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3 years ago

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A paddleboat can move at a speed of 4 km/h in still water. The boat is paddled 12 km downstream in a river in the same time it

takes to go 6 km upstream. What is the speed of the river?

1 answer:

Bas_tet [7]3 years ago

3 0

Answer:

Speed of the river = $\frac{4}{3}$ km per hour

Step-by-step explanation:

Speed of the boat in still water = 4 km per hour

Let the speed of the river = v km per hour

Speed of the boat upstream = (4 - v) km per hour

Time taken to cover 6 km = $\frac{\text{Distance}}{\text{Speed}}$

= $\frac{6}{4-v}$ hours

Speed of the boat downstream = (4 + v) km per hour

Time taken to cover 12 km = $\frac{12}{4+v}$ hours

Since, time taken by the boat in both the cases is same,

$\frac{6}{4-v}= \frac{12}{4+v}$

6(4 + v) = 12(4 - v)

24 + 6v = 48 - 12v

12v + 6v = 48 - 24

18v = 24

v = $\frac{24}{18}$

v = $\frac{4}{3}$ km per hour

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The following table summarises the data from a survey on the ownership of iPods among families with different levels of income.

AURORKA [14]

The two nominal variables are related.

The following table summarises the data from a survey on the ownership of iPods among families with different levels of income.

Ownership C1 C2 C3

No 40 32 48

Yes 30 48 52

The first thing to do in order to determine if they are related or not is to state our null and alternative hypothesis

Null hypothesis

$\mathbf{H_o: Two \nomial \ variables \ are \ related}$

Alternative hypothesis

$\mathbf{H_a: Two \nomial \ variables \ are \ not \ related}$

Using the Chi-square test statistics which can be expressed by using the formula

$X ^2 = \sum \dfrac{(O-E)^2}{E}$

Ownership C1 C2 C3 Total

No 40 32 48 120

Yes 30 48 52 130

Total 70 80 100 250

The expected values are calculated as:

$\mathsf{E_{a,b} = \dfrac{(row \ total \times column \ total )}{grand \ total }}$

$\mathsf{E_{1,1} = \dfrac{(70 \times120 )}{250 }}$

$\mathsf{E_{1,1} = 33.6}$

$\mathsf{E_{1,2} = \dfrac{(70 \times130 )}{250 }}$

$\mathsf{E_{1,2} = 36.4}$

$\mathsf{E_{2,1} = \dfrac{(80 \times120 )}{250 }}$

$\mathsf{E_{2,1} = 38.4}$

$\mathsf{E_{2,2} = \dfrac{(80 \times 130 )}{250 }}$

$\mathsf{E_{2,2} = 41.6}$

$\mathsf{E_{3,1} = \dfrac{(100 \times120 )}{250 }}$

$\mathsf{E_{3,1} = 48}$

$\mathsf{E_{3,2} = \dfrac{(70 \times130 )}{250 }}$

$\mathsf{E_{3,2} = 52}$

∴ Using the Chi-square test statistics, we have:

$X ^2 = \sum \dfrac{(O-E)^2}{E}$

$X ^2 = \Bigg( \dfrac{(40-33.6)^2}{33.6}+ \dfrac{(30-36.4)^2}{36.4}+ \dfrac{(32-38.4)^2}{38.4}+ \dfrac{(48-41.6)^2}{41.6} + \dfrac{(48-48)^2}{48}+ \dfrac{(52-52)^2}{52} \Bigg)$

$X ^2 = \Bigg( \dfrac{40.96}{33.6}+ \dfrac{40.96}{36.4}+ \dfrac{40.96}{38.4}+ \dfrac{40.96}{41.6} + \dfrac{0}{48}+ \dfrac{0}{52} \Bigg)$

$X ^2 = \Bigg( 1.2190+ 1.1253+ 1.0667+ 0.9846+0+ 0 \Bigg)$

$\mathbf{X ^2 =4.3956}$

The degree of freedom df = ((r - 1) × (c - 1))

= (3 - 1) (2 -1 )

= 2 × 1

= 2

∴

Assuming the level of significance = 5%

The p-value of the Chi-square test statistics at df of 2 is:

= $\mathbf{P(X^2 > 4.3956) \implies 0.111}$

Therefore, we can conclude that since the p-value (0.111) is greater than the level of significance (0.05), we fail to reject the null hypothesis.

Hence, the two nominal variables are related.

Learn more about Chi-square test statistics here:

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3 years ago

1/2r + 2(3/4r - 1) = 1/4r + 6

taurus [48]

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3 years ago

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Jskskdndmmxmxmcmxmdmsmsmm?

professor190 [17]

Answer:

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AK =12

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How would the fraction <img src="https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B1-%5Csqrt%7B5%7D%20%7D" id="TexFormula1" title="\frac{

allsm [11]

Answer:

$\frac{7 + 7 \sqrt{5} }{ - 4}$

Step-by-step explanation:

We would multiply the fraction by its conjugate

( A conjugate is a expression that has the same integer or number values but have different signs) for example

$5x + 2$

and

$5x - 2$

ARE Conjugates.

The conjugate of

$1 - \sqrt{5}$

is

$1 + \sqrt{5}$

So this means we will multiply the expression by 1 plus sqr root of 5 on the numerator and denominator.

Our new numerator will be

$7 \times (1 + \sqrt{5} ) = 7 + 7 \sqrt{5}$

We can apply the difference of squares for the denominator.

$(x + y)(x - y) = x {}^{2} - {y}^{2}$

So our denominator will be

$1 - 5 = - 4$

So our rationalized fraction will be

$\frac{7 + 7 \sqrt{5} }{ - 4}$

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3 years ago

(8+24)divided by two to the third power

satela [25.4K]

For this case we have to:

"two to the third power" is equivalent to the algebraic expression: $2 ^ 3$

Therefore, we can rewrite the expression given as:

$\frac {8 + 24} {2 ^ 3} =\\\frac {32} {2 ^ 3} =\\\frac {32} {8} = 4$

Thus, the value of the initial expression is: 4

Answer:

$\frac {8 + 24} {2 ^ 3} = 4$

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3 years ago