Roger has 50 ounces of water. If he drinks 30% of it, how
much water will he have left?

Answer:

b= sin(43°) * 8 / sin(55°) ≈ 6.7

Step-by-step explanation:

Regarding the law of sines, each angle corresponds to the side opposite of it. Here, that means that the 82 degree angle is opposite of side c (so they correspond) and that the 55 degree angle corresponds to the side with 8cm. However, we are trying to find the length of side b. Therefore, assuming that the side with 8cm is side A, if we know that

sin A / a = sinB/b = sin C / C

= sin(55°)/8 = sinB/b = sin(82°) / c, we can take c out of the equation to get

sin(55°)/8 = sinB/b

If we know sinB, we can multiply both sides by 8 to remove a denominator to get

sin(55°) * b / 8 = sinB

multiply both sides by 8 to remove the other denominator to get

sin(55°) * b = sinB * 8

divide both sides by sin(55°) to isolate the b

b = sinB * 8/sin(55°).

Therefore, if we know sinB, we can figure out the length of b.

Because the angles of a triangle add up to 180 degrees, we can say that

180 = 82 + 55 + angle B

180 = 137 + B

subtract both sides by 137 to isolate B

43 = B

b= sin(43°) * 8 / sin(55°) ≈ 6.7

Answer:

(x+2)^2 + (y-5)^2 = 9

Step-by-step explanation:

The equation of a circle is given by

(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius

(x- -2)^2 + (y-5)^2 = 3^2

(x+2)^2 + (y-5)^2 = 9

Answer: The marked price is 40% more than the original price

40% - 25% = 15% or 1450

Marked price = 140%

140 × 1450 ÷ 15 = 13533. 33

Step-by-step explanation:

Answer:

c = 9.7

Step-by-step explanation:

Using the law of sines

sin 55       sin 82

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

8                    c

Using cross products

c sin 55 = 8 sin 82

c = 8 sin 82 / sin 55

c=9.67115

To the nearest tenth

c = 9.7

Answer:

A. 314 in^3

Step-by-step explanation:

To solve the volume of a cone:

[tex]v = \pi r^2\frac{h}{3}[/tex]

Answer:

0.1294

Step-by-step explanation:

Number of chocolates in box = 38

Number of nuts = 8

Number of caramel = 16

Number of solid chocolate = 14

Since 2 are selected in a row and not replaced, then;

Probability of first being solid chocolate = 14/38

Probability of second being solid chocolate after first one = 13/37

Thus;

P(2 selected in a row being solid chocolate) = 14/38 × 13/37 = 0.1294

Answer:

c

Step-by-step explanation:

Answer:

C. y - 7 < 2x - 6

Step-by-step explanation:

A. y + 7 < 2x + 6

0 + 7 < 2(0) + 6

7 < 0 + 6

7 < 6 —————- FALSE

B. y + 7 < 2x - 6

0 + 7 < 2(0) - 6

7 < 0 - 6

7 < -6 —————FALSE

C. y - 7 < 2x - 6

0 - 7 < 2(0) - 6

-7 < 0 - 6

-7 < -6 —————TRUE

D. y - 6 < 2x - 7

0 - 6 < 2(0) - 7

-6 < 0 - 7

-6 < -7 ————— FALSE

Answer:

72?

Step-by-step explanation:

V=whl=4 x 2 x9=72

Answer:

17

Step-by-step explanation:

8+2+(3×3-2)=8+2+(9-2)=8+2+7=17

mistake in the first step

firstly we do × and ÷

then + and -

Answer:

SA = 37.5 units^2

Step-by-step explanation:

2 1/2 = 2.5

the Surface Area of the cube

SA = 6a^2

SA = 6(2.5)^2

SA = 6(6.25)

SA = 37.5 units^2

Answer:

H. 40 inches

Step-by-step explanation:

On Wednesday, he is 40 inches taller. ... That would make 5 days of growth, for 100 inches. But this is only 3 days therefore he would grow 40 inches taller

Answer:0.6666...

Step-by-step explanation:

Dividing

Answer:

Call option and put option ( D )

Step-by-step explanation:

During hedging in stock/financial markets both the Call and put option can be used to hedge the trading position of the trader against the change in exchange. This is because the call or put option is used depending on the initial position of the trader.

Call option is used when the trader is currently holding a short position

Put option is used when the trader is currently holding a long position

Answer:

Step-by-step explanation:

Use the Pythagorean Theorem

diagonal² = 16² + 12² = 400

diagonal = √400 = 20 cm

Answer:

Step-by-step explanation:

Answered by Gauthmath

Answer:

See below.

Step-by-step explanation:

When Brian passes Alex they both have travelled the same distance.

Call this distance d.

Let the speed that Brian passes = x miles/hour.

Distance = speed * time  so:

For Alex:

d = (x - 5) * 1.5        ( Alex cycles for 1 + 30 minutes =  1.5 hours)

For Brian:

d = x * 1

So substituting d = x in Alex's equation:

x = 1.5(x - 5)

x = 1.5x - 7.5

7.5 = 0.5x

7/5 / 0.5 = x

15 = x.

ANSWER:

Brian's speed is 15 miles/hour.

Alex's speed is 15 - 5 = 10 miles/hour.

Answer: c. BC/YZ=6/3

Step-by-step explanation:

trust

Answer: The answer is C. BC/YZ = 6/3

Step-by-step explanation:

Got it right on edge 2023

Answer:

4

Step-by-step explanation:

4 because 4^2 = 16.

Answer:

16⅜ cups

Step-by-step explanation:

Start by getting the same denominator on both fractions and by eliminating the mixed fraction. So our problem is:

15¾ cups + ⅝ cups = ?

15¾ = 63/4 = 126/8

126/8 + ⅝ = 131/8 = 16⅜

х=10

I'm so sorry, i don't know how it's called (because English isn't my native language) but there are angles that have the same value

maybe u'll tell me..

Answer:

2 solutions

Step-by-step explanat

ion:|2x-3|-|3x-2|=0

<=>|2x-3|=|3x-2|

<=>2x-3=3x-2

Or 2x-3=-3x+2

<=>2x-3x=-2+3

or 2x+3x=2+3

<=>x=-1

Or x=1

Answer: ∠A = 20°; ∠B = 59°; ∠C = 101°

Step-by-step explanation:

According to the problem:

All interior angles within a triangle adds up to 180°:

∠A + ∠B + ∠C = 180°

[tex]A+(4A-21)+(5A+1)=180\\\\A+4A+5A-21+1=180\\\\10A=180+21-1\\\\10A=200\\\\A=20\°[/tex]

Substitute in the value of ∠A into the other equations:

∠B = 4 · ∠A - 21° = 4(20°) - 21° = 80° - 21° = 59°

∠C = 5 · ∠A + 1° = 5(20°) + 1° = 100° + 1° = 101°

Answer:

g(x) = [tex](\frac{x}{3})^2[/tex] which is A.

Step-by-step explanation:

I did this before. You have to trust me.

Answer:

abcd is a quadrilateral

so , d is ( -1,4 )

c is ( 0,-4 )

b is ( 0,-2)

and

a is ( 2,-2 )

Answer:

Hello,

Step-by-step explanation:

0 girls and 8 boys :

[tex]\left(\begin{array}{c}10\\ 8\end{array}\right)=10*9*8*7*6*5*4*3/8!=45\\\\[/tex]

1 girl and 7 boys:

[tex]\left(\begin{array}{c}6\\ 1\end{array}\right)*\left(\begin{array}{c}10\\7\end{array}\right)=6*10*9*...*4/7!=6*120=720\\\\[/tex]

2 girl and 6 boys:

[tex]\left(\begin{array}{c}6\\ 2\end{array}\right)*\left(\begin{array}{c}10\\6\end{array}\right)=60*210=1260\\[/tex]

3 girl and 5 boys:

[tex]\left(\begin{array}{c}6\\ 3\end{array}\right)*\left(\begin{array}{c}10\\5\end{array}\right)\\[/tex]

4 girls and 4 boys:

[tex]\left(\begin{array}{c}6\\ 4\end{array}\right)*\left(\begin{array}{c}10\\4\end{array}\right)[/tex]

5 girls and 3 bys:

[tex]\left(\begin{array}{c}6\\ 5\end{array}\right)*\left(\begin{array}{c}10\\3\end{array}\right)[/tex]

I let you to calculate and make the sum.

Answer:

2.5L of 10% salt solution and 7.5L of the 30% salt solution

Step-by-step explanation:

let the amount of L in the 10% solution be 'x'

let the amount of L in the 30% solution be '10-x'

* because they add up to a total of 10L

10%(x) + 30%(10-x) = 25%(10)

0.1x + 3 - 0.3x = 2.5

-0.2x = -0.5

x = 2.5

x =2.5

10-x = 7.5

2.5 of 10% solution and 7.5% of 30% solution

Answer:

1. 3x^3 - 2x^2 - x

2. -4x^2 + x

Step-by-step explanation:

Answer:

(-9,1.5)

Step-by-step explanation:

(-6*1.5, 1*1.5)

Answer:

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