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torisob [31]
2 years ago
11

The height of a triangular road sign is 1 inch shorter than twice its base. if the area of the sign is 60 in.2, which equation c

ould be used to find the base (b) of the sign?
Mathematics
1 answer:
Gnom [1K]2 years ago
6 0
Comment
We should try the very simplest way of finding triangular areas first.

Formula
A = 1/2 b * h

Substitute
Area = 60 in^2
b = x
h = 2x - 1 
60= 1/2 * x * (2x - 1)

Solve
60 = 1/2 * x (2x - 1) Multiply by 2
60 * 2 = x(2x - 1)
120 = x (2x - 1) Remove the brackets.
120 = 2x^2 - x  Subtract 120 from both sides.
2x^2 -  x - 120 = 0 This factors.
(2x + 15)(x - 8) = 0

Solve for x
2x + 15 = 0
2x = - 15
x = -15/2
x = - 7.5 a negative measurement is useless. Discard this answer.

x - 8 = 0
x = 8 

Area (Check)
base = 8
height = 16 - 1 = 15

Area = 1/2 * 8 * 15 = 60 as it should

Answer
Use Area = 1/2 * b * h to find the base and the height.
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Answer:

Step-by-step explanation:

We want to determine a 95% confidence interval for the mean salary of all graduates from the English department.

Number of sample, n = 400

Mean, u = $25,000

Standard deviation, s = $2,500

For a confidence level of 95%, the corresponding z value is 1.96. This is determined from the normal distribution table.

We will apply the formula

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It becomes

25000 ± 1.96 × 2500/√400

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= 25000 ± 245

The lower end of the confidence interval is 25000 - 245 =24755

The upper end of the confidence interval is 25000 + 245 = 25245

Therefore, with 95% confidence interval, the mean salary of all graduates from the English department is between $24755 and $25245

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2 years ago
A computer program contains one error. In order to find the error, we split the program into 6 blocks and test two of them, sele
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f_X(x)=\begin{cases}\dfrac13&\text{for }x=1\\\\\dfrac23&\text{for }x=0\end{cases}

These are the only two cases since there is only one error known to exist in the code; any two blocks of code chosen at random must either contain the error or not.

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7 0
2 years ago
The smallest natural number divisible by 2,3,4,5,6,8 and 9 is____.
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Answer:

360

Step-by-step explanation:

You will need 2 * 2 * 2 for the smallest number to be divisible by 8 with all the others.

You will need 3 * 3  for the smallest number to be divisible by 9 with all the others.

Finally you will need 1 five

The smallest number divisible by all of these is 2*2*2*3*3*5 = 360

  • 360/2 = 180 works
  • 360/3 = 120 works
  • 360/5 = 72   works
  • 360/6 = 60 works
  • 360/8 = 45 works
  • 360/9 = 40 works.

There is no smaller number below 360 which will work.

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2 years ago
In the United States, 75 percent of adults wear glasses or contact lenses. A random sample of 10 adults in the United States wil
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Answer:

0.4745 is the probability that fewer than 8 of the selected adults wear glasses or contact lenses.

Step-by-step explanation:

We are given the following information:

We treat adult adults wear glasses or contact lenses as a success.

P(Adults wear glasses or contact lenses) = 75% = 0.75

Then the number of adults follows a binomial distribution, where

P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 10

We have to evaluate:

P(fewer than 8 of the selected adults wear glasses or contact lenses)

P(x < 8)\\=1 - P(x = 8) - P(x = 9) - P(x = 10)\\=1 - \binom{10}{8}(0.75)^8(1-0.75)^2 - \binom{10}{9}(0.75)^9(1-0.75)^1- \binom{10}{10}(0.75)^10(1-0.75)^0\\=1 - 0.2815-0.1877-0.0563\\= 0.4745

0.4745 is the probability that fewer than 8 of the selected adults wear glasses or contact lenses.

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