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Marta_Voda [28]
2 years ago
9

Peter has twice as many stickers as Joe. Joe has 40 more stickers than Emily. They have 300 Stickers altogether. How many sticke

rs does Peter have?
Mathematics
1 answer:
GarryVolchara [31]2 years ago
4 0

Answer:

170

Step-by-step explanation:

Equations derived from given info.

  • P=2J
  • J=E+40
  • P+J+E=300

Use some substitution now.

  • P=2(E+40)
  • J=E+40
  • P+J+E=300

Substitute first and second equation into third.

  • 2(E+40)+E+40+E=300
  • 2E+80+E+40+E=300
  • 4E+120=300
  • 4E=180
  • E=45

Emily has 45 stickers. But we want to know what Peter has.

Use P=2(E+40)

  • P=2(45+40)
  • P=90+80
  • P=170

Peter has 170 stickers.

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Step-by-step explanation:

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What is the exact value of the cos F?
Galina-37 [17]

Answer:

cos(F) = 9/41

Step-by-step explanation:

The triangles are similar, so you know that ...

... cos(D) = cos(A) = 40/41.

From trig relations, you know ...

... cos(F) = sin(D)

and

... sin(D)² +cos(D)² = 1

So ...

... cos(F) = sin(D) = √(1 -cos(D)²) = √(1 -(40/41)²) = √(81/1681)

... cos(F) = 9/41

_____

The ratio for cos(A) tells you that you can consider AB=40, AC=41. Then, using the Pythagorean theorem, you can find BC = √(41² -40²) = √81 = 9.

From the definition of the cosine, you know cos(C) = BC/AC = 9/41. Because the triangles are similar, you know

... cos(F) = cos(C) = 9/41

7 0
2 years ago
A mechanical dart thrower throws darts independently each time, with probability 10% of hitting the bullseye in each attempt. Th
Arturiano [62]

Answer:

The probability of hitting the bullseye at least once in 6 attempts is 0.469.

Step-by-step explanation:

It is given that a mechanical dart thrower throws darts independently each time, with probability 10% of hitting the bullseye in each attempt.

The probability of hitting bullseye in each attempt, p = 0.10

The probability of not hitting bullseye in each attempt, q = 1-p = 1-0.10 = 0.90

Let x be the event of  hitting the bullseye.

We need to find the probability of hitting the bullseye at least once in 6 attempts.

P(x\geq 1)=1-P(x=0)       .... (1)

According to binomial expression

P(x=r)=^nC_rp^rq^{n-r}

where, n is total attempts, r is number of outcomes, p is probability of success and q is probability of failure.

The probability that the dart thrower not hits the bullseye in 6 attempts is

P(x=0)=^6C_0(0.10)^0(0.90)^{6-0}

P(x=0)=0.531441

Substitute the value of P(x=0) in (1).

P(x\geq 1)=1-0.531441

P(x\geq 1)=0.468559

P(x\geq 1)\approx 0.469

Therefore the probability of hitting the bullseye at least once in 6 attempts is 0.469.

3 0
2 years ago
If 2x – 3 ≤ 5, what is the greatest possible value of 2x + 3 ? a.4 b.8 c.10 d.11
harina [27]

Answer:

Hope it is correct :) :)

8 0
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