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2 years ago

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Carlon plans to evaporate a number of gallons of water from 90 gallons of a 15% salt solution to make a 25% salt solution. which

equation can he use to find x, the number of gallons that should be evaporated?

2 answers:

Ipatiy [6.2K]2 years ago

8 0

Answer:

The equation can be used to find <em>x</em>, the number of gallons that should be evaporated is: $\frac{13.5}{90-x}=\frac{25}{100}$ .

Step-by-step explanation:

Consider the provided information.

Let us consider <em>x</em> is the amount of water Carlon plans to evaporate.

Thus, 90 - <em>x</em> is the amount of water after being evaporated.

The amount of salt is 15% of 90 gallons which can be written as:

$S=90\times{0.15}$

$S=13.5$

The percentage of salt will be:

$\%S=\frac{13.5}{90-x}=\frac{25}{100}$

Hence, the equation can be used to find <em>x</em>, the number of gallons that should be evaporated is: $\frac{13.5}{90-x}=\frac{25}{100}$ .

Gre4nikov [31]2 years ago

6 0

The answer to this is A

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Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the

xenn [34]

Answer:

As per the given statement:

The region bounded by the given curves about the y-axis, $y = 13e^{-x^2}$ , y=0, x = 0 and x = 1

Using cylindrical shell method:

The volume of solid(V) is obtained by rotating about y-axis and the region under the curve y = f(x) from a to b is;

$V = \int_{a}^{b} 2\pi x f(x) dx$ where $0\leq a$

where x is the radius of the cylinder

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From the given figure:

radius = x

height(h) =f(x) =y= $13e^{-x^2}$

a = 0 and b = 1

So, the volume V generated by rotating the given region:

$V =2 \pi \int_{0}^{1} x ( 13e^{-x^2}) dx\\\\V=2\pi\left [ -\frac{13}{2}e^{-x^2} \right ]_{0}^{1}\\\\V=2\pi\left (-\frac{13}{2e}-\left(-\frac{13}{2}\right) \right )\\\\V=-\frac{13\pi }{e}+13\pi$

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2 years ago

a lunch stand makes a $.75 profit on each chef's salad and $1.20 profit on each caesar salad. On a typical weekday, it sells bet

tangare [24]

Answer:

<em>50 Chef's salads and 50 Caesar salads should be prepared in order to maximize profit.</em>

Step-by-step explanation:

Suppose, the number of Chef's salad is $x$ and the number of Caesar salad is $y$

On a typical weekday, it sells between 40 and 60 Chefs salads and between 35 and 50 Caesar salads.

So, the two constraints are: $40\leq x\leq 60$ and $35\leq y\leq 50$

The total number sold has never exceed 100 salads. So, another constraint will be: $x+y\leq 100$

According to the graph of the constraints, the vertices of the common shaded region are: $(40,35), (60,35), (60,40), (50,50)$ and $(40,50)$ <em>(Refer to the attached image for the graph)</em>

The lunch stand makes a $.75 profit on each Chef's salad and $1.20 profit on each Caesar salad. So, the profit function will be: $P=0.75x+1.20y$

For (40, 35) , $P=0.75(40)+1.20(35)=72$

For (60, 35) , $P=0.75(60)+1.20(35)=87$

For (60, 40) , $P=0.75(60)+1.20(40)=93$

For (50, 50) , $P=0.75(50)+1.20(50)=97.5$ <u><em>(Maximum)</em></u>

For (40, 50) , $P=0.75(40)+1.20(50)=90$

Profit will be maximum when $x=50$ and $y=50$

Thus, 50 Chef's salads and 50 Caesar salads should be prepared in order to maximize profit.

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2 years ago

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julia-pushkina [17]

Answer:

B. Food market

Step-by-step explanation:

You typically buy all of your groceries at Grocery Mart. This week, your favorite cereal is on sale there, 4 boxes for $10. At Food Market, where you don’t typically shop, the same cereal is on sale for $2.25 a box. Based on price, which is the better value option?

A.Grocery Mart

B. Food Market

Grocery market:

4 boxes for $10

Unit price = cost / quantity

= $10 / 4 boxes

= $2.50 per box

Food market:

Price per box = $2.25

The better value option based on price is food market because it cost less to buy a box of cereal than grocery mart

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oksano4ka [1.4K]

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<u></u>

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2 years ago

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Answer:

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Step-by-step explanation:

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2 years ago