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joja [24]
3 years ago
6

Find the missing dimension of each triangle described height 14 inches area 245 inches Square

Mathematics
1 answer:
Amiraneli [1.4K]3 years ago
4 0
Given:
Triangle 
height 14 inches
area 245 inches square

Formula in finding the area of a triangle is:

Area = (height * base) / 2

The base is missing, so we need to compute its value using the given figures.

245 = (14 * b) / 2
245 * 2 = 14b
490 = 14b
490/14 = b
35 = b

The base is 35 inches.
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A researcher wishes to​ estimate, with 99​% ​confidence, the population proportion of adults who think the president of their co
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Answer:

a. n=4148

b. n=3909

c. The sample size is smaller if a known proportion from prior study is used. The difference in sample sizes is 239

Step-by-step explanation:

a. For sample where no preliminary estimate is given, the minimum sample size is calculated using the formula:

n=p(1-p)(\frac{z}{ME})^2

Where:

  • ME=Margin of error
  • p= is the assumed proportion

#Let p=0.5, substitute in the formula to solve for n:

n=0.5(1-0.5)\times (2.576/0.02)^2\\\\=4147.36\approx 4148

Hence, the minimum sample size is 4148

b. If given a preliminary estimate p=0.38, we use the same formula but substitute p with the given value:

n=p(1-p)(z/ME)^2\\\\=0.38(1-0.38)(2.576/0.02)^2\\\\=3908.47\approx3909

Hence, the minimum sample size is 3909

c. Comparing the sample sizes from a and b:

n_{0.5}>n_{0.38}\\\\n_{0.5}-n_{0.38}=4148-3909=239

Hence, the actual sample size is smaller for a known proportion from prior a prior study.

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Two accounts earn simple interest. The balance y (in dollars) of Account A after x years can be modeled by y=10x 500. Account B
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1 year ago
Find the value of k so that 48x-ky=11 and (k+2)x+16y=-19 are perpendicular lines.
Rufina [12.5K]

Answer: k = -1 +/- √769

<u>Step-by-step explanation:</u>

48x - ky = 11

<u>-48x        </u>  <u> -48x</u>

         -ky = -48x + 11

         \frac{-ky}{-k} = \frac{-48x}{-k} + \frac{11}{-k}    

           y =\frac{48x}{k} - \frac{11}{k}

Slope: \frac{48}{k}

*************************************************************************

 (k + 2)x + 16y = -19

<u>- (k + 2)x          </u>   -<u>(k + 2)x </u>

                 16y = -(k + 2)x - 19

                  \frac{16y}{16} = -\frac{(k + 2)x}{16} - \frac{19}{16}

                  y = -\frac{(k + 2)x}{16} - \frac{19}{16}

Slope: -\frac{(k + 2)}{16}

**********************************************************************************

\frac{48}{k} and -\frac{(k + 2)}{16} are perpendicular so they have opposite signs and are reciprocals of each other.  When multiplied by its reciprocal, their product equals -1.

-\frac{(k + 2)}{16} *  \frac{k}{48} = -1

\frac{(k + 2)k}{16(48)} = 1

Cross multiply, then solve for the variable.

(k + 2)(k) = 16(48)

k² + 2k - 768 = 0

Use quadratic formula to solve:

k = -1 +/- √769



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3 years ago
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