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2 years ago

Complete the following statement about the Empirical Rule.

Mathematics

1 answer:

andrezito [222]2 years ago

5 0

Answer:

1. 68%

2. 95%

3. 99.7

Step-by-step explanation:

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You need 660 mL of a 40% alcohol solution. On hand, you have 35% alcohol mixture. You also have a 95% alcohol mixture. How much

ozzi

Answer:

A. 605 mL of the 35% solution

B. 55 mL of the 95% solution

Step-by-step explanation:

It is given that, you need 660 mL of a 40% alcohol solution. On hand, you have 35% alcohol mixture. You also have a 95% alcohol mixture.

Let x and y be the amount of 35% alcohol solution and 95% alcohol solution (in mL) respectively.

So,

Amount equation: $x+y=660$ ...(1)

Alcohol equation : $0.35x+0.95y=0.40(660)\Rightarrow 0.35x+0.95y=264$ ...(2)

On solving (1) and (2), we get

$0.35(660-y)+0.95y=264$

$231-0.35y+0.95y=264$

$0.6y=264-231$

$y=\dfrac{33}{0.6}$

$y=55$

Now, substitute y=55 in (1).

$x+55=660$

$x=660-55$

$x=605$

Therefore, we need 605 mL of the 35% solution and 55 mL of the 95% solution.

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2 years ago

Please help ill give branlist and extra points if yall help me with this

neonofarm [45]

Number 1 is B Number 2 is C

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2 years ago

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The base of the regular triangular pyramid has sides that are 14 cm with a height of 12.1 cm. The slant height of the pyramid is

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Step-by-step explanation:

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3 years ago

At the beginning of an environmental study, a forest covered an area of 1500 km2 . Since then, this area has decreased by 9.8% e

fredd [130]

Answer:

$A(t)=(0.902)^t \cdot 1500$ $[km^2]$

Step-by-step explanation:

In this problem, the initial area of the forest at time t = 0 is

$A_0 = 1500 km^2$

After every year, the area of the forest decreases by 9.8%: this means that the area of the forest every year is (100%-9.8%=90.2%) of the area of the previous year.

So for instance, after 1 year, the area is

$A_1 = A_0 \cdot \frac{90.2}{100}=0.902 A_0$

After 2 years,

$A_2=0.902 A_1 = 0.902(0.902A_0)=(0.902)^2 A_0$

And so on. So, after t years, the area of the forest will be

$A(t)=(0.902)^t A_0$

And by substituting the value of A0, we can find an explicit expression:

$A(t)=(0.902)^t \cdot 1500$ $[km^2]$

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