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Gwar [14]
3 years ago
5

Show that (a-b)/(√a-√b)=√a+√b for all values of a and b such that a> 0 and b> 0 and a≠b.

Mathematics
2 answers:
Nat2105 [25]3 years ago
4 0

Answer:=a-b

Step-by-step explanation:

goldfiish [28.3K]3 years ago
3 0

Answer:

Step-by-step explanation:

\frac{a-b}{\sqrt{a} -\sqrt{b}} =\sqrt{a} +\sqrt{b}\\or ~a-b=(\sqrt{a} +\sqrt{b})(\sqrt{a}  -\sqrt{b} )=(\sqrt{a} )^2-(\sqrt{b} )^2 =a-b

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g Suppose the population 10-year cumulative incidence of prostate cancer among 70-year old men is 0.06. Further, suppose 260 men
Rainbow [258]

Answer:

There is not enough statistical evidence to conclude that the cumulative incidence of prostrate cancer among 50-year old men differs from that of 70-year old men

Step-by-step explanation:

The population 10 year cumulative incidence of prostrate cancer among 70 year old men, p = 0.06

The number of 50 year old men in the sample, n = 260 men

The number of the sampled men that developed prostrate cancer = 13 men

The significance level, α = 0.05

Let the null hypothesis, H₀: \hat{p} = p

The alternative hypothesis, Hₐ: \hat{p} ≠ p

The standard score, z_{\alpha /2} = 1.96

The test statistic, 'z', is given as follows;

z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p \cdot q}{n}}}

\hat{p} = 13/260 = 0.05

q = 1 - p = 1 - 0.06 = 0.94

Therefore,  \ z=\dfrac{0.05-0.06}{\sqrt{\dfrac{0.06 \times 0.94}{260}}} = \dfrac{\sqrt{9165} }{141} \approx -0.68

From the z-table, we find the p-value as follows;

P(z ≈ -0.68) = 0.24825

Therefore, given that the p-value, 0.24825 is larger than the significance level, α/2 = 0.025, we fail to reject the null hypothesis, and therefore, there is not enough statistical evidence to conclude that the cumulative incidence of prostrate cancer among 50-year old men differs from that of 70-year old men

5 0
2 years ago
Shania is planning a party at her home. She has made 126 chocolate truffles and 84 caramel truffles to give to her guests. If th
vodomira [7]
This turns out to be a division problem. To find how many each person can get, you must divide the amount of food by how many guests.
126 divided by 21 is 6
84 divided by 21 is  4
Each guest will get 6 chocolate truffles and 4 caramel truffles.
5 0
3 years ago
Read 2 more answers
Solve.and show your work
Marysya12 [62]

Answer:

a) x > − 24 \frac{3}{4}

b) x < − 3

c) q < 56

Step-by-step explanation:

a) −2/5x−9<9/10

<=> 2/5x + 9 > − 9/10

<=> 2/5x > − 9/10 − 9

<=> 2×2/2×5x > − 9/10 − 9×10/10

<=> 4/10x > − 99/10

<=> x > − 99/4

<=> x > − 24 \frac{3}{4}

b) 4x+6<−6

<=> 4x < − 6 − 6

<=> 4x < − 12

<=> x < − 12/4

<=> x < − 3

c) q+12−2(q−22)>0

<=> q+12−2q −2×(−22)>0

<=> (q−2q) + (12+ 44) >0

<=> −q + 56 >0

<=> q < 56

8 0
2 years ago
Find the angles between -pi and pi that satisfy:<br><br> (−√3) sin(v)+cos(v)=√3
MAXImum [283]

Observe that

\sin\left(\dfrac\pi6-v\right)=\sin\dfrac\pi6\cos v-\cos\dfrac\pi6\sin v=\dfrac12\cos v-\dfrac{\sqrt3}2\sin v

In the original equation, divide both sides by \dfrac12:

-\sqrt3\sin v+\cos v=\sqrt3\implies\dfrac12\cos v-\dfrac{\sqrt3}2\sin v=\dfrac{\sqrt3}2

\implies\sin\left(\dfrac\pi6-v\right)=\dfrac{\sqrt3}2

Next,

\sin x=\dfrac{\sqrt3}2\implies x=\dfrac\pi3+2n\pi,x=\dfrac{2\pi}3+2n\pi

where n is any integer. Then

\sin\left(\dfrac\pi6-v\right)\implies v=-\dfrac\pi6-2n\pi,v=-\dfrac\pi2-2n\pi

Fix n=0 to ensure -\pi, so that

v=-\dfrac\pi6,v=-\dfrac\pi2

3 0
3 years ago
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Wittaler [7]
The answer is Alex Rodriguez
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