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Sedaia [141]
3 years ago
15

AB = 15, BC = 10, and CD= 7. Find the length DA.

Mathematics
1 answer:
harkovskaia [24]3 years ago
4 0

Answer:

  451. No, the angles are wrong.

Step-by-step explanation:

450. AB = 15, BC = 10, and CD= 7. Find the length DA.

  This cannot be done without additional information about the sort of figure that ABCD is. If these are points on a line segment, we need to know their order. If these are points on a quadrilateral, we need to know its description in more detail.

If these are points ordered ABCD on a line, then AD = 15+10+7 = 32.

__

451. See the attached figure. BPQD is not a parallelogram: BCQ is not a straight line. (The internal angles of a pentagon are 108°, but would need to be 120° for BCQ to be a straight line, making BP parallel to DQ.) Instead, BPQD is an isosceles trapezoid.

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Write as an equation: Alice, Barbara, and Carol are sisters. Alice is 3 years younger than Barbara, and Barbara is 5 years young
Dmitrij [34]

a+b+c=68

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c-5=b

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a+b+c=68

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Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 ​students, she finds 2 w
irina1246 [14]

Answer:

A 95​% confidence interval for the proportion of students who eat cauliflower on​ Jane's campus is [0.012, 0.270].

Step-by-step explanation:

We are given that Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 ​students, she finds 2 who eat cauliflower.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

                              P.Q.  =  \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }  ~ N(0,1)

where, \hat p = sample proportion of students who eat cauliflower

           n = sample of students

           p = population proportion of students who eat cauliflower

<em>Here for constructing a 95% confidence interval we have used a One-sample z-test for proportions.</em>

<u>So, 95% confidence interval for the population proportion, p is ;</u>

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                   of significance are -1.96 & 1.96}  

P(-1.96 < \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } < 1.96) = 0.95

P( -1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } < {\hat p-p} < 1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ) = 0.95

P( \hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } < p < \hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ) = 0.95

Now, in Agresti and​ Coull's method; the sample size and the sample proportion is calculated as;

n = n + Z^{2}__(\frac{_\alpha}{2})

n = 24 + 1.96^{2} = 27.842

\hat p = \frac{x+\frac{Z^{2}__(\frac{\alpha}{2}_)  }{2} }{n} = \hat p = \frac{2+\frac{1.96^{2}   }{2} }{27.842} = 0.141

<u>95% confidence interval for p</u> = [ \hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } , \hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ]

 = [ 0.141 -1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } } , 0.141 +1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } } ]

 = [0.012, 0.270]

Therefore, a 95​% confidence interval for the proportion of students who eat cauliflower on​ Jane's campus [0.012, 0.270].

The interpretation of the above confidence interval is that we are 95​% confident that the proportion of students who eat cauliflower on​ Jane's campus is between 0.012 and 0.270.

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Step-by-step explanation:

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