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o-na [289]
3 years ago
5

Is an isosceles triangle. What is the length of RT? Round to the nearest hundredth.Enter your answer in the box

Mathematics
1 answer:
liraira [26]3 years ago
3 0

Answer:

9.33

Step-by-step explanation:

Find the diagram attached, to get the length of RT, we will use the pythagoras theorem as shown:

Hyp² = opp²+adj²

Hyp = 11

Adj = 6

Opposite = RT

Substitute into the formula

11² = opp²+6²

Opp² = 11²-6²

Opp² = 121-36

Opp² = 85

Opp = 9.22

Hence the measurel RT to nearest hundredth is 9.22

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Solid fats are more likely to raise blood cholesterol levels than liquid fats. Suppose a nutritionist analyzed the percentage of
Andrews [41]

Answer:

t = 31.29

Step-by-step explanation:

Given

\begin{array}{ccccccc}{Stick} & {25.8} & {26.9} & {26.2} & {25.3} & {26.7}& {26.1} \ \\ {Liquid} & {16.9} & {17.4} & {16.8} & {16.2} & {17.3}& {16.8} \ \end{array}

Required

Determine the test statistic

Let the dataset of stick be A and Liquid be B.

We start by calculating the mean of each dataset;

\bar x =\frac{\sum x}{n}

n, in both datasets in 6

For A

\bar x_A =\frac{25.8+26.9+26.2+25.3+26.7+26.1}{6}

\bar x_A =\frac{157}{6}

\bar x_A =26.17

For B

\bar x_B =\frac{16.9+17.4+16.8+16.2+17.3+16.8}{6}

\bar x_B =\frac{101.4}{6}

\bar x_B =16.9

Next, calculate the sample standard deviation

This is calculated using:

s = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}

For A

s_A = \sqrt{\frac{\sum(x - \bar x_A)^2}{n-1}}

s_A = \sqrt{\frac{(25.8-26.17)^2+(26.9-26.17)^2+(26.2-26.17)^2+(25.3-26.17)^2+(26.7-26.17)^2+(26.1-26.17)^2}{6-1}}

s_A = \sqrt{\frac{1.7134}{5}}

s_A = \sqrt{0.34268}

s_A = 0.5854  

For B

s_B = \sqrt{\frac{\sum(x - \bar x_B)^2}{n-1}}

s_B = \sqrt{\frac{(16.9 - 16.9)^2+(17.4- 16.9)^2+(16.8- 16.9)^2+(16.2- 16.9)^2+(17.3- 16.9)^2+(16.8- 16.9)^2}{6-1}}

s_B = \sqrt{\frac{0.92}{5}}

s_B = \sqrt{0.184}

s_B = 0.4290

Calculate the pooled variance

S_p^2 = \frac{(n_A - 1)*s_A^2 + (n_B - 1)*s_B^2}{(n_A+n_B-2)}

S_p^2 = \frac{(6 - 1)*0.5854^2 + (6 - 1)*0.4290^2}{(6+6-2)}

S_p^2 = \frac{2.6336708}{10}

S_p^2 = 0.2634

Lastly, calculate the test statistic using:

t = \frac{(\bar x_A - \bar x_B) - (\mu_A - \mu_B)}{\sqrt{S_p^2/n_A +S_p^2/n_B}}

We set

\mu_A = \mu_B

So, we have:

t = \frac{(\bar x_A - \bar x_B) - (\mu_A - \mu_A)}{\sqrt{S_p^2/n_A +S_p^2/n_B}}

t = \frac{(\bar x_A - \bar x_B) }{\sqrt{S_p^2/n_A +S_p^2/n_B}}

The equation becomes

t = \frac{(26.17 - 16.9) }{\sqrt{0.2634/6 +0.2634/6}}

t = \frac{9.27}{\sqrt{0.0878}}

t = \frac{9.27}{0.2963}

t = 31.29

<em>The test statistic is 31.29</em>

3 0
2 years ago
Can someone help me with this one?
Pavel [41]

Answer:

21/25 = 84/100

17/20 = 85/100

21/25 < 17/20

Step-by-step explanation:

∵ The common multiple of 25 and 20 is 100

∵ 100 ÷ 25 = 4

∴ 21/25 = (21 × 4)/(25 × 4) = 84/100

∵ 100 ÷ 20 = 5

∴ 17/20 = (17 × 5)/(20 × 5) = 85/100

∵ 84 < 85

∴ 84/100 < 85/100

∴ 21/25 < 17/20

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