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denis-greek [22]
3 years ago
12

“Solve for x” x/2 + x/5 = 1

Mathematics
1 answer:
AlladinOne [14]3 years ago
4 0

Answer:

x=1/7

Step-by-step explanation:

x/2+x/5=1

make same denominators;

5x/10+2x/10=1

simplify;

7x=1

x=1/7

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Find the population mean or sample mean as indicated.<br> Sample: 17, 11, 8, 12, 22
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Answer:

mean:12

Step-by-step explanation:

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3 years ago
The length of a swimming pool is 4 feet longer than 2 times its width. If the perimeter of the pool is 128 feet, what is the wid
alexandr1967 [171]
P = 2(L + W)
P = 128
L = 2W + 4

128 = 2(2W + 4 + W)
128 = 2(3W + 4)
128 = 6W + 8
128 - 8 = 6W
120 = 6W
120/6 = W
20 = W <=== width is 20 ft

L = 2W + 4
L = 2(20) + 4
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5 0
4 years ago
6 points are placed on the line a , 4 points are placed on the line b . How many triangles is it possible to form such that thei
BaLLatris [955]

Answer:

96

Step-by-step explanation:

Using side b as the base, 4 points makes 3 bases (the space in between).  With three bases, you can have 3 bases of 1 segment, 2 bases of 2 segments, and 1 base of 3 segments.  This equals 6 bases. Each of these can connect to a point on line a. 6x6=36

Using side a as the base, 6 points makes 5 bases.  With 5 bases, you can have 5 bases of 1 segment, 4 bases of 2 segments, 3 bases of 3 segments, 2 bases of 4 segments, and 1 base of 5 segments.  This equals 15 bases.  Each of these can connect to a point on line b.  15x4=60

36+60=96

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3 years ago
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2 years ago
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How many times must we toss a coin to ensure that a 0.95-confidence interval for the probability of heads on a single toss has l
musickatia [10]

Answer:

(1) 97

(2) 385

(3) 9604

Step-by-step explanation:

The (1 - <em>α</em>) % confidence interval for population proportion is:

CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}

The margin of error in this interval is:

MOE= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}

The formula to compute the sample size is:

\\n=\frac{z_{\alpha/2}^{2}\times \hat p(1-\hat p)}{MOE^{2}}

(1)

Given:

\hat p = 0.50\\MOE=0.1\\z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96

*Use the <em>z</em>-table for the critical value.

Compute the value of <em>n</em> as follows:

\\n=\frac{z_{\alpha/2}^{2}\times \hat p(1-\hat p)}{MOE^{2}}\\=\frac{1.96^{2}\times0.50\times(1-0.50)}{0.1^{2}}\\=96.04\\\approx97

Thus, the minimum sample size required is 97.

(2)

Given:

\hat p = 0.50\\MOE=0.05\\z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96

*Use the <em>z</em>-table for the critical value.

Compute the value of <em>n</em> as follows:

\\n=\frac{z_{\alpha/2}^{2}\times \hat p(1-\hat p)}{MOE^{2}}\\=\frac{1.96^{2}\times0.50\times(1-0.50)}{0.05^{2}}\\=384.16\\\approx385

Thus, the minimum sample size required is 385.

(3)

Given:

\hat p = 0.50\\MOE=0.01\\z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96

*Use the <em>z</em>-table for the critical value.

Compute the value of <em>n</em> as follows:

\\n=\frac{z_{\alpha/2}^{2}\times \hat p(1-\hat p)}{MOE^{2}}\\=\frac{1.96^{2}\times0.50\times(1-0.50)}{0.01^{2}}\\=9604

Thus, the minimum sample size required is 9604.

8 0
3 years ago
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