Please answer this question

katrin2010 [14]

BC = 13
AC = 10
BD = x

We want to find what x is. You know what we can do? We can use the PYTHAGOREAN THEOREM. The PT states:

$a^{2} + b^{2} = c^{2}$

But we need to know DC in order to use the PT. But in Geometry there’s this theorem (I forgot sorry!) that states that BD divides ABD and CBD. Thus DC = 5 (half).
Pythagorean Theorem:

$13^{2} - 5^{2} = BD^{2}$
169 - 25 = 144
$\sqrt{144}$ = 12
BD = 12.

Hope this helps!

6 0

3 years ago

30/20 and 19/30 with common denominators

Aloiza [94]

30/20 and 19/30

To find the common denominator; we must get the least common multiple of each denominator.

20: 20, 40, 60
30: 30, 60, 90

The common denominator is 60.

We then multiply each denominator a number that will produce 60. Whatever number will be used to multiply the denominator will also be the number used to multiply the numerator.

30/20 * 3/3 = 90/60
19/30 * 2/2 = 38/60

With both fractions having the same denominator, we can use the numerator to evaluate the value of each fraction.

90 is greater than 38. Thus, 90/60 is greater than 38/60.

7 0

4 years ago

The following data represent the pH of rain for a random sample of 12 rain dates. A normal probability plot suggests the data co

pshichka [43]

Answer:

(1) The point estimate for the population mean is 4.925.

(2) Therefore, a 95% confidence interval for the population mean pH of rainwater is [4.715, 5.135] .

(3) Therefore, a 99% confidence interval for the population mean pH of rainwater is [4.629, 5.221] .

(4) As the level of confidence increases, the width of the interval increases.

Step-by-step explanation:

We are given that the following data represent the pH of rain for a random sample of 12 rain dates.

X = 5.20, 5.02, 4.87, 5.72, 4.57, 4.76, 4.99, 4.74, 4.56, 4.80, 5.19, 4.68.

(1) The point estimate for the population mean is given by;

Point estimate, $\bar X$ = $\frac{\sum X}{n}$

= $\frac{5.20+5.02+ 4.87+5.72+ 4.57+ 4.76+4.99+ 4.74+ 4.56+ 4.80+5.19+ 4.68}{12}$

= $\frac{59.1}{12}$ = 4.925

(2) Let $\mu$ = mean pH of rainwater

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

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean = 4.925

s = sample standard deviation = 0.33

n = sample of rain dates = 12

$\mu$ = population mean pH of rainwater

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-2.201 < $t_1_1$ < 2.201) = 0.95 {As the critical value of t at 11 degrees of

freedom are -2.201 & 2.201 with P = 2.5%}

P(-2.201 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.201) = 0.95

P( $-2.201 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.201 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.201 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.201 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-2.201 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.201 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $4.925-2.201 \times {\frac{0.33}{\sqrt{12} } }$ , $4.925+2.201 \times {\frac{0.33}{\sqrt{12} } }$ ]

= [4.715, 5.135]

Therefore, a 95% confidence interval for the population mean pH of rainwater is [4.715, 5.135] .

The interpretation of the above confidence interval is that we are 95% confident that the population mean pH of rainwater is between 4.715 & 5.135.

(3) Now, 99% confidence interval for the population mean, $\mu$ is ;

P(-3.106 < $t_1_1$ < 3.106) = 0.99 {As the critical value of t at 11 degrees of

freedom are -3.106 & 3.106 with P = 0.5%}

P(-3.106 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 3.106) = 0.99

P( $-3.106 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $3.106 \times {\frac{s}{\sqrt{n} } }$ ) = 0.99

P( $\bar X-3.106 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+3.106 \times {\frac{s}{\sqrt{n} } }$ ) = 0.99

99% confidence interval for $\mu$ = [ $\bar X-3.106 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+3.106 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $4.925-3.106 \times {\frac{0.33}{\sqrt{12} } }$ , $4.925+3.106 \times {\frac{0.33}{\sqrt{12} } }$ ]

= [4.629, 5.221]

Therefore, a 99% confidence interval for the population mean pH of rainwater is [4.629, 5.221] .

The interpretation of the above confidence interval is that we are 99% confident that the population mean pH of rainwater is between 4.629 & 5.221.

(4) As the level of confidence increases, the width of the interval increases as we can see above that the 99% confidence interval is wider as compared to the 95% confidence interval.

4 0

4 years ago

What is the minimum or maximum value if the function X^2 + 30x + 21

Margaret [11]

Answer:

x2-30x-21=0

Step-by-step explanation:

x =(30-√984)/2=15-√ 246 = -0.684

x =(30+√984)/2=15+√ 246 = 30.684

3 0

3 years ago

Can u pls help me with this question

miss Akunina [59]

Answer:

1/8

Step-by-step explanation:

1/8 = 0.125

4 0

3 years ago