four problems to get you started.

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Problem 1

This sequence is arithmetic because we add the same amount (4) each time to get the next term. The first term is -2. The first five terms are: -2, 2, 6, 10, 14

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Problem 2

This sequence is geometric. We multiply each term by 1/4 to get the next term. We start with 8 as the first term. The first five terms are 8, 2, 1/2, 1/8, 1/32.

============================

Problem 3

Similar to problem 1. This time we're adding -19 to each term to get the next one. The starting term is -6. This sequence is arithmetic and the first five terms are -6, -25, -44, -63, -82

============================

Problem 4

Similar to problem 2. This sequence is geometric with common ratio 2/3. First term is 6. The first five terms are 6, 4, 8/3, 16/9, 32/27

Answer:

6000 square millimeters

Step-by-step explanation:

Side length of the slanting side can be calculated using the Pythagorean theorem,

L = sqrt(30^2+40^2) = 50

sufrace area of a triangular prism

= surface area of the end sections + the surface area of the three side faces

= 2*(30*40/2) + 40*(30+40+50)

= 1200 + 4800

= 6000 mm^2

Answer:

D) 6,000 square mm

Step-by-step explanation:

To find the surface area of the triangular prism, find the are of each face.

After adding all the sides' together, you get 6,000 square mm.

Answer:

26 degrees.

Step-by-step explanation:

From the figure it is clear that HI is the diameter and [tex]acr(GI)=128^{\circ}[/tex]. So,

[tex]\angle GOI=128^{\circ}[/tex]

[tex]\angle GOI+\angle GOH=180^{\circ}[/tex]          (linear pair)

[tex]128^{\circ}+\angle GOH=180^{\circ}[/tex]

[tex]\angle GOH=180^{\circ}-128^{\circ}[/tex]

[tex]\angle GOH=52^{\circ}[/tex]

Using central angle theorem of a circle, we get

[tex]\angle HIG=\dfrac{\angle GOH}{2}[/tex]

[tex]\angle HIG=\dfrac{52^{\circ}}{2}[/tex]

[tex]\angle HIG=26^{\circ}[/tex]

Therefore, the measure of angle HIG is 26 degrees.

Answer:

B) x=64, y=21, z=64

Step-by-step explanation:

X=180-116=64

Y cannot equal 115, and one angle is already 95, and that would put it over 180.  The only remaining choice for y=21

z=180-95-21=64

Answer:

an=1*2.5^(n-1)

=2.5^(n-1)

Step-by-step explanation:

Complete question below:

What value, written as a decimal, should Lena use as the common ratio? Lena is asked to write an explicit formula for the graphed geometric sequence. On a coordinate plane, 3 points are plotted. The points are (1, 1), (2, 2.5), (3, 6.25).

Solution

Point (1, 1), (2, 2.5), (3, 6.25).

a=1

ar=2.5

ar^2=6.25

From ar and ar^2

r=6.25/2.5

=2.5

r=2.5

an=ar^(n-1)

Therefore, the explicit formula is

an=1*2.5^(n-1)

=2.5^(n-1)

Answer:

150 I believe but don't quote me on that

Answer:

AX=2 BY=5 CZ=3

Step-by-step explanation:

Lets call AX (x). Once you do so, one can tell that AZ=5-x. CZ is also 5-x. BX is also x. Therefore you can say that BY=7-x which makes CY 7-x. Now for side YZ, CZ is 5-x and CY is 7-x.

5-x+7-x=8

solving that you get x=2

AX=2

BY=7-x=5

CZ=5-x=3

Hope this explains some more than the other answer. Please ask any questions.

Answer:

212

Step-by-step explanation:

3m² + 2p² - 15

Plug in the values.

3(3)² + 2(10)² - 15

Evaluate.

3(9) + 2(100) - 15

27 + 200 - 15

200 + 12

= 212

Answer: 212

Step-by-step explanation:

substitute the given values into the expression

3 ( 3 ) ^ 2 + 2 (10)^ 2 − 15 =

(3 ×9 ) + (2 × 100 ) - 15

= 27 + 200 - 15 =212

Hope this helped

Answer:

4n

Step-by-step explanation:

Answer:

The 4th choice

Step-by-step explanation:

    To figure this out you would have to just lug in all of the numbers into the equation to find the correct answer.

    So first we would plug in the first number for a1 which will be -15. Then we would put in d or the common difference (the number of numbers in between the 2 numbers). So d in this case would be positive 4 since every single time the number is being added to 4.

    Now we can solve, so we would just find all of the choices that do not have  +4 because that will be wrong. Automatically you can see that choices 1 and 2 are wrong and 3 also looks wrong and the only one that matched our formula is 4 and 4 is the correct answer.

Answer:

1/3

Step-by-step explanation:

The slope of the line is found by

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

we have two point ( 0,0) and ( 3,1)

   = ( 1-0)/( 3-0)

   = 1/3

Answer: Undefined

Step-by-step explanation:

In geometry there are three  undefined terms that we use to define other terms:

Hence, the correct option is "Undefined".

Answer:

[tex]\boxed{D. 9x + 36}[/tex]

Step-by-step explanation:

Hey there!

Given info

9(x + 4)

Solve!

9*x = 9x

9*4 = 36

Answer

9x + 36

D. 9x + 36

Hope this helps :)

Answer:

[tex] \boxed{9x + 36}[/tex]

Option D is the correct option.

Step-by-step explanation:

[tex] \mathrm{9(x + 4)}[/tex]

Distribute 9 through the parentheses

[tex] \mathrm{ = 9 x + 9 \times 4}[/tex]

Multiply the numbers

[tex] \mathrm{ = 9x + 36}[/tex]

Hope I helped!

Best regards!

Answer:

.06x

Step-by-step explanation:

So 20 percent of x has to first be represented. So would do .2x. So then we have to find 30% of that number. So we multiply .2x*.3 and we get 0.06x.

I believe this is correct but tell me if I'm wrong

Answer:

0.06x

Step-by-step explanation:

.2x*.3=0.06x

Answer: 12

Step-by-step explanation:

Order requirement:

Size ; flavor and topping

Available variety:

Size = 2

Flavor = 1

Toppings = 6

Number of different ice-cream desserts which can be ordered :

Since one of each of size, topping and flavor must be selected :

(Number of available flavors * number of Toppings available * number of sizes available)

1 * 6 different Toppings = 6 varieties

6 varieties * 2 different sizes = 12 varieties

Therefore, there are 12 different variety of ice-cream dessert she can order.

Answer:

$3.50

Step-by-step explanation:

23.6÷4=5.90   5.90-2.40=3.50

Answer:

$3.50

Step-by-step explanation:

cost of beads - $2.40

cost of pendant - x

2.40(4) + 4x = $23.60

9.60 + 4x = $23.60

4x = $14

x = $3.50

Each pendant costs $3.50.

Hope this helps.

Answer:

it is D. 5

Step-by-step explanation:

The long side (B) will always be (A root 3) meaning, if you just take away the square root of 3, then you get the short side A

Answer:

[tex]\boxed{Shortest\ Leg = 5}[/tex]

Step-by-step explanation:

Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

Where θ = 60 , opposite = [tex]5\sqrt{3}[/tex] and adjacent = shortest leg

=> Tan 60 = [tex]5\sqrt{3}[/tex] / shortest leg  (Tan 60 = √3)

=> Shortest Leg = [tex]\frac{5\sqrt{3} }{\sqrt{3} }[/tex]

=> Shortest Leg = 5

Answer:

90601

Step-by-step explanation:

we have to find  smallest number by which 2408 should be multiplied to get a perfect cube.

First lets find prime factor of 2408 and power these prime factors have

2408 = 2*1204 = 2*2*602 = 2*2*2*301= 2*2*2*7*43

thus,

2408 = 2^3*7*31

we know that a cube is a number raised to the power three

in 2408

2 has a power of three

but 7 and 31 and there is power of one,

thus we need to make

power of 7 and 31 three by multiplying

7 with 7*7

and 31 with 31*31

thus,

2^3*7*31*7*7*31*31 is the minimum cube value for this number

2^3*7*31*7*7*31*31 = 2^3*7^3*31^3 = 2408 * 7^2*31^2 = 2408*90601

Thus, smallest number which should be multiplied with 2408 to make it a perfect cube is 90601

Answer:

x=10

Step-by-step explanation:

The triangles are similar so we can use ratios to solve

6.5      (6.5+6.5)

------ = -----------------------

5              x

6.5      (13)

------ = -----------------------

5              x

Using cross products

6.5x = 65

Divide by 6.5

6.5x/6.5 = 65/6.5

x = 10

Answer:

Yes

Step-by-step explanation:

We can draw a quadrilateral with no parallel lines and at least one right angle

Answer:

Yes

Step-by-step explanation:

It's possible to draw a quadrilateral with no parallel lines and with 1 right angle        

I really hope this helps I know how you feel (:-D)