Given that DE is a midsegment for ABC and the length of DE is 8 units. What is the length of BC?

Answer:

220 possible ways

Step-by-step explanation:

Given

[tex]n = 12[/tex] --- people

[tex]r = 3[/tex] -- posts [tex](President, Vice\ President\ and\ Secretary)[/tex]

Required

Determine the number of selection

Since there is no condition attached, the number of selection is:

[tex]Selection = ^nC_r[/tex]

Substitute values for n and r

[tex]Selection = ^{12}C_3[/tex]

Apply combination formula

[tex]Selection = \frac{12!}{(12-3)!3!}[/tex]

[tex]Selection = \frac{12!}{9!3!}[/tex]

[tex]Selection = \frac{12*11*10*9!}{9!*3*2*1}[/tex]

[tex]Selection = \frac{12*11*10}{6}[/tex]

[tex]Selection = \frac{1320}{6}[/tex]

[tex]Selection = 220[/tex]

Hence, there are 220 possible ways

Answer:

Step-by-step explanation:

$8.75

hope it helps

Answer:

24

Step-by-step explanation:

half 32 and half it again u get 8 then u do 32-8

Answer:

{0, infinity)

Step-by-step explanation:

range is always the y coords

Answer:

By opting for the second option, Alice would save $ 15,740.00  in total mortgage cost

Step-by-step explanation:

In order to determine the better of the two options available, we need to determine the total cost under each option as follows:

Option 1:

cost of house=$625,000

loan amount=$625,000-(20%*$625,000)=$500,000

loan amount=monthly payment*(1-(1+r)^-n/r

monthly payment is the unknown

r=monthly interest rate=4%/12=0.33333333%

n=number of monthly payments in 30 years=30*12=360

500,000=monthly payment*(1-(1+0.33333333% )^-360/0.33333333%

500,000=monthly payment*(1-0.301795869 )/0.003333333

500,000=monthly payment*0.698204131 /0.003333333

monthly payment=500,000*0.003333333 /0.698204131

monthly payment=$ 2,387.08  

total monthly payments=$ 2,387.08*360=$859,348.80

Option 2:

upfront fee=$10,000

loan amount=monthly payment*(1-(1+r)^-n/r

monthly payment is the unknown

r=monthly interest rate=3.75%/12=0.3125%

n=number of monthly payments in 30 years=30*12=360

500,000=monthly payment*(1-(1+0.3125%  )^-360/0.3125%

500,000=monthly payment*(1-0.325222459  )/0.003125

500,000=monthly payment*0.674777541  /0.003125  

monthly payment=500,000*0.003125  /0.674777541=$2,315.58  

Total cost=total monthly payments+upfromt fee

total cost=($2,315.58 *360)+$10,000=$843,608.80  

savings by opting for the second option=$859,348.80-$843,608.80  

Step one: (((x2)+x)+1)+((0-(2x23•x))+5)

Step two: Check for a perfect cube.  2.1    -2x24+x2+x+6  is not a perfect cube.

2.2      Factoring:  -2x24+x2+x+6

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  x+6

Group 2:  -2x24+x2

Pull out from each group separately :

Group 1:   (x+6) • (1)

Group 2:   (2x22-1) • (-x2)

The groups have no common factor and can not be added up to form a multiplication.

So the answer would be,  -2 (x24) + (x2) ++ 6.

Answer:

The toll on a bridge is $1.00 \:for\: cars\: and\: $2.50 for trucks. In one hour, a tollbooth operator collects a total of $105 in tolls.

Equation :---

[tex]\boxed{c + 2.5t = 105}[/tex]

Above equation represents the relationship between the number of cars, c, and the number of trucks, t, which could have passed by this tollbooth.

Answer: Numbers of servings: 10 and 13, Liters of punch: 14

Step-by-step explanation:

Number of servings - 6 = Liters of punch.

Answer:

The answer is 646.02 tell me if you need an explaination

Answer:

there are 12 cans

Step-by-step explanation:

6 x 2 =12

Given:

In triangle ABC, m∠A=(8x-2)°, m∠B=(2x-8)° and m∠C=(94-4x)°.

To find:

The sides of the triangle ABC in order from shortest to  longest.

Solution:

In triangle ABC,

[tex]m\angle A+m\angle B+m\angle C=180^\circ[/tex]              (Angle sum property)

[tex](8x-2)^\circ+(2x-8)^\circ+(94-4x)^\circ=180^\circ[/tex]

[tex](6x+84)^\circ=180^\circ[/tex]

[tex]6x+84=180[/tex]

[tex]6x=180-84[/tex]

[tex]6x=96[/tex]

Divide both sides by 6.

[tex]x=\dfrac{96}{6}[/tex]

[tex]x=16[/tex]

Now,

[tex]m\angle A=(8(16)-2)^\circ[/tex]

[tex]m\angle A=(128-2)^\circ[/tex]

[tex]m\angle A=126^\circ[/tex]

Similarly,

[tex]m\angle B=(2(16)-8)^\circ[/tex]

[tex]m\angle B=(32-8)^\circ[/tex]

[tex]m\angle B=24^\circ[/tex]

And,

[tex]m\angle C=(94-4(16))^\circ[/tex]

[tex]m\angle C=(94-64)^\circ[/tex]

[tex]m\angle C=30^\circ[/tex]

In a triangle the smaller angle has shorter opposite side and larger angle has longer opposite side.

[tex]24^\circ<30^\circ<126^\circ[/tex]

[tex]m\angle B<m\angle C<m\angle A[/tex]

[tex]AC<AB<BC[/tex]

List the sides of triangle ABC in order from shortest to  longest is AC:AB:BC.

Therefore, the correct option is A.

Answer:

(a)

A single avocado costs $1

A single tomato costs $0.5

(b)

An avocado costs twice as much as a tomato

Step-by-step explanation:

Represent the tomatoes with T and the avocados with A.

So, we have:

[tex]4T + 8A = 10[/tex] --- (1)

[tex]6T + 14A = 17[/tex] --- (2)

Solving (a): The price of each

Multiply (1) by 1.5

[tex]1.5(4T + 8A = 10)[/tex]

[tex]6T + 12A = 15[/tex] --- (3)

Subtract (3) from (2)

[tex](6T + 14A = 17) - (6T + 12A = 15)[/tex]

[tex]6T - 6T + 14A - 12A = 17 - 15[/tex]

[tex]14A - 12A = 17 - 15[/tex]

[tex]2A = 2[/tex]

Divide both sides by 2

[tex]A = 1[/tex]

Substitute 1 for A in (1)

[tex]4T + 8A = 10[/tex]

[tex]4T + 8(1) = 10[/tex]

[tex]4T + 8 = 10[/tex]

Make 4T the subject

[tex]4T = 10 - 8[/tex]

[tex]4T = 2[/tex]

Divide both sides by 4

[tex]T = \frac{2}{4}[/tex]

[tex]T = 0.5[/tex]

Solving (b): Analysis

In (a), we have:

[tex]T = 0.5[/tex]

[tex]A = 1[/tex]

We can say that an avocado costs twice as much as a tomato

Answer:

B

Step-by-step explanation:

Okay, so we know they can run 1/4 a mile in 25 seconds. Now we want to know how far they can run in a minute ( 60 sec.). Because there is 25 seconds in 60 seconds 2.4 times, we multiply 1/4 by 2.4. We get 0.6. We know that there is 60 minutes in an hour, so we multiply 0.6 by 60. Now we know they can run 36 miles in an hour/ 36 miles per hour. So that eliminates C and D.

Anyways, B is correct because if you divide 1/4 by 25 you get 0.01. Multiply that by 60 to get a minute. (Because there is 60 seconds in a minute) Which is 0.6. Then multiply it again by 60 for an hour( because there is 60 minutes in an hour), and you get 36 hours.

Answer:

70 units

Step-by-step explanation:

Answer:

1) Emilio's total saving - $127.5

2) 33.6ft

Step-by-step explanation:

1) $63.75 x 2 = $127.5

2) 308ft - 274.4ft = 33.6ft

Answer:

30+(−17) is the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

((((((.5 mile = .25 hour<<<<<<<<<<<<<<<<<<<<<<<<<<

Multiply both sides by 4, because there are 4 quarters in 1 hour

(4)(.5) = (.25)(4)

2 miles =1 hr

Multiply both sides of the original equation by 3 to figure out how far in 3/4 of an hour

(3)(.5) = (3)(.25)

1.5 miles = 3/4 of an hour

now add the two answers together to figure out that the person walked 3.5 miles in 1 3/4 hours

***You also could have multiplied both sides of the original equation by 7, recognizing that that there are 7 quarters in 1.75 hours.

Answer:

225

Step-by-step explanation:

8+7=15

15*15=225

Answer:

225

Step-by-step explanation:

8 + 7 = 15

15² = 225

hope this helps...

Answer:

x in all equations just normally means 1

Step-by-step explanation:

x is always 1

Answer:

Step-by-step explanation:

ΔSRQ and ΔVTU are similar Triangle.

Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.

Given two triangles, ΔRQS and ΔVUT such that,

RS = 16, QR= 64 and VT = 8, UT = 32

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.

From the above condition since,

∠R = ∠T

and

[tex]\frac{QR}{SR} = \frac{UT}{VT} = \frac{4}{1}[/tex]

Thus,

ΔSRQ and ΔVTU are similar from the congruency  property of SAS.

Learn more about congruent triangles here:

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Answer:

I need  a picture or something else to give answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

I HOPE IT HELPS :)

Answer:

96 feet squared

Step-by-step explanation:

to find the triangles area you would have to multiply 16 times 12 which would get you 192 then you would have to divide it by 2. Therefore the answer is 96.

Answer:

3 feet

Step-by-step explanation:

720ft

1ft:240ft

720/240=3

3ft:720ft

Answer: Angle ABD is 39°

Step-by-step explanation:

Angle CBA is 90° (given by "box" on the corner of the right triangle)

Angle CBD is given as 51°

Subtract:

90° - 51° = 39°

The probability that more than one coin lands heads up is 0.9375.

In an experiment with two possible outcomes, the likelihood of exactly x successes on n repeated trials is known as the binomial probability.

The binomial probability is [tex]^nC_xp^xq^{n-x}[/tex].

Given, Four fair coins are flipped and the number of heads that land face up are counted.

Let, 'p' be the probability of getting a head and 'q' be the probability of getting a tail,

So, p = 1/2 and q= 1/2.

Therefore, The probability that more than one coin lands heads up is,

P(X ≥ 1) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 3).

P(X ≥ 1) = [tex]^4C_1p^1q^3 + ^4C_2p^2q^2 + ^4C_3p^3q^1 + ^4C_4p^4q^0[/tex].

P(X ≥ 1) = [tex]^4C_1(1/2)^1(1/2)^3 + ^4C_2(1/2)^2(1/2)^2 + ^4C_3(1/2)^3(1/2)^1 + ^4C_4(1/2)^4(1/2)^0[/tex].

P(X ≥ 1) = 4(0.5×0.125) + 6(0.25×0.25) + 4(0.125×0.5) + 1(0.0625).

P(X ≥ 1) = 0.25 + 0.375 + 0.25 + 0.0625.

P(X ≥ 1) = 0.9375.

So, The probability of getting one or more heads is 0.9375.

learn more about the binomial distribution of probability here :

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Answer:

A will be at 6,6

Step-by-step explanation:

I think this because the graph is the same so it most likely will be the at the same position. Hope this is right !