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2 years ago

The level of a lake was 8 inches below normal. It decreased 1

Mathematics

1 answer:

solmaris [256]2 years ago

4 0

Answer:

$-9\dfrac{5}{8}$ inches.

Step-by-step explanation:

The level of a lake was 8 inches below normal.

Now, it is given that the water level decreases $1\dfrac{1}{4} = 1.25$ inches in June and $2\dfrac{3}{8} =2.375$ inches more in July.

Therefore, the new level of water with respect to the normal level will be

= - 8 - 1.25 - 2.375

= - 9.625 inches

= $-9\dfrac{5}{8}$ inches. (Answer)

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Answer: Option: (B) The range of both f(x) and g(x) is all nonzero real numbers is correct.

Step-by-step explanation: ..................Because I said so............................

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2 years ago

Read 2 more answers

A restaurant owner was experimenting with the taste of her homestyle lemon drink. She started with 60 litres of water. She remov

Burka [1]

Answer:

ratio of pure lemon juice to water in the homestyle lemon drink is 5 : 19.

Step-by-step explanation:

In order to solve the final ratio of lemon juice to water, let us start by determining the initial ratio of pure lemon juice to water in the first mix. This is done as follows:

Total volume of mixture = 60 liters

initial volume of water = 60 liters

initial volume of lemon juice = 0 liters

1) She removed 15 liters of the water and replaced it with 15 liters of pure lemon juice.

Volume of water = 60 - 15 = 45 liters

Volume of lemon juice = 15 liters

$\therefore \frac{15}{60}\ = \frac{1}{4}\ of\ the\ first\ mix\ is\ lemon\ juice\\\frac{45}{60}\ = \frac{3}{4}\ of\ the\ first\ mix\ is\ pure\ water$

2) She removed 10 liters of the new mixture

Let us convert this amount removed into ratio:

$lemon\ juice\ = \frac{1}{4}\ \times 10 = \frac{10}{4} = \frac{5}{2}\ liters.\\ \therefore the\ owner\ removes\ \frac{5}{2}\ liters\ of\ pure\ lemon\ juice\\pure\ water\ = \frac{3}{4}\ \times 10 = \frac{30}{4} = \frac{15}{2}\ liters\\ \therefore\ the\ owner\ removes\ \frac{15}{2}\ liters\ of\ water\ from\ the\ first\ mix.$

New volumes of water and lemon juice after removing the 10 liters of mixture is calculated as follows:

$lemon\ juice\ = 15 - \frac{5}{2} = \frac{30-5}{2} = \frac{25}{2}\ liters\ of\ lemon\ juice\\pure\ water\ = 45 - \frac{15}{2} = \frac{90-15}{2} = \frac{75}{2}\ liters\ of\ pure\ water$

3) and replaced it with 10 liters of water.

$New\ volume\ of\ water\ = 10 + \frac{75}{2} = \frac{20+ 75}{2} = \frac{95}{2}\ liters$

The final ratio of lemon juice to water:

$\frac{25}{2} : \frac{95}{2}\\= 25 : 95\\= 5 : 19$

Therefore, the final ratio of pure lemon juice to water in the homestyle lemon drink is 5 : 19.

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2 years ago

The graphs shown are of the form y = ax2. Which graph has the smallest value for a?

Talja [164]

$y= x^{2}$ is a parabola (looks like the letter U).

The letter a represents the coefficient of $x^{2}$ and it controls two things (1) how wide or narrow the parabola is and (2) whether it is concave up (like a U) or concave down (like an up-side-down).

The absolute value of a (the number without the sign) controls how wide or narrow it is. If the absolute value is a fraction less than 1 the graph gets wider. The smaller the absolute value of the fraction the wider the graph gets.

If the absolute value of a is greater than 1 the graph gets narrower (it gets skinnier). The bigger the absolute value the narrower the graph.

So, if all the graphs look like a U (concave up) then the one with the smallest a is the one that is the widest.

The a also controls whether the graph is concave up or concave down. If a is negative

If a is negative the graph is concave down so any graph that is concave down has a smaller value of a than any graph that is concave up. However, if the graph is concave down the one with the smallest a would be the most narrow one.

So to find the one with the smallest a...
If they are all concave up (like a U) pick the widest one
and
If they are not all concave up pick the narrowest one that is concave down (looks like an upside down U)

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2 years ago

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oksian1 [2.3K]

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