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Nostrana [21]
3 years ago
9

Express 3^2 = x as a logarithmic equation.

Mathematics
1 answer:
Dennis_Churaev [7]3 years ago
5 0
Remember
a^b=c translates to log_a(c)=b

so

3^2=x translates to log_3(x)=2
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2. When a large truckload of mangoes arrives at a packing plant, a random sample of 150 is selected and examined for
kirza4 [7]

a) The 90% confidence interval of the percentage of all mangoes on the truck that fail to meet the standards is: (7.55%, 12.45%).

b) The margin of error is: 2.45%.

c) The 90% confidence is the level of confidence that the true population percentage is in the interval.

d) The needed sample size is: 271.

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions has the bounds given by the rule presented as follows:

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

The margin of error is given by:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

The variables are listed as follows:

  • \pi is the sample proportion, which is also the estimate of the parameter.
  • z is the critical value.
  • n is the sample size.

The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of \frac{1+0.90}{2} = 0.95, so the critical value is z = 1.645.

The sample size and the estimate are given as follows:

n = 150, \pi = \frac{15}{150} = 0.1

The margin of error is of:

M = z\sqrt{\frac{0.1(0.9)}{150}} = 0.0245 = 2.45\%

The interval is given by the estimate plus/minus the margin of error, hence:

  • The lower bound is: 10 - 2.45 = 7.55%.
  • The upper bound is: 10 + 2.45 = 12.45%.

For a margin of error of 3% = 0.03, the needed sample size is obtained as follows:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.03 = 1.645\sqrt{\frac{0.1(0.9)}{n}}

0.03\sqrt{n} = 1.645\sqrt{0.1(0.9)}

\sqrt{n} = \frac{1.645\sqrt{0.1(0.9)}}{0.03}

(\sqrt{n}})^2 = \left(\frac{1.645\sqrt{0.1(0.9)}}{0.03}\right)^2

n = 271 (rounded up).

More can be learned about the z-distribution at brainly.com/question/25890103

#SPJ1

3 0
1 year ago
How many 2 1⁄4 meter lengths of tape can be cut from 36 meters of tape?
Fed [463]
Answer 16

36/2.25= 16 pieces of rope
6 0
3 years ago
Read 2 more answers
8 5/12 x 3 6/13 as a fraction please
Olin [163]

Answer:

29 7/52

Step-by-step explanation:

5 0
2 years ago
wrtie an equation in slope intercept form. A horizontal line that passes through a point 3 units below the origin
antoniya [11.8K]
In slope intercept form this would just be: y=-3
4 0
3 years ago
Evaluate 3(c + d) if c = 8 and d = -5
Sloan [31]
Substitution time :D

c = 8

d = -5


All you have to do is replace the variables(letters) with the numbers!


3(8 + (-5))

Do parentheses first! And remember that adding a negative is the same as subtracting :)

3(3) = 9
4 0
3 years ago
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