Write the expression as the sine, cosine, or tangent of an angle.sin 9x cos x - cos 9x sin x

Answers

Answer 1
Answer: sin 9x cos x - cos 9x sin x = sin(9x - x) = sin 8x

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A runner has a track lap of one minute while at a run, five minutes while at a jog, 7 minutes while at a walk. If 2/5 of the lap is paced at a run, 1/2 at a jog and 1/10 at a walk what is the total track lap time of the runner. Write the solution as a mixed number or a fraction in lowest terms

Answers

24 seconds running
2 minutes 30 seconds jogging
42 seconds walking
3 minutes 36 seconds in that lap

Final answer:

The total track lap time of the runner is 2 2/5 minutes or 2.4 minutes.

Explanation:

The total track lap time of the runner can be calculated by summing up the individual time spent at each pace (run, jog, walk). Each pace's time is first multiplied by the fraction of the lap completed at that pace.

For the run, the calculation is 2/5 of 1 minute which is 2/5 minute.

For the jog, the calculation is 1/2 of 5 minutes which is 5/2 = 2 1/2 minutes or 2.5 minutes in decimal form.

For the walk, the calculation is 1/10 of 7 minutes which is 7/10 = 0.7 minutes.

Adding these times together gives a total of (2/5) + (5/2) + (7/10) = 12/5 = 2 2/5 minutes or 2.4 minutes in decimal form.

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How do I solve for the equation s=3f-24? Solve for f

Answers

s-3f=-24
-3f=-24-s
3f=24+s
f=24+s/3

Final answer:

To solve for 'f' in the algebraic equation 's=3f-24', add 24 to 's' and then divide the result by 3.

Explanation:

To solve the algebraic equation 's=3f-24' for 'f', you would first decide to isolate 'f'. To do this, start by getting rid of the '-24' on the right side of the equation by adding 24 to both sides. This would simplify the equation to 's+24=3f'. Next, divide both sides of the equation by 3. This step will result in a final solution of 'f=(s+24)/3'. So, to solve for 'f' in the provided equation, simply add 24 to the original 's' value and then divide the result by 3.

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Tres amigos: Andrés, Braulio y Ciro, juegan 3 apuestasentre sí, con la condición de que el que pierde duplique
el dinero de los demás. Si cada uno pierde una apuesta en el orden de presentación y al final terminan con
S/.48, S/.56 y S/.28 respectivamente, ¿Quién de los
amigos ganó más dinero y cuánto?

Answers

Answer:

La persona que ganó más dinero fue Braulio por S/.16

Step-by-step explanation:

Deje que la cantidad inicial sea Andrés X, Braulio Y y Ciro Z

Luego, dado que cada uno pierde una apuesta en el orden presentado, tenemos;

Después de la primera apuesta, tenemos;

Andrés X-Y-Z, Braulio (Y + Y), Ciro (Z + Z)

En la segunda apuesta, tenemos;

2 (X-Y-Z), 2Y - (X-Y-Z) - 2Z, 2Z + 2Z

2 (X-Y-Z), 3Y - X -Z, 4Z

En el tercero

4 (X-Y-Z), 6Y - 2X - 2Z, 4Z-2 (X-Y-Z) - (3Y - X -Z)

4 (X-Y-Z), 6Y - 2X - 2Z, 7Z - X - Y

4 (X-Y-Z) = 0.48 .............................. (1)

6Y - 2X - 2Z = 0.56 ...................... (2)

7Z - X - Y = 0.28 ............................ (3)

Multiplicamos las ecuaciones (2) por 2 y restamos la ecuación (1), tenemos;

12Y - 4X - 4Z - 4X + 4Y + 4Z = 0.56 * 2 - 0.48 = 0.64

16Y - 8X = 0.64 ...................... (4)

Multiplicamos las ecuaciones (2) por 7/2 y sumamos a la ecuación (3), tenemos;

21Y - 7X - 7Z + 7Z - X - Y = 7/2 * 0.56 + 0.28

20Y - 8X = 2.24 ...................... (5)

Restando la ecuación (4) de la ecuación (5) tenemos;

20Y - 8X - 16Y - 8X = 2.24 - 0.64 =

4Y = 1.6

Y = 1.6 / 4 = 0.4

De la ecuación (5), tenemos;

20Y - 8X = 20 * 0.4 - 8X = 2.24

8X = 8 - 2.24 = 5.76

X = 5,76 / 8 = 0,72

De la ecuación (3), tenemos;

7Z - X - Y = 7Z - 0.72 - 0.4 = 0.28

7Z = 1.4

Z = 1.4 / 7 = 0.2

Por lo tanto tienen inicialmente

X₁ = 0.72

Y₁ = 0.4

Z₁ = 0.2

Después de jugar tienen;

X₂ = 0.48

Y₂ = 0.56

Z₂ = 0.28

Los cambios son

Andrés 0.48 - 0.72 = -0.24

Braulio; 0.56 - 0.4 = 0.16

Ciro 0.28 - 0.2 = 0.08

La persona que ganó más dinero fue Braulio por S/.16

4. You have a deck of 40 number cards: five of each number 2 to 9. You shuffle the deck, pick a card, look at it, return it to the deck, and then repeat for a second card. Determine each theoretical probability. a) sum is 12 b) difference is less than 5 c) product is odd​

Answers

To determine the theoretical probabilities, we'll analyze the different possible outcomes for each case.

Total number of cards = 40 (5 cards for each number from 2 to 9)

a) Sum is 12:

There are several combinations of cards that can result in a sum of 12:

  • 3 and 9
  • 4 and 8
  • 5 and 7
  • 7 and 5
  • 8 and 4
  • 9 and 3

Total favorable outcomes = 6 (since there are 6 possible combinations)

Total possible outcomes (since you're drawing two cards) = 40 * 40 = 1600

Probability (sum is 12) = (Number of favorable outcomes) / (Total possible outcomes)

Probability (sum is 12) = 6 / 1600 = 0.00375

b) Difference is less than 5:

There are several combinations of cards that can result in a difference less than 5:

  • 2 and 3
  • 3 and 2
  • 3 and 4
  • 4 and 3
  • 4 and 5
  • 5 and 4
  • 5 and 6
  • 6 and 5
  • 6 and 7
  • 7 and 6
  • 7 and 8
  • 8 and 7
  • 8 and 9
  • 9 and 8

Total favorable outcomes = 14

Total possible outcomes = 1600

Probability (difference is less than 5) = 14 / 1600 = 0.00875

c) Product is odd:

For the product to be odd, one or both of the numbers drawn must be odd. Since there are five odd numbers (3, 5, 7, 7, 9), and each number has five cards, the total number of favorable outcomes is 5 + 5 + 5 + 5 + 5 = 25.

Total possible outcomes = 1600

Probability (product is odd) = 25 / 1600 = 0.015625

To summarize:

  • a) Probability (sum is 12) ≈ 0.00375
  • b) Probability (difference is less than 5) ≈ 0.00875
  • c) Probability (product is odd) ≈ 0.015625

Help me please !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

we have an geometric progression:
nth term=a₁r^(n-1)
nth term=y
a₁ is the first term=10
r=common ratio=a₂/a₁=20/10=2
n=x
nth term=a₁r^(n-1)

Therefore
y=10.2^(x-1)=(2*5)2^(x-1)=(5)2^(x-1+1)=(5)2^x

Answer: y=[5][(2)]^[x]

To check:
if x=1   ⇒y=(5)(2)=10
if x=2    ⇒y=(5)(4)=20
if x=3    ⇒y=(5)(8)=40

When ordering a sundae, you may choose three toppings from their list of 10 available. Assuming that your chosen toppings must be different, how many different sundaes with three toppings can you order?

Answers

Answer:

there are 120 different sundaes with three toppings you can order.

Step-by-step explanation:

If the chosen toppings must be different, then that means it's a Combination where the order doesn't matter (as long as they're all different).

Equation: 10C3

Forming Equation: 10!/(10-3)!*3!=10*9*8*7!/7!*3!=10*9*8/6=720/6=120

Therefore, there are 120 different sundaes with three toppings you can order.