Find the congruence transformation that maps ABC TO ABC

Measurements of the sodium content in samples of two brands of chocolate bar yield the following results (in grams):

Tpy6a [65]

Answer:

98% confidence interval for the difference μX−μY = [ 0.697 , 7.303 ] .

Step-by-step explanation:

We are give the data of Measurements of the sodium content in samples of two brands of chocolate bar (in grams) below;

Brand A : 34.36, 31.26, 37.36, 28.52, 33.14, 32.74, 34.34, 34.33, 29.95

Brand B : 41.08, 38.22, 39.59, 38.82, 36.24, 37.73, 35.03, 39.22, 34.13, 34.33, 34.98, 29.64, 40.60

Also, $\mu_X$ represent the population mean for Brand B and let $\mu_Y$ represent the population mean for Brand A.

Since, we know nothing about the population standard deviation so the pivotal quantity used here for finding confidence interval is;

P.Q. = $\frac{(Xbar -Ybar) -(\mu_X-\mu_Y)}{s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }$ ~ $t_n__1+n_2-2$

where, $Xbar$ = Sample mean for Brand B data = 36.9

$Ybar$ = Sample mean for Brand A data = 32.9

$n_1$ = Sample size for Brand B data = 13

$n_2$ = Sample size for Brand A data = 9

$s_p = \sqrt{\frac{(n_1-1)s_X^{2}+(n_2-1)s_Y^{2} }{n_1+n_2-2} }$ = $\sqrt{\frac{(13-1)*10.4+(9-1)*7.1 }{13+9-2} }$ = 3.013

Here, $s^{2}_X$ and $s^{2} _Y$ are sample variance of Brand B and Brand A data respectively.

So, 98% confidence interval for the difference μX−μY is given by;

P(-2.528 < $t_2_0$ < 2.528) = 0.98

P(-2.528 < $\frac{(Xbar -Ybar) -(\mu_X-\mu_Y)}{s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }$ < 2.528) = 0.98

P(-2.528 * $s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2}$ < $(Xbar -Ybar) -(\mu_X-\mu_Y)$ < 2.528 * $s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2}$ ) = 0.98

P( (Xbar - Ybar) - 2.528 * $s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2}$ < $(\mu_X-\mu_Y)$ < (Xbar - Ybar) + 2.528 * $s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2}$ ) = 0.98

98% Confidence interval for μX−μY =

[ (Xbar - Ybar) - 2.528 * $s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2}$ , (Xbar - Ybar) + 2.528 * $s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2}$ ]

[ $(36.9 - 32.9)-2.528*3.013\sqrt{\frac{1}{13} +\frac{1}{9}$ , $(36.9 - 32.9)+2.528*3.013\sqrt{\frac{1}{13} +\frac{1}{9}$ ]

[ 0.697 , 7.303 ]

Therefore, 98% confidence interval for the difference μX−μY is [ 0.697 , 7.303 ] .

4 0

2 years ago

Kyle drew three line segments with lengths: 2/4 inch 2/3inch, and 2/6 inch list the fractions in order from least to greatest

Sati [7]

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Method 1
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Since the numerators are the same, the smaller the denominators, the greater the fraction is.

Arranging from the least to the greatest
$\dfrac{2}{6} \ , \ \dfrac{2}{4} \ , \ \dfrac{2}{3}$

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Method 2
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Lets change all to the same denominators

$\dfrac{2}{4} = \dfrac{2 \times 3}{4 \times 3} = \dfrac{6}{12}$

$\dfrac{2}{3} = \dfrac{2 \times 4}{3 \times 4} = \dfrac{8}{12}$

$\dfrac{2}{6} = \dfrac{2 \times 2}{6 \times 2} = \dfrac{4}{12}$

Now that all the denominators are the same, we can arrange the fractions by comparing the numerators. The bigger the numerators, the greater the fraction.

Arranging from the least to the greatest
$\dfrac{2}{6} \ , \ \dfrac{2}{4} \ , \ \dfrac{2}{3}$

3 0

3 years ago

Read 2 more answers

PLEASE HELP DO QUESTION 5 FOR BRAINLEYIST AWNSER.

zavuch27 [327]

There is no question 5?

5 0

3 years ago

could someone out there perhaps help me? i’m so lost even though it’s probably so simple. i’ll give you brainleist :)

Temka [501]

Answer:

y= -x+7, b= sqrt(2P/a), c=3P^2-b

Step-by-step explanation:

First, make a table regarding both of the equations. You will eventually find out that both lines intersect at the point (2, 5) after you find the points on the table. From there, subtract x from both sides in the equation x + y = 2. You will get y = -x + 2. Since they said the line was parallel, find a line that has the slope of negative one. Since we know that this line intersects the point in which the first two lines intersect, we know that the y-intercept will be 7. The equation of the line would be y=-x+7.

Multiply both sides by 2. Then, divide both sides by a to get b^2=(2P/a). Take the square root to get the value of b, which is sqrt(2P/a).

Square both sides of the equation to get P^2=(b+c)/3. Cross multiply to get 3P^2=b+c. Subtract b from both sides to get c=3P^2-b.

8 0

3 years ago

5x-6y=-15 5x+6y=12 use elimination

Vlad [161]

<span>5x-6y=-15
5x+6y=12
---------------add
10x = -3
x = -3/10
x = -0.3

</span>5x+6y=12
5(-0.3) + 6y = 12
6y = 12 + 1.5
6y = 13.5
y = 13.5 / 6

y = 2.25

4 0

2 years ago