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nasty-shy [4]
3 years ago
6

A square mirror has sides measuring 2 ft less than the sides of a square painting. If the difference between their areas is 32 f

t. Find the lengths of the sides of the mirror and the painting.
Mathematics
1 answer:
kari74 [83]3 years ago
5 0

Answer:  The side lengths of mirror and painting are 7 ft and 9 ft respectively.

Step-by-step explanation:  Given that a square mirror has sides measuring 2 ft less than the sides of a square painting and the difference between their areas is 32 ft.

We are to find the lengths of the sides of the mirror and the painting.

Let x ft represents the length of the side of mirror. Then, the side length of square painting is (x+2) ft.

According to the given information, we have

\textup{area of painting}-\textup{area of mirror}=32\\\\\Rightarrow (x+2)^2-x^2=32\\\\\Rightarrow x^2+4x+4-x^2=32\\\\\Rightarrow  4x=28\\\\\Rightarrow x=\dfrac{28}{4}\\\\\Rightarrow x=7.

Therefore, the side length of mirror is 7 ft and the side length of painting is (7+2) = 9 ft.

Thus, the side lengths of mirror and painting are 7 ft and 9 ft respectively.

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Answer:

a. \ \dfrac{1}{36}

b. \ \dfrac{4}{9}

c. \ \dfrac{5}{6}

Step-by-step explanation:

The given probabilities are; P(Orange) = 1/3, P(Blue) = 1/6, P(Purple) = 1/2

The probability of rolling any of the six numbers of the six-sided die = 1/6

a. The probability of simultaneously 'rolling a 3' and 'spinning blue', P(3 and Blue) is given as follows;

P(rolling a 3) = 1/6, P(Blue) = 1/6

∴ P(3 and Blue) = (1/6) × (1/6) = 1/36

P(3 and Blue) = 1/36

P(3 \ and \ Blue) = \dfrac{1}{36}

b. The probability of either 'rolling a 1' or 'spinning Orange', P(1 or Orange), is given as follows;

P(rolling a 1) = 1/6, P(Orange) = 1/3

P(1 or Orange) = P(rolling a 1) + P(Orange) - P(1 and Orange)

Where;

P(1 and Orange) = (1/6) × (1/3) = 1/18

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P(1 or Orange) = 4/9

P(1 \ or \ Orange) = \dfrac{4}{9}

c. The probability of not spinning a blue, P(not Blue) is given as follows;

P(not Blue) = P(rolling all outcomes of the die) and (The sum of the spin probabilities - P(Blue)

∴ P(not Blue) = 1 × ((1/3 + 1/6 + 1/2) - 1/6) = 1 × (1 - 1/6) = 5/6

P(not Blue) = 5/6

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2 years ago
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Sydney invested $440 in an account paying an interest rate of 5.6% compounded daily. Assuming no deposits or withdrawals are mad
stealth61 [152]

Answer:

The time required to get  a total amount of $ 640.00  from compound interest on a principal of $ 440.00  at an interest rate of 5.6% per year  and compounded 365 times per year  is approximately 7 years.

Step-by-step explanation:

Given

  • Principle Amount P = $440
  • Accrued Amount A = $640
  • Interest rate r = 5.6% = 0.056
  • Compounded daily n = 365

To determine:

Time period t = ?

Using the formula

A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}

solving for t

t = ln(A/P) / n[ln(1 + r/n)]

substituting the values A = 640, P = 440, n = 365 and r = 0.056

t = ln(640/440) / ( 365 × [ln(1 + 0.00015342465753425/365)] )

t = 6.691

t ≈ 7  (nearest year)

Therefore, the time required to get  a total amount of $ 640.00  from compound interest on a principal of $ 440.00  at an interest rate of 5.6% per year  and compounded 365 times per year  is approximately 7 years.

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Answer:

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Step-by-step explanation:

<u>(n-2)180 = 108</u>

          n

Distribute

180n-360=108n

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n=5

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