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3 years ago

Simplify 4/(√5+ √2) - 3/(√5- √2)

Mathematics

1 answer:

MakcuM [25]3 years ago

8 0

Step-by-step explanation:

$\frac{4}{ \sqrt{5} + \sqrt{2}} - \frac{3}{ \sqrt{5} - \sqrt{2} } = \\ = \frac{4( \sqrt{5} - \sqrt{2} ) - 3( \sqrt{5} + \sqrt{2} ) }{( \sqrt{5} + \sqrt{2} )\times ( \sqrt{5} - \sqrt{2} )} = \\ = \frac{4 \sqrt{5} - 4 \sqrt{2} - 3 \sqrt{5} - 3 \sqrt{2} }{5 - \sqrt{10} + \sqrt{10} - 2 } = \\ = \frac{ \sqrt{5} - 7 \sqrt{2} }{3}$

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Alyssa starts with $40 and saves $10 each week. Bill has $24 and saves $12 each week. For numbers 5a. – 5c., determine whether e

adelina 88 [10]

Answer: See explanation

Step-by-step explanation:

Alyssa starts with $40 and saves $10 each week. This can be written as:

= 40 + 10x

Bill has $24 and saves $12 each week. This can be written as:

= 24 + 12x

where, x = number of weeks

a. Bill will never have more money than Alyssa.

False.

From the 9th week, Bill will have more money than Alyssa. To check goes below.

Alyssa = 40 + 10x = 40 + 10(9) = 40 + 90 =$130

Bill = 24 + 12x = 24 + 12(9) = 24 + 108 = $132

b. Bill's savings can be represented by the equation = 12 + 24 where x is the number of weeks and y is his savings.

False.

Bill savings can be represented by:

= 24 + 12x

where, x = number of weeks

c. Alyssa and Bill will have the same amount of money at Week 6.

False.

Alyssa = 40 + 10x

= 40 + 10(6)

= 40 + 60

= $100

Bill = 24 + 12x

= 24 + 12(6)

= 24 + 72

= $96

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3 years ago

2<br> 4-(28 divided 7)+111

nikitadnepr [17]

4-( $\frac{28}{7}$ )+111
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3 years ago

Alex is running a recycling business. The weight of collected used Iron in a day is a variable, X, which is normally distributed

qwelly [4]

Answer:

$a.\ \ \ \mu_T=5345, \ \ \sigma_T=600$

$b.\ \ K=$5,995$

$C.\ \ \mu_B=6360, \ median(B)=6360 ,\ \ \sigma_B=800$

Step-by-step explanation:

The expense function is expressed as $T=15X+2300$ where X is the weight of collected iron.

-This function is normal distributed as $X \sim \mathcal{N}(\mu,\,\sigma^{2})$ , $\mu_x=203, \sigma_x=40$

-We use the formula for normal distribution to calculate the mean as:

$=\mu_T=15\mu_x+2300,\ \mu_x=203\\\\=15\times 203+2300\\\\=5345$

#We then calculate the standard deviation as:

$Var(T)=\sigma_T^2\\\\=15^2\times \sigma_x^2\\\\=225\times 40^2\\\\=360000\\\sigma_T=\sqrt{\sigma_T^2}\\\\\therefore \sigma_T=\sqrt{360000}=600$

b. From a above, we know that the cost, T is normally distributed with mean=5345 and standard deviation=600, $T\sim \mathcal{N}(5345,\,\ 600^2)$

#Given a 13.8% chance that the total daily expense of the business is more than $K, we calculate K as:

$T \sim \mathcal{N}(5345,\,360000)\\\\\\\\Z=\frac{T-5345}{600} \sim \mathcal{N}(0,\,1)\\=P(T>K)=0.138\\\\\\P(T\leq K)=1-0.138=0.862\\\\P(Z\leq Z^*)=0.8620\\=>Z^*\approx 1.08935\\\\\frac{T^*-5345}{600}=1.08395\\\\T^*=1.08395\times 600+5345\\\\=5995.37\approx5995$

Hence, the value of K is approximately $5995

c. Now given that each kilo or iron collected can be sold for $35, the mean, sd and median of the daily profit is calculated as:

Let B be the profit made:

$B=35X-T\\\\=20X-2300$

#Mean profit is calculated as:

$\mu_B=20\mu_x-2300, \ \mu_x=203\\\\=20\times 203-2300\\\\=6360$

#In a normal distribution:

$mean=mode=median\\\\\\\therefore median(B)=6360$

#The standard deviation is calculated as:

$\sigma_B=\sqrt{\sigma_B^2}\\\\=\sqrt{20^2\sigma_x^2}\\\\=\sqrt{20^2\times 40^2}\\\\=800\\\\\therefore \sigma_B=800$

d. A government allowance is applicable if theres 10+% of a negative profit;

$B \sim \mathcal{N}(6360,\,\ 800^{2})\\\\\therefore Z=\frac{B\leq -6360}{800} \sim \mathcal{N}(0,1)\\\\P(Z\leq Z^*)=0.1, Z^*\approx-1.2816\\\\\frac{B^*-6360}{800}=-1.2816\\\\B^*=-1.2816\times 800+6360\\\\=5334\\\\B=1-\frac{5334.72}{6360}=0.1612 \ or \ 16.12\%$

16.2%>10%.

Hence, he can apply for government allowance.

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Answer:

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3 years ago

Simplify 4/(√5+ √2) - 3/(√5- √2)​

Simplify 4/(√5+ √2) - 3/(√5- √2)