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Phoenix [80]
3 years ago
8

Last week, Sarah bought a designer shirt at the sale price of $24. The original cost of the shirt was $40. What percent represen

ts the discount that Sarah received when buying the sweater?
Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
7 0

Answer:

40%

Step-by-step explanation:

Amount of money discounted

= $40 - $24

= $16

Percentage of discounted money

= 16/40 x 100%

= 40%

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Answer:

P(A_{1}|B ) =\frac{mp}{1+p(m-1)}

Step-by-step explanation:

For mutually exclusive events as A1, A2, A3, etc, Bayes' theorem states:

P(A|B)= \frac{P(B|A)P(A)}{P(B)}

P(A|B) is a conditional probability: the likelihood of event A occurring given that B is true.

P(B|A) is a conditional probability: the likelihood of event B occurring given that A is true.

P(A) is the probability that A occurs

P(B) is the probability that B occurs

For this problem:

A1 is the probability that the student knows the answer

A2 is the probability that the student guesses the answer

B is the probability that the student answer correctly

P(A_{1})=p \\P(A_{2})=1-p \\P(B|A_{1})=1 \\P(B|A_{2})=\frac{1}{m} \\P(B)= P(A_{1})P(B|A_{1}) + P(A_{2})P(B|A_{2})= p+\frac{1-p}{m} \\

P(B|A₁) means the probability that the answer is correct when he knew the answer

P(B|A₂) means the probability that the answer is correct when he guessed the answer

P(A₁|B) means the probability that he knew the answer when the answer was correct

Replacing everything in the Bayes' theorem you get:

P(A_{1}|B)= \frac{P(B|A_{1})P(A_{1})}{P(B)}=\frac{(1)(p)}{p+\frac{1-p}{m}} =\frac{mp}{mp+1-p} =\frac{mp}{1+p(m-1)}

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Step-by-step explanation:

<h2>[1]</h2>

  • SI = $250
  • Rate (R) = 12\sf \dfrac{1}{2} %
  • Time (t) = 4 years

\longrightarrow \tt { SI = \dfrac{PRT}{100} } \\

\longrightarrow \tt { 250 = \dfrac{P \times 12\cfrac{1}{2} \times 4}{100} } \\

\longrightarrow \tt { 250 = \dfrac{P \times \cfrac{25}{2} \times 4}{100} } \\

\longrightarrow \tt { 250 = \dfrac{P \times 25 \times 2}{100} } \\

\longrightarrow \tt { 250 = \dfrac{P \times 50}{100} } \\

\longrightarrow \tt { 250 \times 100 = P \times 50} \\

\longrightarrow \tt { 25000 = P \times 50} \\

\longrightarrow \tt { \dfrac{25000}{50} = P } \\

\longrightarrow \underline{\boxed{ \green{ \tt { \$ \; 500 = P }}}} \\

Therefore principal is $500.

<h2>__________________</h2>

<h2>[2]</h2>

  • 2/7 of the balls are red.
  • 3/5 of the balls are blue.
  • Rest are yellow.
  • Number of yellow balls = 36

Let the total number of balls be x.

→ Red balls + Blue balls + Yellow balls = Total number of balls

\longrightarrow \tt{ \dfrac{2}{7}x + \dfrac{3}{5}x + 36 = x} \\

\longrightarrow \tt{ \dfrac{10x + 21x + 1260}{35} = x} \\

\longrightarrow \tt{ \dfrac{31x + 1260}{35} = x} \\

\longrightarrow \tt{ 31x + 1260= 35x} \\

\longrightarrow \tt{ 1260= 35x-31x} \\

\longrightarrow \tt{ 1260= 4x} \\

\longrightarrow \tt{ \dfrac{1260 }{4}= x} \\

\longrightarrow \underline{\boxed{  \tt { 315 = x }}} \\

Total number of balls is 315.

A/Q,

3/5 of the balls are blue.

\longrightarrow \tt{ Balls_{(Blue)} =\dfrac{3 }{5}x} \\

\longrightarrow \tt{ Balls_{(Blue)} =\dfrac{3 }{5}(315)} \\

\longrightarrow \tt{ Balls_{(Blue)} = 3(63)} \\

\longrightarrow \underline{\boxed{ \green {\tt { Balls_{(Blue)} = 189 }}}} \\

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