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Serhud [2]
4 years ago
5

Clara has $67 in her piggy bank. She spent x dollars on a dog bowl and now has $57.4 remains.

Mathematics
1 answer:
kolezko [41]4 years ago
6 0

Answer:

B) 57.4+x=67

Step-by-step explanation:

We take the amount in the piggy bank.  Then we take the amount spent and add it to the amount she has left.  These two amounts should be equal

piggy bank = spent + left

67 = x + 57.40


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An urn initially contains 5 white and 7 black balls. Each time a ball is selected, its color is noted and it is replaced in the
iragen [17]

Answer:

A. P("Select 2 black balls and then select 2 white balls")=35/768

Step-by-step explanation:

A. First, we have to get an idea of what our experiment talks about:

If I take a black ball, then we note its color and put it back to the urn with 2 more balls of the same color.

So, every time that we take a ball the quantity of balls in the urn changes with the probability that we had before replacing. The first case (that the first ball you select is black) would go like this:

P("Select a black ball first try") = 7 (number of black balls)/12 (total of balls in the urn)

P(B₁)=7/12

Then, the amount of balls in the urn rise to 14 (12 + 2 balls added) and now the quantity of black balls it´s 9 (7 + 2 added). The urn currently has 9 black balls and 5 white balls, of course:

P("Select black ball second try after getting a black ball before") = 9 (number of black balls)/ 14 (total of balls in the urn)

P(B₁B₂)=9/14

<u>Notice that while we keep taking black balls, the quantity of white ball keeps constant</u> and, for the probability that we take a white ball, we just consider the change in the number of balls in the urn

P(B₁B₂W₃)=5/16

And now, we consider the new white balls that are put in the urn (2 white balls, for a total of 18 and 7 white balls):

P(B₁B₂W₃W₄)=7/18

Because all these probabilities are chained and everything comes from the first ball we choose <u>(if you use a tree diagram, they will be in the same branch</u>), we multiply the probabilities to find the probability that all happens in the same experiment:

P(B₁)*P(B₁B₂)*P(B₁B₂W₃)*P(B₁B₂W₃W₄) = 7/12 * 9/14 * 5/16 * 7/18 = 2205/48384

P(B₁)*P(B₁B₂)*P(B₁B₂W₃)*P(B₁B₂W₃W₄)=35/768

And this is the final answer

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\huge\mathfrak{\underline{answer:}}

\large\bf{\angle ACD = 105°}

__________________________________________

\large\bf{\underline{Here:}}

  • BCD is an isosceles right triangle , right angled at D
  • ABC is an equilateral triangle

\large\bf{\underline{To\:find:}}

  • ∠ ACD

\large\bf{In\: triangle\:ABC:}

❒ Sum of all angles is 180° , since it is an equilateral triangle all the three angles would be same

\large\bf{\underline{So}}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\bf{⟼\angle ACB = \frac{180}{3}}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\bf{⟼\angle ACB = 60°}

\large\bf{In\: triangle\:BDC}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\bf{⟼\angle D = 90°}

\bf{⟼\angle DBC =\angle DCB }(Isosceles triangle)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\bf{⟼\angle DBC + \angle BDC + \angle DCB = 180° }

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\bf{⟼2\angle DCB + 90° = 180°}

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\large\bf{\underline{Therefore,}}

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